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3 years ago

Find a function of the form y=Asin(kx)+C or y=Acos(kx)+C whose graph matches this one:

Mathematics

1 answer:

kumpel [21]3 years ago

4 0

Answer:

y = 4cos((π/5)x) +3

Step-by-step explanation:

The graph shows the peak of the function to be at x=0, so a cosine function is an appropriate choice for the model.

The value of A is half the difference between the minimum and maximum, so is ...

A = (1/2)(7 -(-1)) = 4

The value of C is the average of the maximum and the minimum, so is ...

C = (1/2)(7 +(-1)) = 3

The value of k must be chosen so that for one full period, kx is 2π. We note that one minimum is at -5, and the next is at +5, so the period of this waveform is (5 -(-5)) = 10. Then ...

k·10 = 2π

k = π/5 . . . . . divide by 10 and reduce the fraction

Now, we have all the parameters of our function:

y = 4cos((π/5)x) +3

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777dan777 [17]

Step-by-step explanation:

(2x-3)(2x+3)

2x(2x+3)-3(2x+3)

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3 years ago

What is the value of 3x2 - 5xy + 5y2 for x = -6 and y = 2?

crimeas [40]

Answer is 188 3x2 - 5xy + 5y2 Now put x = -6 and y = 2 3(-6)2 - 5(-6)(2) + 5(2)2 3(36) - 5(-12) + 5(4) 108 + 60 + 20 188

4 0

4 years ago

Ed bought 3 liters of water and 2750 milliliter of sports drink. Which did he have more of and how much more?

MAXImum [283]

1 liter = 1000 milliliter
3 (1000) = 3000 milliliter of water

water has more

3000-2750= 250 millimiter more than sports drink

8 0

3 years ago

Help!! Please please answer quickly and in the next 9 hours! <br><br> Solve these questions.

lutik1710 [3]

Answer:

Please refer to step-by-step.

Step-by-step explanation:

Let's solve all of these one at a time.

15. -2x - y = -5

To find the x-intercept, we need to equate the value of y to 0.

-2x - 0 = -5

$\dfrac{-2x}{-2}=\dfrac{-5}{-2}$

$x=2.5$

To find the y-intercept, we need to equate the value of x to 0.

-2(0) - y = -5

Now since we cannot have a negative value, we need to divide both sides by -1.

$\dfrac{-y}{-1}=\dfrac{-5}{-1}$

$y=5$

To find the slope form, we can simply transpose the value of -2x to the other sides of the equal sign.

-y = 2x - 5

Now we cannot have a negative value for the slope, we need to divide both sides by -1, leaving us with.

y = -2x + 5

16. 6x + 3y = -9

Let's start with the x-intercept.

6x + 3y = -9

6x + 3(0) = -9

$\dfrac{6x}{6}=\dfrac{-9}{6}$

$x=1.5$

Now we solve for the y-intercept.

6x + 3y = -9

6(0) + 3y = -9

$\dfrac{3y}{3}=\dfrac{-9}{3}$

$y = -3$

Now for the slope.

3y = -6x - 9

Now we need to divide all our variables by 3 to get y.

$\dfrac{3y}{3}=\dfrac{-6x}{3}-\dfrac{9}{3}$

$y=-2x-3$

17. x - y = 4

Let's start with the x-intercept.

x - y = 4

x - 0 = 4

$x=4$

Now we solve for the y-intercept.

x - y = 4

0 - y = 4

-y=4

$\dfrac{-y}{-1}=\dfrac{4}{-1}$

$y = -4$

Now for the slope.

x - y = 4

-y = -x + 4

We need to divide all our variables by -1 to get y.

$\dfrac{-y}{-1}=\dfrac{-x}{-1}+\dfrac{4}{-1}$

$y=x-4$

18. 3x + 4y = 12

Let's start with the x-intercept.

3x + 4y = 12

3x + 4(0) = 12

$\dfrac{3x}{3}=\dfrac{12}{3}$

$x=4$

Now we solve for the y-intercept.

3x + 4y = 12

3(0) + 4y = 12

$\dfrac{4y}{4}=\dfrac{12}{4}$

$y = 3$

Now for the slope.

3x + 4y = 12

4y = -3x + 12

$\dfrac{4y}{4}=-\dfrac{3x}{4}+\dfrac{12}{4}$

$y=-\dfrac{3x}{4}+3$

19. -7x + 2y = -16

Let's start with the x-intercept.

-7x + 2y = -16

-7x + 2(0) = -16

$\dfrac{-7x}{-7}=\dfrac{-16}{-7}$

$x=-2\dfrac{2}{7}$

Now we solve for the y-intercept.

-7x + 2y = -16

-7(0) + 2y = -16

$\dfrac{2y}{2}=\dfrac{-16}{2}$

$y=-8$

Now for the slope.

-7x + 2y = -16

2y = -7x - 16

$\dfrac{2y}{2}=-\dfrac{7x}{2}-\dfrac{16}{2}$

$y=-\dfrac{7x}{2}-8$

20. x - 5y = 55

Let's start with the x-intercept.

x - 5y = 55

x - 5(0) = 55

x = 55

Now we solve for the y-intercept.

x - 5y = 55

0 - 5y = 55

$\dfrac{-5y}{-5}=\dfrac{55}{-5}$

$y=-11$

Now for the slope.

x - 5y = 55

-5y = x + 55

$\dfrac{-5y}{-5}=-\dfrac{x}{-5}+\dfrac{55}{-5}$

$y=-\dfrac{x}{5}-11$

8 0

3 years ago

What is the area of this figure?

Zolol [24]

$a \: = \: square \: area \: + \: triangle \: area \: + \: rectangle \: area \: \\$

$a \: = (3 \times 3) + ( \frac{1}{2} \times 3 \times 11) + (3 \times 11) \\$

$a = 9 + \frac{33}{2} + 33 \\$

$a = 9 + 16.5 + 33$

$a = 25.5 + 33$

$a = 58.5 \: \: {ft}^{2}$

5 0

2 years ago