All categories

1 year ago

I need help with this practice problem solving This is trigonometry from my ACT prep guide

Mathematics

1 answer:

Novay_Z [31]1 year ago

6 0

Take into account, that in general, a cosine function of amplitude A, period T and vertical translation b, can be written as follow:

$f(x)=A\cos (\frac{2\pi}{T}x)+b$

In the given case, you have:

A = 4

T = 3π/4

b = -3

By replacing you obtain:

$\begin{gathered} f(x)=4\cos (\frac{2\pi}{\frac{3\pi}{4}}x)-3 \\ f(x)=4\cos (\frac{8}{3}x)-3 \end{gathered}$

Hence, the answer is:

f(x) = 4cos(8/3 x) - 3

You might be interested in

What is 23.791 rounded to the nearest tenth?

sergejj [24]

The nearest tenth would be the first decimal place, so the answer would be 23.8

6 0

3 years ago

Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at x = 30 and at y = 10,000, P is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

3 years ago

A landscaper wishes to make a rectangle flower garden that is twice as king as it is wide. Express the area of the garden as a f

Dima020 [189]

Answer:

L = 2w

A = L*W

A = 2w*w

A = 2w^2

Step-by-step explanation:

7 0

3 years ago

Sanjay picked p peaches. Zach picked 17 times as many peaches as Sanjay. Write an expression that shows how many peaches Zach pi

oksano4ka [1.4K]

Answer:

17p

Step-by-step explanation:

Since you don't know how much Sanjay picked you can only explain as a variable. So just put 17 next to p which is 17*p

5 0

3 years ago

La suma de las probabilidades de todos los posibles resultados de un experimento aleatorio debe ser igual a

Digiron [165]

Respuesta: Uno

La suma de la probabilidad de todos los resultados posibles de un experimento aleatorio debe ser igual a uno.

Porque algunos resultados más ocurren en cada sendero y la suma de todas las probabilidades es 100% o uno.

Espero haber ayudado, buena suerte! :)

3 0

3 years ago