which part of this graph shows a nonlinear relationship

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:  C

Hope this helps :)

I believe that the answer is D

Answer:

44

Step-by-step explanation:

36/9 * 11 will get the answer

9/11 * x = 36

x = 44

(multiplied each side by 11/9 to cancel out fraction)

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

Answer:

Step-by-step explanation:

Answer:

$3228

Step-by-step explanation:

39236 - 500 = 38736

38736 / 12 = 3228

Triangle ABC is reflected across the y-axis. The two congruent triangles are mirrored across the y-axis, thus they are reflected.

6: Give the translation rule, any coordinate point will shift 4 units to the left and rise up 8 units.

The translation rule describes how each coordinate point of the original triangle ABC moves to form the reflected triangle after the reflection across the y-axis.

To reflect a triangle across the y-axis, all you need to do is change the sign of the x-coordinate while keeping  the y-coordinate the same. Using this rule, every point on the original triangle ABC will move 4 units to the left and go up 8 units to create the reflected triangle A'B'C' after the reflection.

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The two unit vectors orthogonal to both (0, 1, 2) and (1, -2, 3) are:

Unit Vector 1 = (-4/√21, 2/√21, -1/√21)

Unit Vector 2 = (-10/√21, 0, 0)

To find two unit vectors that are orthogonal (perpendicular) to both vectors (0, 1, 2) and (1, -2, 3), we can use the cross product of the two vectors.

Let's denote the given vectors as vector A = (0, 1, 2) and vector B = (1, -2, 3).

Calculate the cross product of A and B.

To find the cross product, we perform the following calculation:

A × B = (A2 * B3 - A3 * B2, A3 * B1 - A1 * B3, A1 * B2 - A2 * B1)

= (1 * 2 - 2 * 3, 2 * 1 - 0 * 3, 0 * (-2) - 1 * 1)

= (-4, 2, -1)

Normalize the resulting vector to obtain a unit vector.

To normalize a vector, we divide each component by the magnitude of the vector. In this case, the magnitude of (-4, 2, -1) can be calculated as:

|A × B| = sqrt((-4)^2 + 2^2 + (-1)^2) = sqrt(21)

To obtain a unit vector, we divide each component of (-4, 2, -1) by the magnitude:

Unit Vector 1 = (-4/√21, 2/√21, -1/√21)

Find another vector orthogonal to both A and B.

To find a second unit vector orthogonal to A and B, we can take the cross product of A and the first unit vector we calculated.

A × Unit Vector 1 = (0, 1, 2) × (-4/√21, 2/√21, -1/√21)

Performing the cross product calculation, we get:

(2 * (-1/√21) - (-4/√21) * (2/√21), (-4/√21) * (0) - (0) * (-1/√21), (0) * (2/√21) - 1 * (-4/√21))

= (-2/√21 - 8/√21, 0, 0)

Simplifying, we have:

Unit Vector 2 = (-10/√21, 0, 0)

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Answer:

The population after 7 years will be 11887

Step-by-step explanation:

Given

Population = P_0 = 10000

Growth Rate = r = 2.5%

Time = t = 7

The formula for calculating the population after given time at given rate is:

The population after 7 years will be 11887

Step-by-step explanation:

Answer:

Cannot be determined

Step-by-step explanation:

You get that angles 4 + 5 and 2 + 1 are equal to 180 each. We still have angle 3 left over, and that angle could be anything, so it cannot be determined

Answer:

well 4+5=180°, 1+3=180°, that's 360, so I guess can't be determined since there's still another angle???

Step-by-step explanation:

idk, the answer choices could be wrong or im just wrong

Answer:

18

Step-by-step explanation:

9 + 18 = 27

9 x 2 = 18

Answer:

80 total to spent evrytin is 20 percent

Step-by-step explanation:

The function to show the amount of tiles laid as a function of time is

The reasonable domain is 0 ≤ t ≤ 9.6

Information gotten from the question include

Jeremy and Travis are placing 1200 tiles in a building

hey have already place 200 tiles, and they are able to place 125 tiles every hour.

The relationship is expressed in the form.

y = mt + c

Definition of variables to suit the problem to be solved

y = Total number of tiles laid

m = tiles laid per hour = 125

t = number of time

c = tiles already placed

200 = 1200 - 125t

The reasonable domain is the range between zero tiles to laying up the 1200 tiles

0 = 1200 - 125t

1200 = 125t

t = 9.6

1200 = 1200 - 125t

0 = -125t

t = 0

the domain is 0 ≤ t ≤ 9.6

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The amount that will be withheld from his paycheck for income tax in all is d. $189.42.

The amount withheld is a credit against the income taxes the employee must pay during the year.

The amount withheld from his paycheck for income tax in all is given by;

Amount withheld = State income tax + ( State income tax× Percentage of federal income tax)

Where:

State income tax=$154.00

Percentage of federal income tax=23%

Substitute all the values in the formula

Amount withheld=$154.00+($154,00×23%)

Amount withheld=$154.00+$35.42

Amount withheld=$189.42

Hence, the amount that will be withheld from his paycheck for income tax in all is d. $189.42.

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Answer:

Yes

Step-by-step explanation:

Yes, dividing a negative number by a positive number will equate to another negative number.

Applying this logic, -2 divide by 2 is simply -1

Answer: $46.40

Step-by-step explanation: The cost after discount is $17.40. List price $29 per shirt. 40% off of $29 is $11.60. So for the first shirt he will pay $29 and the second he will pay $17.40. In total he pays $46.40 in the two shirts.

Answer:

\(\huge\boxed{\sf S = 0, P = -16}\)

Step-by-step explanation:

Given the equation:

\(\sf x^2 -16 = 0\)

Comparing it with \(\sf x^2-Sx+P= 0\), where S is the sum and P is the product.

So,

Sum = S = 0

Product = P = -16

Hope this helped!

Answer:

Answer: K-2

Step-by-step explanation:

If you think about it’s pretty simple just find the key hints.

Answer:

16 Bicycles

Step-by-step explanation:

Answer:

The x intercepts would be (-6; 0) and (2; 0).

Step-by-step explanation:

Take a look at the picture.

Calculate it replacing f(x) with 0. The result will be: x1 = -6, x2 = 2 (consequently, both y's equal 0).

Answer:

(-6,0),(2,0)

Step-by-step explanation:

x-intercept

at x-intercept y=0

f(x)=x^2+4x-12

x^2+4x-12=0

by using factorisation method

product=-12

sum=4

factors=6,-2

(x^2 -2x)+(6x-12)=0

x(x-2)+6(x-2)=0

(x+6)(x-2)=0

x+6=0, x-2=0

x= -6,x=2

Answer:

Step-by-step explanation:  adding & subtraction section,

a)1/3  b)2/5 c)3/4 d)-3/10 e)19/12 f)35/36  g)7/6 h) 7/3  i)25/24   j) 1 (7/10)

k) 1  (35/36)      l) 0

Answer:

-4/9

Step-by-step explanation:

I used a calculator.

5/6(−8/15) in simplest form is -4/9.

A fraction is written in the form of a numerator and a denominator.There are two types of fractions. One is proper fraction in which numerator is less than the denominator and another one is improper fraction in which denominator is less than the numerator.All fractions can be written in the form of p/q, where q ≠ 0 cause anything divided by 0 is undefined.

According to the given questions we have to multiply two fractions        (5/6)(-8/15) which is

= -40/90.

= -4/9.

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Answer:

  d = 50h

Step-by-step explanation:

  distance = speed × time

Lumpy's distance (d) in miles, after driving h hours at 50 miles per hour, is given by ...

  d = 50h

To find the work needed to pump all the water from a cylindrical tank to a level 1 ft above the rim, we need to calculate the weight of the water and then multiply it by the distance it is pumped. The weight of the water is determined by its volume and specific weight, while the distance is the height of the tank plus the additional 1 ft. By plugging in the given values and using the formulas for the volume of a cylinder and the weight of water, we can calculate the final answer in terms of π.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. In this case, the tank has a radius of 3 ft and a height of 10 ft. The volume of water in the tank is then V = π(3^2)(2) = 18π ft^3.

The weight of the water is determined by its volume and specific weight. The specific weight of water is given as 64 lb/ft^3. Therefore, the weight of the water in the tank is W = (18π)(64) = 1152π lb.

To pump all the water to a level 1 ft above the rim, we need to pump it a total distance of 10 + 1 = 11 ft. The work required is given by the formula W = force × distance. In this case, the force is the weight of the water and the distance is 11 ft. Therefore, the work needed is W = (1152π)(11) = 12672π ft-lb.

Hence, the exact answer for the work needed to pump all the water is 12672π ft-lb.

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Answer:

\(f(x) = 15x^2 -14x - 8\)

\(g(x) = 5x + 2\)

Step-by-step explanation:

Represent the two polynomials with f(x) and g(x)

The question requires that we assume values for f(x) and g(x) as long as the condition in the question is met;

Let

\(f(x) = 15x^2 -14x - 8\)

\(g(x) = 5x + 2\)

To determine if the condition is met, we need to divide f(x) by g(x)

\(\frac{f(x)}{g(x)} = \frac{15x^2 -14x - 8}{5x + 2}\)

Factorize the numerator

\(\frac{f(x)}{g(x)} = \frac{15x^2 - 20x + 6x - 8}{5x + 2}\)

\(\frac{f(x)}{g(x)} = \frac{(5x + 2)(3x - 4)}{5x + 2}\)

Cross out 5x + 2

\(\frac{f(x)}{g(x)} = 3x - 4\)

The result is referred to as quotient, Q

\(Q = 3x - 4\)

Note that Q and g(x) have the same degree of 1

Answer:

64.

Step-by-step explanation:

The digits used are 1 , 2, 7 and 8

To make a number of three digits, the digits are repeated.

To make the three digit number

The ones place is filled by 4 ways.

The tens place is filled by 4 ways.

The hundred place is filled by 4 ways.

So, the total number of ways to make a three digit number is 4 x 4 x 4 = 64.

c is a constant of the function y = ax² + bx + c is -3

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

y = ax² + bx + c

At point (5, 32)

32 = a(5²) + 5b + c   (1)

At point (6,45)

45 = a(6²) + 6b + c   (2)

At point (4, 21)

21 = a(4²) + 4b + c   (3)

Hence:

a = 1, b = 2 and c = -3

The value of c which is a constant of the function y = ax² + bx + c, is -3.

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