find the derivative for part b
(b) y = sec5 () +1 C-1 E (5 points) Let f(x) = (x - 3)(h(x²))? Given that h(4) = 10 and W'(4) = 3, find f'(2).

(a) The complex Fourier series of f(t) is given by ∑(n=-∞)^(∞) c_n exp(jnωt), where c_n = { 6j/(7πn) if n is odd, 0 if n is even }.

(b) The trigonometric Fourier series of f(t) is given by ∑(n=0)^(∞) [a_n cos(nωt) + b_n sin(nωt)], where a_n = 0 for all n, and b_n = { 12/(nπ) if n is odd, 0 if n is even }.

(a) To determine the complex Fourier series of f(t), we first need to find the coefficients c_n. The complex Fourier series representation is of the form ∑(n=-∞)^(∞) c_n exp(jnωt), where ω = 2π/T is the fundamental frequency.

For the given function f(t), we have the following recursive relationship:

f(t) = 4t + 6f(t+7)

To find c_n, we need to compute the Fourier coefficients. Multiplying both sides of the recursive relationship by exp(-jmωt) and integrating over one period T, we get:

∫[0]^[T] f(t) exp(-jωnt) dt = ∫[0]^[T] (4t + 6f(t+7)) exp(-jωnt) dt

Expanding the integral on the right-hand side using the linearity property of the integral, we have:

∫[0]^[T] f(t) exp(-jωnt) dt = 4∫[0]^[T] t exp(-jωnt) dt + 6∫[0]^[T] f(t+7) exp(-jωnt) dt

The first integral on the right-hand side can be evaluated using integration by parts. The second integral involves the function f(t+7), which has a periodicity of 7. Thus, we can rewrite it as:

∫[0]^[T] f(t+7) exp(-jωnt) dt = ∫[7]^[T+7] f(t) exp(-jωnt) dt

Substituting these results back into the equation and simplifying, we get:

c_n = 4(∫[0]^[T] t exp(-jωnt) dt) + 6(∫[7]^[T+7] f(t) exp(-jωnt) dt)

Now, we need to evaluate the integrals. The first integral can be computed using integration by parts or by recognizing it as the Fourier coefficient of t. The result is:

∫[0]^[T] t exp(-jωnt) dt = jT/(nω)^2

The second integral can be simplified using the periodicity of f(t+7):

∫[7]^[T+7] f(t) exp(-jωnt) dt = ∫[0]^[T] f(t) exp(-jωn(t+7)) dt = exp(-j7nω) ∫[0]^[T] f(t) exp(-jωnt) dt

Since f(t) has a periodicity of 7, the integral becomes:

∫[7]^[T+7] f(t) exp(-jωnt) dt = exp(-j7nω) ∫[0]^[7] f(t) exp(-jωnt) dt

Substituting these results

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Answer:

4.25

Step-by-step explanation:

17/4

= 4.25

I hope it helps! Have a great day!

Muffin ^^

Answer:

4.25

Step-by-step explanation:

The answer is 4.25 because you have to divide the feet by min and when you do that you get 4.25.

I hope it helps! Have a great day!

bren~

Answer:

7396

Explanation:

(171 + 897) + 6,328 = 7396

Answer:

The answer is 12 feet. .

Step-by-step explanation:

You have to multiply 3/4 or 0.75 by the number of tiles. So you would go, 0.75 x 10 and then 0.75 x 6 and add the answers together.

Answer:

2.6%

Explanation:

We'll use the below formula to determine the interest rate;

We're given the below parameters in the question;

*Initial purchase price = $5945

*Face value (future value) = $6000

*Days of maturity = 125

Let's now substitute the above values into our formula and solve for the Interest rate as seen below;

The surface area of the pyramid can be calculated by adding the area of the base to four times the area of each triangular face.

To calculate the surface area of a square pyramid, we need to consider its base and triangular faces. The base of the pyramid is a square, so its area is determined by multiplying the length of one side (s) by itself (s^2).

The surface area also includes the sum of the areas of the four triangular faces. Each triangular face can be divided into two congruent right triangles. The slant height of the pyramid (l) is the height of these right triangles. Using the formula for the area of a triangle (0.5 × base × height), we can calculate the area of each triangular face as (0.5 × s × l). Therefore, the total surface area of the square pyramid is given by the equation: Surface Area = s^2 + 4 × (0.5 × s × l).

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No , we cannot have a triangle with 2cm , 3cm and 5cm , because the sum of two sides is not greater than the other sides .

What is a Triangle ?

A triangle can be defined as the closed figure , that is made up of three line segments .

The Condition for any three sides to form a triangle : the sum of any two sides of triangle should be greater than the third side .

The sides of triangle are given to be : 2cm , 3cm and 5cm ;

on adding the two sides ,

we get ;

⇒ 2 + 3 = 5 > 5 ; False

⇒ 3 + 5 = 8 > 2 ; True

⇒ 2 + 5 = 7 > 3 ; True

All the conditions are not met ,

Therefore , the given sides cannot form a triangle .

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Answer: x∈(-5,+∞)

Step-by-step explanation:

\(2x+10 > 0\\\\2x+10-10 > 0-10\\\\2x > -10\)

Divide both parts of the inequality by 2:

\(x > -5\)

The equation \(4x^2u^n + (1-x^2)u = 0\) has two solutions. One solution is given by \(u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\). The other solution is not provided in the given question.

To find the solutions, we can rewrite the equation as \(u^n = -\frac{1-x^2}{4x^2}u\). Taking the square root of both sides gives us \(u = \pm\left(-\frac{1-x^2}{4x^2}\right)^{1/n}\). Now, let's focus on finding the positive solution.

Expanding the expression inside the square root using the binomial series, we have:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{(1-x^2)}{4x^2}\right)^{1/n}\]

Since \(|x| < 1\) (as \(x\) is a fraction), we can use the binomial series expansion for \((1+y)^{1/n}\), where \(|y| < 1\):

\[(1+y)^{1/n} = 1 + \frac{1}{n}y + \frac{1-n}{2n^2}y^2 + \dots\]

Substituting \(y = \frac{1-x^2}{4x^2}\), we get:

\[\left(-\frac{1-x^2}{4x^2}\right)^{1/n} = -\frac{1}{4^{1/n}x^{2/n}}\left(1 + \frac{1}{n}\cdot\frac{1-x^2}{4x^2} + \frac{1-n}{2n^2}\cdot\left(\frac{1-x^2}{4x^2}\right)^2 + \dots\right)\]

Simplifying and rearranging terms, we find the positive solution as:

\[u_1 = x^{1/2}\left(1 + \frac{x^2}{16} + \frac{x^4}{1024} + \dots\right)\]

The second solution is not provided in the given question, but it can be obtained by considering the negative sign in front of the square root.

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To create a histogram, the scientist needs to group the data into categories or bins. The number of bins and the size of each bin can affect the shape of the resulting histogram, so the scientist needs to choose these values carefully.

One common method for determining the number of bins is to use the square root rule, which states that the number of bins should be approximately equal to the square root of the sample size. In this case, the sample size is 15, so the square root rule suggests using around 4-5 bins.

To determine the size of each bin, the scientist can consider the range of the data. The minimum value is 1.1 and the maximum value is 2.45, so the range is 2.45 - 1.1 = 1.35. The size of each bin should be small enough to capture the variation in the data, but not so small that there are too few observations in each bin.

One possible way to group the data into 4 bins with a bin size of 0.3 would be:

1.1 - 1.4

1.4 - 1.7

1.7 - 2.0

2.0 - 2.3

The last observation (2.45) would fall in the bin "2.3-2.6" which is not included in the bins, but can be included in the last bin.

This grouping allows the scientist to see the frequency of growth measurements falling within each bin. The height of each bar in the histogram will represent the frequency of observations in that bin.

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How much a statistic varies from one sample to another is known as the sampling variability of a statistic.

Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.

The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.

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Answer: 30

Step-by-step explanation:

It to be 30 but this look hard so I’m not sure

The dimensions of the rectangle are length = 21 meters and width = 18 meters.

To find the dimensions of the rectangle meeting these conditions, we first need to set up an equation based on the given information. We know that the perimeter is 78 meters, so we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

Substituting in the given information, we get:

78 = 2(3 + width + width)

Simplifying, we can combine like terms:

78 = 2(3 + 2width)

78 = 6 + 4width

Subtracting 6 from both sides:

72 = 4width

Dividing by 4:

width = 18

So we know the width of the rectangle is 18 meters. We also know that the length is 3 meters greater than the width, so:

length = width + 3 = 18 + 3 = 21

Therefore, the dimensions of the rectangle meeting the specified conditions are:

width = 18 meters

length = 21 meters

To find the dimensions of the rectangle meeting the specified conditions, we'll use the information given: the perimeter is 78 meters and the length is 3 meters greater than the width.

Step 1: Write down the formula for the perimeter of a rectangle.
Perimeter (P) = 2(Length (L) + Width (W))

Step 2: Substitute the given values and conditions into the formula.
78 = 2(L + W)
Given that the length is 3 meters greater than the width, we can write L = W + 3.

Step 3: Substitute the expression for L in terms of W into the perimeter formula.
78 = 2((W + 3) + W)

Step 4: Solve the equation for W.
78 = 2(2W + 3)
39 = 2W + 3
36 = 2W
W = 18 meters

Step 5: Find the length (L) using the expression L = W + 3.
L = 18 + 3
L = 21 meters

So, the dimensions of the rectangle are length = 21 meters and width = 18 meters.

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The sampling distribution of the sample mean c. is the probability distribution showing all possible values of the sample mean. The standard error of the proportion will become larger as d. p approaches .5

The sampling distribution of the sample mean is the probability distribution of the possible values of the sample mean, given a certain sample size and population distribution. It is a theoretical construct that describes how the sample mean is likely to vary across different samples of the same size, drawn from the same population. The sampling distribution of the sample mean is approximately normal, with the mean equal to the population mean and a standard deviation known as the standard error.

The standard error is a measure of the variability of a statistic, such as the sample mean.

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Answer:

39

Hope this helps

Answer:

1. 44 GB

2. 12 ft

3a. 49

3b. -155

3c. 6

3d. -53

Answer:

1)44 GB

2)24 FT

3)

A. 49

B. -115

C.6

D.-53

Step-by-step explanation:

For 2 she went down then up to the second floow meaning she is 12x2 ft up the ground, the basement doesnt count

Answer:

3. is a functions and 4 isnt

Step-by-step explanation:

And=2025 students gave 10125 rs

just divide it by 5hope it helps...pls mark me brainliest

Answer: g(4)=-17

Step-by-step explanation:

You just plug in 4 into x.

-3(4)-5
-12-5
=17

Answer:

g(4) = -17

Step-by-step explanation:

Hello!

Substitute 4 for x in the equation.

g(4) is -17.

The volume of the basketball is approximately 1789. Rounding to the nearest tenth of an inch, the volume of the basketball is approximately 1789.1 cubic inches.

To find the volume of a basketball with a given radius, we can use the formula for the volume of a sphere. The formula tells us that the volume of a sphere is equal to four-thirds times pi times the radius cubed.

In this case, we are given that the radius of the basketball is 7.69 inches. So, we can plug this value into the formula to find the volume.

Using a calculator to perform the necessary calculations, we get:

V = (4/3) * pi * (7.69)^3

V ≈ 1789.1 cubic inches

Therefore, the volume of the basketball is approximately 1789.1 cubic inches, rounded to the nearest tenth of an inch. This tells us how much space the basketball takes up in three-dimensional space.

Knowing the volume of an object can be useful in various applications such as designing packaging, calculating the amount of material needed to manufacture the object, or estimating the amount of liquid or gas it can hold.

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