Find relative extrema (x, y) of a function h(x) = x^3 + 3x^2 − 2 using
(a) the first derivative test
(b) the second derivative test
Which test is easiest?

The equation, for the simple harmonic motion of a particle moving uniformly is s ( t ) = A x cos (ωt).

An object undergoing simple harmonic motion follows a periodic oscillation in a straight line, resembling a sinusoidal curve. Likewise, when an object continuously traverses upon a circle with uniform motion, its projection along the diameter travels back and forth in a simple harmonic motion pattern.

Assuming that the particle commences at the highest point of the simple harmonic motion at time t = 0, either the sine or cosine function is utilized to derive the equation for the simple harmonic motion formula. Thus, let us employ the cosine function in this instance:

s ( t ) = A x cos (ωt)

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Therefore, the range of the relation shown is (1, 3, 4, 6, 7). Option C is the correct answer.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are used to model relationships between variables in many areas of mathematics and other fields such as physics, engineering, economics, and computer science. They are used to describe various phenomena, such as the growth of populations, the trajectory of a projectile, or the behavior of financial markets. Functions are also important tools in calculus, where they are used to study rates of change and continuity, among other things.

Here,

The range of a relation refers to the set of all possible output values or y-values of the relation. Looking at the image reference, we can see that the y-values or the outputs are 1, 3, 4, 6, and 7.

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Answer:

Step-by-step explanation:  find the circumference and then consider the shape (circle) after that get rid of options that don't make sense like 7.3 and 7.1, 8 for the radius might be too big leaving you with    7     (use a calculator if needed)

Answer:

Step-by-step explanation:

D is the correct answer.

Answer:

D

Step-by-step explanation:

By reading the graph, place the art museum at location (5,5). Then check all the locations to see which statement is true.

A is not true because the art museum is located 4 units east and 1 unit north from the coliseum.

B is not true because the art museum is located 3 units east and 3 units north of the smith's tower.

C is not true because the art museum is located 1 unit east and 2 units north of the state capital.

This is why D is the correct answer.

The value of the "trigonometric-expressions' are :

(a) tan(5π/2) is undefined,

(b) sec(315°) is √2.

Part(a) : The expression "tan(5π/2)" is undefined because the tangent function is undefined at odd multiples of π/2, which includes 5π/2.

Part(b) : To find the value of sec(315°), we use the identity: sec(θ) = 1/cos(θ),

First, we convert 315° to radians:

Which is : 315° = (7π/4) radians;

Next, we find the value of cos(7π/4):

⇒ cos(7π/4) = cos(π/4) = (√2)/2;

Finally, we substitute in the identity for sec(θ);

So, Sec(7π/4) = 1/cos(7π/4) = 1/[(√2)/2] = √2.

Therefore, value of sec(315°) is √2.

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The given question is incomplete, the complete question is

Find the value of the trigonometric expressions :

(a) tan(5π/2)

(b) sec(315°)

The airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds

Let,

Weight of airplane = y

Amount of fuel = x

The general linear equation can be written as, y=mx + c, where, (m) is slope, and (c) is a constant.

It is given,

2091 = 14m + c ..... (1)

2312 = 48m + c ..... (2)

On subtracting, (1) with (2), we get

221 = 34m

m= (221/34)= 6.5

Now, on putting the value of (m) in (1), we get,

2091 = 14(6.5) + c

So,

c = 2000

Therefore, the linear equation can be written as,

y = (6.5)mx + 2000

Now to find the airplane weight at 52 gallons of fuel, we put x = 52, to find y.

That is,

y = (6.5)(52) + 2000

y = 2338

So, the airplane weigh if it is carrying 52 gallons of fuel will be, 2338 pounds.

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Let's start by setting up a proportion to represent the ratio of Illinois students to Michigan students:

Illinois students / Michigan students = 6/5

We can simplify this proportion by multiplying both sides by 5:

Illinois students = 6/5 * Michigan students

Next, we can use the information in the table to set up an equation that relates the number of Illinois students, Michigan students, and Indiana students:

Illinois students + Michigan students + Indiana students = 175

We can substitute the expression we obtained for the number of Illinois students into this equation:

6/5 * Michigan students + Michigan students + Indiana students = 175

Multiplying both sides by 5 to eliminate the fraction, we get:

6 * Michigan students + 5 * Michigan students + 5 * Indiana students = 875

Combining like terms, we get:

11 * Michigan students + 5 * Indiana students = 875

Now we can use the fact that the ratio of Illinois students to Michigan students is 6:5 to set up another equation:

Illinois students / Michigan students = 6/5

Substituting the values from the table, we get:

Illinois students / Michigan students = 24/20

Cross-multiplying, we get:

Illinois students * 20 = Michigan students * 24

Simplifying, we get:

Illinois students = 6/5 * Michigan students = 24/20 * Michigan students = 6/5 * 24 Michigan students = 28.8 Michigan students

Since the number of students must be a whole number, we can round 28.8 up to 29. This means that there were 29 Michigan students.

Substituting this into the equation we obtained earlier, we get:

11 * 29 + 5 * Indiana students = 875

Solving for Indiana students, we get:

5 * Indiana students = 875 - 11 * 29 = 546

Dividing both sides by 5, we get:

Indiana students = 546/5 = 109.2

Since the number of students must be a whole number, we can round 109.2 up to 110. This means that there were 110 Indiana students.

Therefore, the answer is 110 students from Indiana.

The dimensions of each rectangle are x by (x- y) and y by (x - y); option A and D

The area of each rectangle is x² - 2xy + y²  and x² - xy

The total area of the remaining figure is 2x² - 4xy + 2y²

This figure represents the difference of two squares in that x² - y² = (x + y)(x -y)

The area of each rectangle is:

x * (x- y) =  x² -xy

and

y * (x - y) = xy - y²

The total area of the remaining figure is:

x² -xy + xy - y² = x² - y²

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The journal entry to record the transaction is given:

Account Debit Credit

Cash $464,000

Common Stock, $3 par value $87,000

Paid-in capital in excess of par  $377,000

A journal entry is used to record a business transaction in the accounting records of a business.

A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger

Assuming the shares have a $3 par value and sell for $16 cash per share:

Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000

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Answer:

1

Step-by-step explanation:

7+10+1/5

7/10 = 0.7

1/5 = 0.2

0.7+0.2=0.9

Therefore it would be closest to 1.

Answer: 1

Step-by-step explanation:

To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer

Answer:

B. $7.50

Step-by-step explanation:

We know profit or P-----P(n) where n is the quantity/number of the item) is the difference of the revenue-----R(n)-----and the cost-----C(n)

P(n) = R(n) - C(n)

Revenue is

R(n) = pn

Cost is a combination of

The cost function resembles a linear equation:

C(n) = mn + c

Since we're shown that P = 7.5n - (2.25n + 15), we know that R(n) must be R(n) = 7.5n and C(n) must be C(n) = 2.25n + 15

Thus, we know she charges $7.5 per necklace sold.

Using the tangent ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6  units.

The tangent ratio is part of the trigonometry ratios that is applied when solving a right triangle, and it is expressed as:

tan ∅ = length of the opposite side / length of the adjacent side.

We are given the following information from the image above:

Reference angle (∅) = 43 degrees

length of the opposite side = x

length of the adjacent side = 2.8

Plug in the values:

tan 43 = x/2.8

2.8 * tan 43 = x

x = 2.6 [to the nearest tenth]

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The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 32/2 = 16 ft.

By substituting the parameters, we have:

Volume of cylinder, V = 3.14 × 16² × 10

Volume of cylinder, V = 8,038.4 cubic feet.

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globe meaning a sphere, and since it has a diameter of 25.8, that means its radius is half that, or 12.9

[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=12.9 \end{cases}\implies V=\cfrac{4\pi (12.9)^3}{3}\implies \stackrel{ using~\pi =3.14 }{V\approx 8987.47}[/tex]

Answer: 134.

Step-by-step explanation:

First revert 67% into it's decimal form. You get 0.67. Then, multiply 0.67 by 200 because there were 200 problems.

0.67 x 200

67 x 2

134

So, christian got 134 out of 200 problems correct.

The probability of Casey selecting a tie that goes well with the sport coat is 0.517.

The probability of Casey selecting a tie that does not go well with the sport coat is 0.483

The probability of Casey selecting a tie that goes well with the sport coat is:

P(goes well) = 15/29

P(goes well) ≈ 0.517

The probability of Casey selecting a tie that does not go well with the sport coat is:

P(does not go well) = 1 - P(goes well)

P(does not go well) = 1 - 15/29 = 14/29

P(does not go well) ≈ 0.483

The odds in favor of the tie going well with the sport coat are:

P(goes well) : P(does not go well) = 15/29 : 14/29

P(goes well) : P(does not go well) = 15:14

The odds against the tie going well with the sport coat are:

P(does not go well) : P(goes well) = 14/29 : 15/29

P(does not go well) : P(goes well) = 14:15

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The workers percentile score is given as follows:

69.15%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score for this problem is given as follows:

z = 0.5.

Hence the percentile score is of 69.15%, as z = 0.5 has a p-value of 0.6915.

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Based on the image, we can infer that the router cannot cover the kitchen area.

To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

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1. To find the interest we will use = (D6*D5) - B8,  2. To find the total cost we will use = B6 + D7.

Here we are given the financial information of a firm and are required to give an appropriate formula for total interest and total cost

1.

Here we need to multiply D6 and D7 and subtract B8 from the result. We cannot use any function. Hence we will simply write

= (D6*D5) - B8

The bracket is not necessary but can be put s an added satisfaction that the said formula would multiply the cells first and then only will the loan amount would be subtracted.

2.

Similarly, for cell D8, we need to go to the formula bar and write

= B6 + D7

This will add the cells up to give us the total cost.

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Complete Question

(Image Attached)

The values of m and b after evaluation is -2 and 23 under the condition that If x=3t+t² and y=7−2t, and  tangent to the curve at t=2.

In orde to evaluate the equation of the tangent to the curve at t=2, we have to calculate the slope of the curve at t=2.
The slope of the curve at t=2 is presented by the derivative of y with respect to x at t=2.
y = 7 - 2t
x = 3t + t²
dy/dx = -2
Then, the slope of the tangent to the curve at t=2 is -2.
Now we have to evaluate the point on the curve at t=2.
x = 3(2) + (2)² = 10
y = 7 - 2(2) = 3
So, the point on the curve at t=2 is (10,3).
Applying  point-slope form of equation of line:
y - y₁ = m(x -x₁)
Here,
m = slope and (x₁,y1) is a point on the line.
Staging m=-2 and (x₁,y₁)=(10,3),
y - 3 = -2(x - 10)
Applying simplification
y = -2x + 23
Then, the equation of the tangent to the curve at t=2 is y=-2x+23.
So, m=-2 and b=23.
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T(-1, 7)

→

T′(-1, -7)

U(-1, 8)

→

U′(-1, -8)

V(9, 6)

→

V′(9, -6)

The rap about why triangular pyramids are the best shape is given below.

Verse 1:

Listen up, y'all, I'm here to spit some truth

About a shape that's often overlooked, but it's the truth

It's the triangular pyramid, and let me tell you why

It's the best shape out there, and that's no lie

Chorus:

Triangular pyramids, they're the way to go

Strong and sturdy, they're the best, you know

With their pointed tips and angled sides

They're the perfect shape, no need to hide

Verse 2:

When it comes to architecture, they're the top choice

Their shape is so versatile, you can't deny its voice

From ancient pyramids to modern buildings tall

The triangular pyramid can withstand it all

Chorus:

Triangular pyramids, they're the way to go

Strong and sturdy, they're the best, you know

With their pointed tips and angled sides

They're the perfect shape, no need to hide

Verse 3:

And let's not forget their mathematical prowess

Their angles add up to 180, no need to guess

With their faces all congruent, they're a sight to see

The triangular pyramid, it's the shape for me

Chorus:

Triangular pyramids, they're the way to go

Strong and sturdy, they're the best, you know

With their pointed tips and angled sides

They're the perfect shape, no need to hide

Outro:

So there you have it, folks, the triangular pyramid

It's the best shape out there, there's no need to forbid

From its strength to its geometry

The triangular pyramid, it's the shape for me!

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The solution is: x ≥ 6.

What is linear inequalities?

Linear inequality is an equation or expression that do not have a definite solution. Thus it consist of either of greater than, less than, greater than or equal to, less than or equal to etc.

In the given inequality question, we have;

8 is less than or equal to -3x +26

This can be expressed as;

8 ≤ -3x +26

so that collecting like terms,

8 - 26 ≤ -3x

-18 ≤ -3x

-18/ -3 ≤ x

6 ≤ x

Therefore, x ≥ 6.

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In a circle, the measure of a central angle is equal to the measure of its intercepted arc. Since ∠RST is a central angle of circle S and its measure is 102 degrees, the measure of its intercepted arc ⌢RT is also 102 degrees.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since RS is a radius of circle S and its length is 6 units, the circumference of circle S is C = 2π * 6 = 12π units.

The length of an arc is proportional to its measure in degrees. Since the measure of ⌢RT is 102 degrees and the total measure of a circle is 360 degrees, the length of ⌢RT is (102/360) * 12π = 3.4π units.

Rounded to the nearest hundredth, this is approximately 10.68 units.

We can see from the calculation that the angle of elevation of the building is 22.6 degrees.

The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object that is above the observer's level. It is the upward angle from the observer's eye to the object being observed.

We have that;

Tan θ = 500/1200

θ = tan-1 (500/1200)

θ = 22.6 degrees

Thus the angle of elevation is obtained as 22.6 degrees as we can see here.

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Answer:

364 cents or $3.64

Step-by-step explanation:

We can first convert $4 into cents. There are a 100 cents in $1, so there are 400 cents in $4. Now we can subtract.

400 - 36 = 364

Difference is 364 cents or $3.64

The given angles are 7π/4, 10π/3 & 510°.

Calculations for 7π/4(4th Quadarant)

sin(7π/4) = -1/√2

cos(7π/4) = 1/√2

tan(7π/4) = -1

cosec(7π/4) = -√2

cot(7π/4) = -1

sec(7π/4) = √2

Calculations for 10π/3(3rd Quadarant)

sin( 10π/3) = -√3/2

cos(10π/3) = -1/2

tan(10π/3) = √3

cosec(10π/3) = - 2/√3

cot(10π/3) = 1/√3

sec(10π/3) = -2

Calculations for 510°(2nd Quadarant)

sin( 510°) = 1/2

cos(510°) = -√3/2

tan(510°) = -1/√3

cosec(510°) = 2

cot(510°) = -√3

sec(510°) = -2/√3

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