Help with geometry on equations of circles. Point C is a point of tangency. How would I solve this to get DA and DE?

Help With Geometry On Equations Of Circles. Point C Is A Point Of Tangency. How Would I Solve This To

Answers

Answer 1

Answer:

DA = 17DE = 9

Step-by-step explanation:

You want the segment lengths DA and DE of the hypotenuse in the triangle shown in the figure.

Right triangle

The radius to a point of tangency always makes a right angle with the tangent. This is a right triangle with legs 8 and 15, so you know from your knowledge of Pythagorean triples that the hypotenuse is 17.

  DA = 17

  DE = 17 -8 = 9

__

Additional comment

In case you haven't memorized a few of the useful Pythagorean triples, {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, you can always figure the missing side length of a right triangle using the Pythagorean theorem.

It tells you the sum of the squares of the legs is the square of the hypotenuse:

  AC² +CD² = DA²

  8² +15² = DA²

  64 +225 = 289 = DA²

  DA = √289 = 17

Of course, AE is the radius of the circe, 8, so ...

  AE + DE = DA

  8 +DE = 17

  DE = 17 -8 = 9

Alternatively, you can solve this using the relation between tangents and secants. If the line DA is extended across the circle to intersect it again at X, then ...

  DC² = DE·DX

  15² = DE·DX = DE(DE +16) . . . . . . . EX is the diameter, twice the radius of 8

  DE² +16DE -225 = 0

  (DE +25)(DE -9) = 0 . . . . factor

  DE = 9  . . . . the positive solution

  DA = 9 +8 = 17

We like the Pythagorean theorem solution better, as the factors of the quadratic may not be obvious.


Related Questions

3. 14


2. The volume of the cylinder is 141. 3 cubic


centimeters. What is the radius of the cylinder?


Use 3. 14 for T.


Need answer ASAP right now

Answers

The radius of the cylinder with volume of 141.3and height of 7 cm is 2.53cm.

The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Given that V = 141.3 cm³ and using π ≈ 3.14, we can solve for r.

Rearranging the formula, we get r² = V/(πh), and plugging in the given values, we get r² = 141.3/(3.14*7). Since we don't know the height of the cylinder, we cannot solve for r exactly.

However, we can say that the radius of the cylinder is proportional to the square root of the volume, the height is 7 cm, then r = √(141.3/3.14*7) ≈  2.53cm. If the height is different, the radius will change accordingly.

In summary, using the formula for the volume of a cylinder andheight of 7 cm, the radius of the cylinder with volume 141.3 cm³ and using π ≈ 3.14 is approximately 2.53 cm.

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Complete question:

The volume of the cylinder is 141. 3 cubiccentimeters. What is the radius of the cylinder given that height is 7cm? use  π ≈ 3.14

FRANK IS DESIGNING 30-KILOMETERS TRAIL RUN WATER WILL BE GIVEN TO THE RUNNERS 4000 OW MANY WATER STATIONS WILL THERE BE

Answers

Based on the above,  Frank will need to have about 533 water stations per kilometer for the 30-kilometer trail run.

What is the  water stations?

If each runner is said to have about 250 milliliters (0.25 liters) of water per station and there are said to be 4000 liters of water available in total, we have to calculate the total number of water stations  by:

4000 liters of water ÷ 0.25 liters of water per station

= 16000 stations

we have 30-kilometer run, we have to divide the total number of stations by the distance and it will be:

16000 stations ÷ 30 kilometers

= 533.33 stations per kilometer

Therefore, about 533 water stations per kilometer for the 30-kilometer trail run is needed by Frank.

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see full question below

frank is designing a 30-kilometers trail run water that will be given to runners. if 4000 liters of water is available,  each runner was given about 250 milliliters (0.25 liters) of water per station.  how many water stations will there be 30-kilometer run.

A wheatfarmer is converting to com because he believes that com is a more lucrative crop. It is not feasible for him to convert all his creace to com at onceHe is farming 100 acres of com in the current year and is increasing that number by 30 acres per year. As he becomes more experienced in growing com his output increas. He currently harvests 130 buhof com per acre. But the yield be increasing by buhol per acre per year. When both the increasing berage and the increasing yield are considered, how rapidly Withe total number of but of corn currently increasing bushes per year

Answers

The rate at which the total number of bushels of corn currently increases per year depends on the value of "b", which represents the annual increase in yield per acre. If the yield per acre is not increasing (i.e., b = 0), then the rate of increase is a constant 1300 bushels per year.

Let's call the total number of acres the farmer is farming in corn in a given year as "a". We know that initially, a = 100 acres, and that it increases by 30 acres per year. So, in general:

a = 100 + 30t

where "t" is the number of years since the farmer started converting to corn.

Now, let's call the yield in bushels per acre in a given year as "y". We know that initially, y = 130 bushels per acre, and that it increases by "b" bushels per acre per year. So, in general:

y = 130 + bt

Finally, we can calculate the total number of bushels of corn produced in a given year by multiplying the number of acres by the yield per acre:

bushels per year = a * y

Substituting the expressions we have for "a" and "y", we get:

bushels per year = (100 + 30t) * (130 + bt)

Expanding this expression, we get:

bushels per year = 13000 + 1300t + 3900bt + 30tb

Now we can differentiate this expression with respect to time to find how rapidly the total number of bushels of corn currently increases per year:

d(bushels per year)/dt = 1300 + 3900b + 30b

Simplifying, we get:

d(bushels per year)/dt = 1300 + 3930b

So the rate at which the total number of bushels of corn currently increases per year depends on the value of "b", which represents the annual increase in yield per acre. If the yield per acre is not increasing (i.e., b = 0), then the rate of increase is a constant 1300 bushels per year. If the yield per acre is increasing, then the rate of increase will be greater than 1300 bushels per year, and the rate of increase will depend on the value of "b".

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HELP ME PLEASE ANYBODY I NEED IT URGENTLY

I also have to show my work

Thank you.

Answers

here is the answer BUT HOW DO THEY WANT YOU TO SHOW YOUR WORK FOR THIS?

[4 marks) Find the unit tangent vector T and the principal unit normal vector N at t=0 for = r(t) = ti+at+j+ + 3 tk. NI

Answers

The unit tangent vector T is (1/√10)i + (3/√10)k

The principal unit normal vector N is j.

vector function r(t) = ti + at²j + 3tk.
Step 1: Find the derivative of r(t) with respect to t, which gives us the tangent vector.
r'(t) = (1)i + (2at)j + (3)k
Step 2: Evaluate r'(t) at t=0.
r'(0) = (1)i + (2a*0)j + (3)k = i + 3k
Step 3: Find the magnitude of r'(0).
|r'(0)| = √(1^2 + 3^2) = √10
Step 4: Normalize r'(0) to find the unit tangent vector T.
T = r'(0) / |r'(0)| = (1/√10)i + (3/√10)k
Step 5: Find the second derivative of r(t) with respect to t.
r''(t) = (0)i + (2a)j + (0)k
Step 6: Evaluate r''(t) at t=0.
r''(0) = (0)i + (2a)j + (0)k = 2aj
Step 7: Find the magnitude of r''(0).
|r''(0)| = √(2a)^2 = 2a
Step 8: Normalize r''(0) to find the principal unit normal vector N.
N = r''(0) / |r''(0)| = (2a/2a)j = j
So, at t=0, the unit tangent vector T is (1/√10)i + (3/√10)k, and the principal unit normal vector N is j.

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On the same coordinate plane, mark all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2

Answers

The marked points are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4), under the condition that they are on the same coordinate plane having (A) y=x-2, (B) y=-x-2, (C) y=|x|-2.

In the given graph points on the coordinate plane, we have to plot the points (x,y)
Here
x = horizontal axis
y = vertical axis.

In the given point A, y=x-2, we can continue at the origin (0,0) and move 2 units go down on the y-axis and 2 units right on the x-axis to plot point A at (2,0).

In the given point B, y=-x-2, we can continue at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point B at (-2,0).

In the given point C, y=|x|-2, we can continue plotting two points for this equation.
When x is considered negative, we can procees at the origin (0,0) and transfer 2 units down on the y-axis and 2 units left on the x-axis to plot point C at (-2,0).
When x is positive, we can start at the origin (0,0) and move 2 units down on the y-axis and 2 units right on the x-axis to plot point C at (2,0).

Then, all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2 are (-2,-4), (-2,-1), (0,-2), (2,-1), and (2,-4).
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A teacher writes the following product on the board:
(372) (675) =18k7
Ana says that 3k2 is a factor of 18k7
Felipe says that 18k? is divisible by 372
Who is correct?

Answers

In the equation , Felipe is correct.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is (372) (675) =18k7.

We know that the factor is a number that divides the another number and leaves no reminder .

If we divide 18k7 by 372 the we get remainder 675. So 372 is not factor of 18k7.

But 372 is divides the number 18k7.

Hence Felipe is correct.

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In 2015, there were roughly 1 X 10^6 high school football players and 2 X 10^3 professional football players in the United States. About how many times more high school football players are there? Explain how you know

Answers

There are approximately 500 times more high school football players than professional football players in the United States.

How to determine ratio of football players?

To determine how many times more high school football players there are than professional football players in the United States, we need to divide the number of high school players by the number of professional players:

1 x 10⁶ / 2 x 10³ = 500

Therefore, there are approximately 500 times more high school football players than professional football players in the United States.

We can determine this by dividing the two numbers and finding the ratio of high school players to professional players. The result tells us how many times greater the number of high school players is than the number of professional players. In this case, the ratio is 500:1, which means that for every professional football player, there are 500 high school football players.

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Can someone help me asap? It’s due today!! Show work! I will give brainliest if it’s correct and has work

Answers

Answer:

10 outcomes

Step-by-step explanation:

if 2 coins were selected with replacement=10×10=100

number of outcomes if 2 coins were selected without replacement=10×9=90

Finally, 100-90= 10 outcomes!

A cylinder has volume 108 cm? What is the volume of a cone with the same


radius and height? Use 3. 14 for it and be sure to add units to your answer.

Answers

The volume of the cone with the same radius and height as the cylinder is 36 cm³.

To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

We are given that the volume of the cylinder is 108 cm^3.

So, 108 = πr^2h

To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.

The formula for the volume of a cone is V = (1/3)πr^2h.

Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.

V = (1/3)π( r^2 )(h)

V = (1/3)π( r^2 )(108/π)

V = (1/3)( r^2 )(108)

V = 36( r^2 )

Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³

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What is a minimum monthly payment?

Answers

To prevent loan or credit card payment default, borrowers must make a minimum monthly payment.

What is a minimum monthly payment?

Based on the outstanding debt amount, this payment includes interest and other fees along with portions of principal. The lender/creditor typically sets these payments to ensure progress towards paying off existing debt.

However, by making just minimum payments, borrowers may end up shelling out significantly more in added interest over the lifetime of the debt. Furthermore, prolonging the repayment time is another possible outcome to such a practice; hence, it remains crucial to determine suitable ways of meeting higher than expected monthly payments on debts.

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23


Luke invested £4000 in a savings account for 3 years. So


Compound interest was paid at a rate of 1. 8% each year.


Alexa also invested £4000 in a savings account for 3 years. Si


Simple interest was paid at a rate of 1. 8% each year.


0002


Luke got more interest than Alexa in total over the 3 years.


00025


00021


How much more?

Answers

To calculate the interest earned by Luke and Alexa, we can use the following formulas:

For compound interest:

A = P(1 + r/n)^nt

I = A - P

where:

A = the total amount

P = the principal amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

I = the interest earned

For simple interest:

I = P*r*t

where:

P = the principal amount

r = the annual interest rate (as a decimal)

t = the time period (in years)

I = the interest earned

Using these formulas, we can calculate the interest earned by Luke and Alexa as follows:

For Luke:

P = £4000

r = 0.018 (1.8% as a decimal)

n = 1 (compounded annually)

t = 3 years

A = 4000(1 + 0.018/1)^(1*3) = £4316.83

I = 4316.83 - 4000 = £316.83

For Alexa:

P = £4000

r = 0.018 (1.8% as a decimal)

t = 3 years

I = 4000*0.018*3 = £216

Therefore, the total interest earned by Luke is £316.83 and the total interest earned by Alexa is £216. The difference between these two amounts is:

316.83 - 216 = £100.83

So Luke earned £100.83 more in interest than Alexa over the 3 years.

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Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and
z are positive.
Maximize: f(x, y, z) = xyz
Constraint: × + y + z - 9 = 0

Answers

To use Lagrange multipliers, we need to define the Lagrangian function:

L(x, y, z, λ) = xyz + λ(x + y + z - 9)

Now, we need to find the partial derivatives of L with respect to x, y, z, and λ and set them equal to 0:

∂L/∂x = yz + λ = 0
∂L/∂y = xz + λ = 0
∂L/∂z = xy + λ = 0
∂L/∂λ = x + y + z - 9 = 0

From the first three equations, we can see that:

yz = -λ
xz = -λ
xy = -λ

Multiplying these equations together, we get:

(xyz)^2 = (-λ)^3

Substituting λ = -yz into the fourth equation, we get:

x + y + z - 9 = 0

Substituting λ = -yz into the first equation and solving for x, we get:

x = -λ/yz = (yz)^2/(-yz) = -y^2z^2

Similarly, we can solve for y and z:

y = -x^2z^2
z = -x^2y^2

Substituting these expressions into the constraint equation, we get:

(-y^2z^2) + (-x^2z^2) + (-x^2y^2) - 9 = 0

Simplifying and solving for xyz, we get:

xyz = sqrt(9/(x^2 + y^2 + z^2))

To maximize xyz, we need to minimize x^2 + y^2 + z^2. Therefore, we can set:

x^2 + y^2 + z^2 = 3

Substituting this into the expressions for x, y, and z, we get:

x = -y^2z^2
y = -x^2z^2
z = -x^2y^2

Substituting these expressions into xyz, we get:

xyz = sqrt(9/3) = 3

Therefore, the maximum value of f(x, y, z) = xyz subject to the constraint x + y + z - 9 = 0 is 3.
To solve this problem using Lagrange multipliers, we first set up the Lagrangian function L(x, y, z, λ) with the constraint function g(x, y, z) = x + y + z - 9.

L(x, y, z, λ) = f(x, y, z) - λ(g(x, y, z))

L(x, y, z, λ) = xyz - λ(x + y + z - 9)

Now we take the partial derivatives with respect to x, y, z, and λ, and set them equal to 0:

∂L/∂x = yz - λ = 0
∂L/∂y = xz - λ = 0
∂L/∂z = xy - λ = 0
∂L/∂λ = x + y + z - 9 = 0 (the constraint)

From the first three equations, we get:

yz = xz = xy

Since x, y, and z are positive, we can divide the first two equations:

y/z = x/z => y = x
x/z = y/z => x = y

So x = y = z. Now we can use the constraint equation:

x + x + x - 9 = 0 => 3x = 9 => x = 3

Thus, x = y = z = 3. Now we can find the maximum value of f(x, y, z):

f(3, 3, 3) = 3 * 3 * 3 = 27

So the maximum value of f(x, y, z) = xyz subject to the constraint x + y + z - 9 = 0 is 27, and this occurs at the point (3, 3, 3).

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Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3 to 1. How many tablespoons of salt does Debnil have?

Answers

Answer: Debnil has 2 Tablespoons of salt.

Step-by-step explanation:

3/1 is the ratio for teaspoons to tablespoons.

Substitute the 1 with the 6. What is six divided by three? 2.

I have no congruent sides. One of my angles has a measure of 100 degrees. Answer with drawing of the triangle

I am a(n and triangle

Answers

You are an scalene triangle.

How can you identify the type of triangle when given the information that it has no congruent sides and one angle measuring 100 degrees?

You are a scalene triangle.

A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.

Here's a simple diagram of a scalene triangle to help illustrate:

    \

     \

      \

       \

        \

         \

In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.

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This year, a French restaurant used 377,020 ounces of cream. That is 50% less than last year, when the restaurant had a different menu. How much cream did the restaurant use last year?

Answers

the restaurant used 754,040 ounces of cream last year.

What is an Equations?

Equations are statements in mathematics that consist of two algebraic expressions separated by an equals (=) sign, indicating the equivalence between the expressions on either side. Equations can be solved to determine the value of a variable that represents an unknown quantity. A statement that does not have an "equal to" symbol is not considered an equation and is instead referred to as an expression.

If the restaurant used 50% less cream this year compared to last year, then it means that this year's usage is 50% of last year's usage.

Let x be the amount of cream used last year.

Then we can set up the following equation:

x * 50% = 377,020

To solve for x, we need to isolate it on one side of the equation.

x * 50% = 377,020

x = 377,020 / 50%

To convert 50% to a decimal, we divide it by 100:

x = 377,020 / 0.5

x = 754,040

Therefore, the restaurant used 754,040 ounces of cream last year.

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helppppppp please!!!!!!!

Answers

Thus, the height of cone for the given values of circumference an f volume is found as: 4 cm.

Explain about the conical shape:

A tri shape that resembles a cone is what is known as a conical shape. A cone has a flat end that gradually taper towards a single point at the top known as the apex. Most commonly, a conical shape's flat end has an oval or circular shape. Conical shapes are on your mind when you imagine an ice cream cone with only a pointed end.

Volume of a cone = 1/3 * π *r²*h

r is the radiush is the height π = 3.14

Given that:

circumference c = 6π Volume = 12π

using circumference c = 6π

c = 2πr (for circular base)

6π  = 2πr

r = 3 cm

Now, using the volume;

Volume of a cone = 1/3 * π *r²*h

1/3 * π *3²*h = 12π

3h = 12

h = 4 cm

Thus, the height of the cone for the given values of circumference an f volume is found as: 4 cm.

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Find the equation of the tangent line of y=xlog(x) at the point(1,0).

Answers

The equation of the tangent line is y = x - 1.

To find the equation of the tangent line of y=xlog(x) at the point (1,0), we will first need to find the derivative of the function y=xlog(x) with respect to x.

Step 1: Find the derivative of y=xlog(x) with respect to x.
Using the product rule, (uv)' = u'v + uv', where u=x and v=log(x).

u' = derivative of x with respect to x = 1
v' = derivative of log(x) with respect to x = 1/x

Now, apply the product rule:
y' = u'v + uv' = 1*log(x) + x*(1/x) = log(x) + 1

Step 2: Find the slope of the tangent line at the point (1,0).
Evaluate y' at x=1:
y'(1) = log(1) + 1 = 0 + 1 = 1

The slope of the tangent line at (1,0) is 1.

Step 3: Find the equation of the tangent line.
We will use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is the point (1,0) and m is the slope (1).

y - 0 = 1(x - 1)
y = x - 1

The equation of the tangent line of y=xlog(x) at the point (1,0) is y = x - 1.

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Help please asap need help.

Answers

The surface areas of the pyramids are listed below:

125 in² 304 ft² 420 yd² 57 yd² 336 in² 104 ft²

How to determine the surface area of the square pyramid

In this problem we find six cases of square pyramids, whose surface areas shall be found by means of the following formulas:

A = 4 · 0.5 · b · s + b²

Where:

b - Base sides - Slant heightA - Surface area

Now we proceed to determine the surface area of the square pyramid:

Case 1:

A = 4 · 0.5 · (5 in) · (10 in) + (5 in)²

A = 125 in²

Case 2:

A = 4 · 0.5 · (8 ft) · (15 ft) + (8 ft)²

A = 304 ft²

Case 3:

A = 4 · 0.5 · (10 yd) · (16 yd) + (10 yd)²

A = 420 yd²

Case 4:

A = 4 · 0.5 · (3 yd) · (8 yd) + (3 yd)²

A = 57 yd²

Case 5:

A = 4 · 0.5 · (8 in) · (17 in) + (8 in)²

A = 336 in²

Case 6:

A = 4 · 0.5 · (4 ft) · (11 ft) + (4 ft)²

A = 104 ft²

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Ms. Redmon gave her theater students an assignment to memorize a dramatic monologue to present to the rest of the class. The graph shows the times, rounded to the nearest half minute, of the first 10 monologues presented.

A number line going from 0.5 to 5. 0 dots are above 0.5 0 dots are above 1. 2 dots area above 1.5. 1 dot is above 2. 3 dots are above 2.5. 1 dot is above 3. 2 dots are above 3.5. 1 dot is above 4. 0 dots are above 2.5. 0 dots are above 5.
The next student presents a monologue that is about 0.5 minutes long. What effect will this have on the graph?

The median will decrease.
The mean will decrease.
The median will increase.
The mean will increase.

Answers

The effect of the student presenting such a monologue would be B. The mean will decrease.

How to find the effect ?

Order the data points:

1. 5, 1. 5, 2, 2. 5, 2. 5, 2. 5, 3, 3. 5, 3. 5, 4

Find the mean ;

= (1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 10

= 27 / 10

= 2. 7

Then find the new mean after the student presents the monologue:

= ( 0. 5 + 1. 5 + 1. 5 + 2 + 2. 5 + 2. 5 + 2. 5 + 3 + 3. 5 + 3. 5 + 4) / 11

= 2. 5

The mean therefore reduced.

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Answer:

b

Step-by-step explanation:

Let f be a differentiable function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3. f 6 . The function g is differentiable and g(x) = f-1(x) for all x. What is the value of g'(4) =

Answers

The value of g'(4) is -1/3 if f is a differential function such that f (2) = 4, f(4) = 6, f'(2) = -4, and f'(6) = -3.

First, let's use the information given to find the equation of the tangent line to f at x=2. We know that f(2) = 4 and f'(2) = -4, so the equation of the tangent line at x=2 is

y - 4 = -4(x - 2)

Simplifying, we get

y = -4x + 12

Now let's use the fact that g(x) = f-1(x) for all x. This means that g(f(x)) = x for all x. We want to find g'(4), which is the derivative of g at x=4.

Using the chain rule, we have

g'(4) = [g(f(4))]'

Since f(4) = 6 and g(f(4)) = g(6) (since g(x) = f-1(x)), we can rewrite this as

g'(4) = [g(6)]'

Now we can use the fact that g(x) = f-1(x) to rewrite g(6) as f-1(6)

g'(4) = [f-1(6)]'

Now we need to find the derivative of f-1(x) with respect to x. To do this, we can use the fact that f(f-1(x)) = x for all x. Differentiating both sides with respect to x using the chain rule, we get

f'(f-1(x)) * (f-1)'(x) = 1

Solving for (f-1)'(x), we get

(f-1)'(x) = 1 / f'(f-1(x))

Now we can plug in x=6 and use the information given to find f'(f-1(6)). Since f(4) = 6, we know that f-1(6) = 4. Therefore

f'(f-1(6)) = f'(4)

Using the tangent line equation we found earlier, we know that f(2) = 4 and f'(2) = -4. Therefore, the slope of the line connecting (2,4) and (4,6) is

(6 - 4) / (4 - 2) = 1

Since the line connecting (2,4) and (4,6) is the tangent line to f at x=2, we know that this slope is equal to f'(2). Therefore

f'(4) = f'(f-1(6)) = f'(4)

Now we can plug in x=6 and f'(4) into our expression for (f-1)'(x)

(f-1)'(6) = 1 / f'(4)

Substituting this into our expression for g'(4), we get

g'(4) = [f-1(6)]' = (f-1)'(6) = 1 / f'(4)

Plugging in f'(4) = f'(f-1(6)) = f'(4), we get

g'(4) = 1 / f'(4) = 1 / (-3) = -1/3

Therefore, g'(4) = -1/3.

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Lan shuffles a standard deck of 52 playing cards and turns over the first four cards, one at a time. He records the


number of aces he observes.


Have the conditions for a binomial setting been met for this scenario?


O Yes, a success is "ace. "


O Yes, all four conditions in BINS have been met.


No, we do not know how many aces will occur in those first four cards.


O No, the cards are not being replaced, so the independence condition is not met.


Next


Submit


Save and Exit


Mark this and return

Answers

The binomial conditions are not met as the cards are not being replaced, so the independence condition is not met. So, the correct answer is D).

The conditions for a binomial setting are

there are a fixed number of trials,

the trials are independent,

there are only two possible outcomes (success or failure),

the probability of success is constant for each trial.

In this scenario, the first two conditions are met as Lan is turning over the first four cards and they are independent events. The third condition is also met as the success is defined as observing an ace and the failure is observing any other card.

However, the fourth condition is not met as the probability of success changes for each trial. After the first card is turned over, the probability of observing an ace changes for the second trial. Therefore, the scenario does not meet all the conditions for a binomial setting. So, the correct option is D).

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what two double inequalities define shaded region

Answers

The calculated two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2

Determining the two double inequalities that define shaded region

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following properties

Shaded region is between y = 1 and y = 5 (exclusive of y = 5)Shaded region is between x = -3 and x = 2 (exclusive of y = 5)

Using the above as a guide, we have the following:

1 ≤ y < 5

-3 < x ≤ 2

Hence, the two double inequalities that define shaded region are 1 ≤ y < 5 and -3 < x ≤ 2

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The captain of the baseball team hit a homerun 1 out of every 6 at-bats. What is the probability that the captain will hit a homerun on his next 2 at-bats?


Determine which simulation models the situation. Select Yes if the simulation can be used to model the situation or No if the simulation cannot be used to model the situation.


Yes No


OO


Using a six-sided number cube to model the situation, assign the number 1 to represent the captain hitting a homerun and the number 2 to represent not hitting a homerun.


Using a stre-sided number cube to model the situation, assign the number 1 to represent the captain hitting a homerun and the numbers 2 to 6 to represent not hitting a homerun


Using a coin flip to model the situation, assign heads to represent the captain hitting a homerun and tails for not hitting a homerun


O


Using a random number generator between 1 and 60 to model the situation, assign the numbers 1 to 10 to represent the captain hitting a homerun and the numbers 11 to 60 to represent not hitting a homerun.

Answers

The probability of the captain hitting a home run in his next two at-bats is 1/36, and the best simulations to model the situation are using a six-sided number cube or a random number generator between 1 and 60.

Determine the probability that the captain will hit a home run in his next two at-bats and find the best simulation to model the situation.
The probability of the captain hitting a home run in one at-bat is 1/6. To find the probability of hitting a home run in two consecutive at-bats, you can multiply the individual probabilities:

Probability = (1/6) * (1/6) = 1/36

Now let's evaluate the provided simulations:

1. Using a six-sided number cube: Yes, this can be used to model the situation because the probability of hitting a home run (1/6) and not hitting a home run (5/6) can be represented accurately by the numbers 1 and 2-6, respectively.
2. Using a three-sided number cube: No, this cannot be used to model the situation because the probability distribution is not accurately represented with only three sides.
3. Using a coin flip: No, this cannot be used to model the situation because the probability distribution is not accurately represented with only two outcomes (heads and tails).
4. Using a random number generator between 1 and 60: Yes, this can be used to model the situation because the probability of hitting a home run (1/6) and not hitting a home run (5/6) can be represented accurately by the numbers 1-10 and 11-60, respectively.

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Given logaMN = 6, log aN/M = 2 and logaN^m = 16, find M.

Answers

The value of M is a^4.

Given the information, we can express the given logarithms as follows:

1) log_a(MN) = 6
2) log_a(N/M) = 2
3) log_a(N^m) = 16

From equation (1), we can write:
MN = a^6

From equation (2), we can write:
N/M = a^2 → N = a^2 * M

Now, substitute N from equation (2) into equation (3):
log_a((a^2 * M)^m) = 16

Using the power rule of logarithms, we get:
m * log_a(a^2 * M) = 16

Since log_a(a^2 * M) = 2log_a(a) + log_a(M) = 2 + log_a(M), we have:
m * (2 + log_a(M)) = 16

We don't have enough information to determine the value of 'm', but we don't need it to find the value of 'M'.

Now, substitute N back into the equation MN = a^6:
M * a^2 * M = a^6

Divide both sides by M * a^2:
M = a^(6-2) = a^4

So, the value of M is a^4.

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Ann lives on the shoreline of a large lake. A market is located 20 km south and 21 km west of her home on the other side of the lake. If she takes a boat across the lake directly


toward the market, how far is her home from the market in km?

Answers

If Ann takes a boat then the distance between Ann's home and the market across the lake is approximately 29 km.

To find the distance from Ann's home to the market, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, Ann's home, the market, and the point where she crosses the lake form a right triangle, with the distance she travels across the lake being the hypotenuse.

To calculate the distance, we can use the following formula:

c^2=a^2+b^2

where c is the distance from Ann's home to the market, a is the distance from her home to the point where she crosses the lake, and b is the distance from the market to the point where she crosses the lake.

We know that a = 20 km and b = 21 km, so we can plug these values into the equation:

c^2=20^2+21^2

c^2=400+441

c^2=841

To solve for c, we take the square root of both sides of the equation:

c=sqrt(841)

c=29

Therefore, the distance from Ann's home to the market is approximately 29 km, when she takes the shortest path across the lake directly toward the market.

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t/12+5=t/3+t/4 please hepl me

Answers

Answer:

Step-by-step explanation:

To solve the equation (T/12) + 5 = (T/3) + (T/4), we need to simplify the right-hand side of the equation by finding a common denominator for T/3 and T/4.

The least common multiple of 3 and 4 is 12, so we can rewrite T/3 and T/4 as (4T/12) and (3T/12), respectively. Substituting these expressions into the equation, we get:

(T/12) + 5 = (4T/12) + (3T/12)

Simplifying the right-hand side, we get:

(T/12) + 5 = (7T/12)

Subtracting (T/12) from both sides, we get:

5 = (6T/12)

Simplifying the right-hand side, we get:

5 = (T/2)

Multiplying both sides by 2, we get:

T = 10

Therefore, the solution to the equation is T = 10.

SolutioN:-

[tex]\sf\longrightarrow \: \frac{t}{12} + 5 = \frac{t}{3} + \frac{t}{4} \\ [/tex]

[tex]\sf\longrightarrow \: \frac{t + 60}{12} = \frac{t}{3} + \frac{t}{4} \\ [/tex]

[tex]\sf\longrightarrow \: \frac{t + 60}{12} = \frac{4t + 3t}{12} \\ [/tex]

[tex]\sf\longrightarrow \: 12(t + 60) = 12(4t + 3t) \\ [/tex]

[tex]\sf\longrightarrow \: 12t + 720 = 48t + 36t \\ [/tex]

[tex]\sf\longrightarrow \: 12t + 720 = 84t \\ [/tex]

[tex]\sf\longrightarrow \: 720 = 84t - 12t\\ [/tex]

[tex]\sf\longrightarrow \: 720 =72t\\ [/tex]

[tex]\sf\longrightarrow \: 72t = 720\\ [/tex]

[tex]\sf\longrightarrow \: t = \frac{720}{72} \\ [/tex]

[tex]\sf\longrightarrow \: t = 10 \\ [/tex]

[tex]\longrightarrow { \underline{ \overline{ \boxed{ \sf{\: \: \: t = 10 \: \: \: }}}}} \: \: \bigstar\\ [/tex]

Evelyn has a coupon that will reduce her grocery bill by 8%. If c represents the cost of Evelyn's groceries, which expression represents Evelyn's grocery bill?
a) c-0. 08
b) c+0. 92
c) 0. 08c
d) 0. 92c​

Answers

Therefore, the correct answer is option (b) c + 0.92.

What is The expression that represents Evelyn's grocery bill?

The expression that represents Evelyn's grocery bill after the 8% discount is:

c - 0.08c

This can be simplified as:

0.92c

Therefore, the correct answer is option (b) c + 0.92.

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The expression that represents Evelyn's grocery bill after the coupon is applied is 0.92c. Therefore, the correct option is D.

If Evelyn has a coupon that will reduce her grocery bill by 8% and c represents the cost of her groceries, the expression that represents Evelyn's grocery bill after using the coupon is 0.92c. It is determined as follows.

1. The coupon reduces the bill by 8%, which means Evelyn will pay 100% - 8% = 92% of the original cost.

2. Convert the percentage to a decimal: 92% = 0.92

3. Multiply the original cost (c) by the decimal: 0.92c

So, the correct answer is option D: 0.92c.

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To build a triangular shaped raised bed frame for her tomato plants, chris has three pieces of lumber whose length are 4 feet 5 feet and 9 feet. can chris build her planter? explain

Answers

Chris cannot build the triangular raised bed frame with the given lumber.

How can Chris build a triangular raised bed frame?

To determine if Chris can build her triangular raised bed frame, we need to check if the length of any one of the lumber pieces is greater than the sum of the other two. If this condition is not met, the pieces can be used to build the frame.

Let's check:

4 + 5 = 9 (no)

4 + 9 = 13 (no)

5 + 9 = 14 (yes)

Since the length of the 5-foot and 9-foot lumber pieces add up to be greater than the 4-foot piece, Chris can build her triangular raised bed frame. She can use the 4-foot and 5-foot pieces for the two shorter sides of the triangle and the 9-foot piece for the longer side.

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Ive been stuck on this one question for a while can someone teach me how to do this?

Answers

The value of x is 6 and the perimeter is 52 unints

Calculating the value of x and the perimeter

From the question, we have the following parameters that can be used in our computation:

The figure

If the lines that appear to be tangent are tangent, then we have the following equation

x + 2 = 8

Evaluate the like terms

x = 6

The perimeter is the sum of the side lengths

So, we have

Perimeter = x + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4

This gives

Perimeter = 6 + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4

Evaluate

Perimeter = 52

Hence, the perimeter is 52 unints

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