< Question 6 of 6
Use the Shell Method to find the volume of a solid obtained by rotating the region B about the x-axis.
0
y=x²³ +b
Assume a = 2 and b = 2.
(Use symbolic notation and fractions where needed.)
volume:

The total money raised is (15/7) * $88,000 = $188,571.43.

a) Let x be the total amount raised.

Charity A received (1/3)(x - A), Charity C received (1/4)(x - C). We have A = (1/3)(B+C) and C = (1/4)(A+B).

Solving these equations, we find B's share to be 7/15 of the total amount.

p) Since Charity B received $88,000, which is 7/15 of the total amount, the total money raised is (15/7) * $88,000 = $188,571.43.

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Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].

In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.

Here,

The linear approximation of sin⁻¹(x) at a = 0 is given by:

sin⁻¹(x) ≈ x

To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:

d/dx(sin⁻¹(x)) = 1/√(1-x²)

d/dx(sin⁻¹(x))|x=0 = 1

Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.

To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.

Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:

-0.099 ≤ x ≤ 0.099

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To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.

Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.

First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.

Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.

Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.

The number of kg of maize was left with Ali is 73350 Kg.

Given that, Ali had 3469 bags of maize each weighing 90 kg.

Ali sold 2654 of them.

Number of bags left = 3469-2654

= 815

Number of Kg's of maize left = 815×90

= 73350 Kg

Therefore, the number of kg of maize was left with Ali is 73350 Kg.

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The value of x in the equation x² = -20 is x  = 2i√5

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

x² = -20

To start with, we take the square root of both sides of the equation

So, we have

√x² = √-20

When the square roots are evaluated, we have

x  = √-20

Express -20 as 4 * -5

So, we have

x  = √4 * -5

This gives

x  = 2√-5

The expression √-5 is a complex number

So, we have

x  = 2i√5

Hence, the value of x in x² = -20 is x  = 2i√5

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The synthetic division of the polynomial indicates that other factor of the polynomial is; x² - 3·x + 13

A polynomial consists of terms that have positive integer powers or index of variables joined together by addition and subtraction symbols.

The possible polynomial in the question is; x³ + 5·x² - 11·x + 104

The factor of the polynomial is; (x + 8)

The steps for the synthetic division includes on the left side of the vertical line, placing the opposite sign of the constant term of the factor.

The other steps of synthetic division can then be presented, summarily as follows;

Therefore;

-8 | 1[tex]{}[/tex]   5     -11   104

   |   [tex]{}[/tex]   -8    24  104          

     1   -3    [tex]{}[/tex] 13      0

The factors of the polynomial

The values in the above last row of the long division indicates that the other factor of the polynomial is; x² - 3·x + 13

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By looking at the y-values of the points, we can see that the first four terms are.

2, -2, -6, -10

We know that the x-value of each of the points is the index of the term, so:

x = 1 is the first term

x = 2 is the second term.

And so on.

The y-value will be the actual value of the term.

Here we can see 4 points graphed, these are:

(1, 2), (2, -2), (3, -6), (4, -10)

Then the values of the first four terms of the sequence are:

2, -2, -6, -10

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The equation of the ellipse  derived as is

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1.

The equation of foci is

F₁ = (h - √(a^2 - b^2), k) , F₂ = (h + √(a^2 - b^2), k)

An ellipse is  described as a set of points in a plane such that the sum of the distances from each point to two fixed points, called foci, is constant.

We can write the equation of an ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

where (h, k) = the center of the ellipse,

a = the semi-major axis,

and b = the semi-minor axis.

The foci of the ellipse are located along the major axis and are equidistant from the center, with a distance of : √(a^2 - b^2).

we know also the formula to find the foci of an ellipse is:

F₁ = (h - √(a^2 - b^2), k)

F₂ = (h + √(a^2 - b^2), k)

The sum of the distances from each point on the ellipse to the foci is constant. The equation can then be written as:

2a = √((x - h + √(a^2 - b^2))^2 + (y - k)^2) + √((x - h - √(a^2 - b^2))^2 + (y - k)^2)

Simplifying, we then can write  the equation of the ellipse as:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

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Answer:

$2,440 + $1,220 = $3,660

Step-by-step explanation:

If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:

$61,000 x 0.04 = $2,440

Since her employer has a 50% match on the first 4% of her salary, they would contribute:

$2,440 x 0.5 = $1,220

Answer:

\( A=\frac{d^2}{2} \).

Step-by-step explanation:

Area of Square by Applying Formula for the Diagonal

We can use the relationship between diagonal length d and the side a length of a square to find its area A. So, the formula for area of square using diagonal is \( A=\frac{d^2}{2} \).

Answer:

The walking distance that is saved by cutting across the lot is approximately 18 feet.

Answer:

15

Step-by-step explanation:

Let's call the number we try to find "[tex]x[/tex]"

In the problem, we know that "26 is less than twice a number" is the same as "4". So we can write this as an equation:

[tex]2x - 26 = 4[/tex]

Now we can solve for x by isolating it on one side of the equation.

First, we isolate "2x" by flipping "-26" to the other side, which will now be "26".

[tex]2x = 4 + 26[/tex]

Then we add

[tex]2x = 30[/tex]

finally, we isolate the x by dividing each side with 2

2x ÷ 2 = 30 ÷ 2
x = 15

Answer: The answer is 6.25

Step-by-step explanation:

Answer:

6.25

Step-by-step explanation:

The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.

The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.

The y-coordinate of this point is 1, so sin(183π/2) = sin(16,470 degrees) = 1.

It should be noted that go find cos(5π), we first need to convert 5π to degrees. We know that π radians is equal to 180 degrees, so 5π radians is equal to 5π × (180/π) = 900 degrees. The x-coordinate of this point is -1, so cos(5π) = cos(900 degrees) = -1.

Also, to find sin(-9π/2), we first need to convert -9π/2 to degrees. We know that π radians is equal to 180 degrees, so -9π/2 radians is equal to -9π/2 × (180/π) = -810 degrees. The y-coordinate of this point is -1, so sin(-9π/2) = sin(-810 degrees) = -1.

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Answer:

17/x = x/8

x^2 = 136, so x = 2√34

The simplified expression of  2x multiplied by 7 with the exponent of 4 is 4,802x.

The expression is simplified by applying the rules of multiplication and exponent rules.

the expression = 2x(7⁴)

simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401

Multiply the resultant solution of 2,401 as follows;

= 2,401 x (2x)

= 4,802x

Thus, the simplified expression of  2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.

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a

1.5/4

b

0.5/4

c

0.5/4

because half of 3 is 1.5

Answer:

I'm pretty sure the answer is B(

Answer: x=4, sides = 12, 8, 6, 8

Step-by-step explain

Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.

X+8+x+4+2x-2+x²-2x=34

x²+2x+10=34

x²+2x-24

(x-4)(x+6)

x=4, x=-6

x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.

Now to find side lengths just plug in 4 for x

4+8=12

4+4=8

2*4-2=6

4*4-2*4=8

Answer:

1,3,5,7,9

Step-by-step explanation:

0 can't be, let's take 10 or 20 or 30 for example, not a prime number.

1 can be because let's take 11, 31 as example, they're prime numbers.

2, 4, 6, 8 can't be the answer because they have factors

The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59

Answer:

64.14

Step-by-step explanation:

Reading the passage I see that you have to multiply then divide

The surface area of the larger solid is,  171.7 mm²

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

The volumes of two similar solids are 857.5 mm³ and 540 mm³.

And, The surface area of the smaller solid is 108 mm².l

Now, Let us assume that;

The surface area of the larger solid is, x

Hence, We get;

857.5 / x = 540 / 108

Solve for x as;

857.5 x 108 = 540 x

92,718 = 540x

x = 171.7 mm²

Thus, The surface area of the larger solid is,  171.7 mm²

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The volume of the solid obtained by rotating the region over the function is given by the integral and V = 44.46 units³

Given data ,

The volume of the solid obtained by rotating the region underneath the graph of the function f(x)=√x² +9 over the interval [0,2] about the y-axis

The formula for Area under definite integral is

∫ₐᵇ f ( x ) = f ( b ) - f ( a )

Since we are rotating the region about the y-axis, the radius is simply the x-coordinate of each point on the curve, or r = x

The height h of each shell is equal to the difference between the y-coordinates of the curve at x and x + Δx, or h = f(x + Δx) - f(x)

Using these expressions for r and h, we can write the volume of each cylindrical shell as:

V(x) = 2πx[f(x + Δx) - f(x)]Δx

V = ∫₀² 2πx[f(x + Δx) - f(x)]dx

As Δx approaches zero, this integral becomes:

V = ∫₀² 2πx√(1 + (f'(x))²) dx

where f'(x) is the derivative of f(x), which is:

f'(x) = x/√(x² + 9)

Substituting this expression for f'(x) into the integral, we get:

V = ∫₀² 2πx√(1 + (x/√(x² + 9))²) dx

This integral can be evaluated using a substitution, u = x² + 9, du/dx = 2x, and dx = du/2x, to get:

V = ∫₉¹³ 2π(x² + 9)^(3/2)/2 dx

V = [4/5 π(x² + 9)^(5/2)]₉¹³

V = 44.46 units³

Hence , the volume of the solid is 44.46 units³

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Carlos can expect the value of the computer to be $580 three years after purchase.

To model the value of the computer, we can use the formula:

y = abˣ

We know that the initial value of the computer is $1,350, so a = 1350.

We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:

810 = 1350b

b= 0.6

b = 0.6

So our exponential equation is:

y = 1350(0.6)ˣ

To find the value of the computer 3 years after purchase, we can substitute x = 3:

y = 1350(0.6)³

y = 583

Hence, Carlos can expect the value of the computer to be $580 three years after purchase.

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The solutions to the equation over the interval [0°, 360°) are: x = 45°, 135°, 225°, 315°.

We can rewrite this equation as:

1 - sin² x = sin²x

Solving for sin x, we get:

sin x = ±✓(1/2)

Since sin x is positive in the first and second quadrants and negative in the third and fourth quadrants, we have:

sin x = ✓(1/2) = 1/✓(2) in the first and second quadrants, corresponding to x = 45° and 135°.

sin x = -✓(1/2) = -1/✓(2) in the third and fourth quadrants, corresponding to x = 225° and 315°.

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Answer:  

C is the answer

Given :   dilation with a scale factor of 3

To find :  Which statement is true

Step-by-step explanation:

Solution: A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

if Dilation factor  N then image Size is multiplied  by  N

if Scale factor  < 1 then image get reduced

if scale factor > 1  then image get enlarged

scale factor = 1 lead to Same size image

Here is given that Scale factor of 3

=> image will be enlarged to 3 times the original image

Hence correct option is :

C)Each side in the pre-image is multiplied by three to find the corresponding side length in the image

Answer: C

Step-by-step explanation: Edge Unit Test

Answer:

B. 1

Step-by-step explanation:

Let's use the formula for finding the mean of a set of data:

mean = (sum of all data values) / (number of data values)

We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:

2.2 = (sum of all 10 data values, including x) / 10

Multiplying both sides by 10, we get:

22 = sum of all 10 data values, including x

We can then subtract the sum of the known data values from both sides to find the missing value:

22 - (01 + 12 + 23 + 31 + 42 + 51) = x

22 - (0 + 2 + 6 + 3 + 8 + 5) = x

x = 22 - 24 = -2

However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:

If the missing score is 0:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10

2.2 = 18 / 10

2.2 = 1.8

This is not true, so the missing score cannot be 0.

If the missing score is 1:

2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10

2.2 = (18 + ?) / 10

22 = 18 + ?

? = 4

So the missing score is 1, and the answer is B.

Answer:

Answer is B

Total scores/total frequency =mean

54/24=2,25

If you added a score of 1

55/25=2,2

Step-by-step explanation:

hope that helps you

Answer:

C

Step-by-step explanation:

The area of a rectangle is 2 dimensions so it would be measured in square meters.

a = lwh

26241 = lw(17)  Divide both sides by 17

1542 = lw

The lw is he area of the base.

Helping in the name of Jesus.

Answer:

a) In 2 hours

b) 16 km

Step-by-step explanation:

Let's first find out how far Abel has traveled in 2 hours. We can use the formula:

distance = speed x time

distance = 4 km/h x 2 h = 8 km

So when Jack starts cycling, Abel has already covered 8 km.

Now, let's say it takes Jack t hours to catch up to Abel. During this time, Abel has continued walking for t + 2 hours. So we can write:

distance covered by Abel = distance covered by Jack

4 km/h x (t + 2 h) = 8 km/h x t

Simplifying this equation, we get:

4t + 8 = 8t

4t = 8

t = 2

So Jack will overtake Abel after 2 hours of cycling. To find out how far they will have traveled, we can use the formula:

distance = speed x time

distance = 8 km/h x 2 h = 16 km

Therefore, when Jack overtakes Abel, they will have traveled 16 km in total.

The value of the points is,

(1/5, 7/5)  or (0.2, 1.4)

The given equation may be simplified as follows:

x² + 14xy + 49y² = 100

(x + 7y)(x + 7y) = 100

(x + 7y)² = 10²

x + 7y = 10

This is a straight line with the equation.

y = -(1/7)x + 10/7

The minimum distance from the origin to this line is provided by a straight line that passes through the origin and which is perpendicular to the straight line.

The slope of the perpendicular line is 7 because the product of the two slopes should be -1.

The perpendicular line is of the form

y = 7x + c.

Because the line passes through (0,0), therefore c = 0.

The line y = 7x intercepts the original line when

y = 7x = -(1/7)x + 10/7

Therefore

7x = -(1/7)x + 10/7

Multiply through by 7.

49x = -x + 10

50x = 10

x = 1/5

y = 7x = 7/5

Hence, The minimum distance is

d = √(x² + y²)

  = √[(1/5)² + (7/5)²]

  = √2

Thus, The point is (1/5, 7/5).

So, Solution are, (1/5, 7/5)  or (0.2, 1.4)

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Let x be the length of each of the equal sides of the isosceles triangle. Then the length of the base is x - 4. The perimeter of the triangle is the sum of the lengths of the three sides, which is:

x + x + (x - 4) = 3x - 4

We know that the perimeter is 32, so we can set 3x - 4 equal to 32 and solve for x:

3x - 4 = 32

Adding 4 to both sides gives:

3x = 36

Dividing by 3 gives:

x = 12

Therefore, one of the equal sides of the triangle is 12 inches long, and the length of the base is 12 - 4 = 8 inches.

So the three sides of the triangle are 12 inches, 12 inches, and 8 inches.

The correct equation to solve the problem is (C) 3x - 4 = 32.