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3 years ago

Which function, g or h, is the inverse function for function f?

Mathematics

1 answer:

olga2289 [7]3 years ago

8 0

Answer:

Step-by-step explanation:

the last one

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Write each expression as an algebraic (nontrigonometric) expression in u, u > 0.

max2010maxim [7]

Answer:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

Step-by-step explanation:

We want to write the trignometric expression:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0$

As an algebraic equation.

First, we can focus on the inner expression. Let θ equal the expression:

$\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)$

Take the secant of both sides:

$\displaystyle \sec(\theta)=\frac{u}{10}$

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

$\displaystyle o=\sqrt{u^2-10^2}=\sqrt{u^2-100}$

By substitutition:

$\displaystyle= \sin(2\theta)$

Using an double-angle identity:

$=2\sin(\theta)\cos(\theta)$

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

$\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)$

Simplify. Therefore:

$\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0$

4 0

3 years ago

Rewrite the equation in slope-intercept form. x=4y+2

Dafna1 [17]

Answer:

y = x/4 - 1/2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write equation

x = 4y + 2

Step 2: Subtract 2 on both sides

x - 2 = 4y

Step 3: Divide both sides by 4

x/4 - 1/2 = y

7 0

3 years ago

Read 2 more answers

Help please!!

Reil [10]

I hope this helps you

4r=p-3t

r=p-3t/4

3 0

3 years ago

R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} Select all numbers that are in the domain. -3 -2 -1 0 1 2

Andrei [34K]

Answer:

-3, -1, 1

Step-by-step explanation:

the x-coordinates are the domain

8 0

3 years ago

The perimeter of one face of a cube is 16cm. Calculate the volume of the cube.

erastova [34]

Answer:

Step-by-step explanation:

Perimeter equation: Length + Width * 2

so divide 2 by 16

which gives you 8 and minus that by its half so you get 4

4 0

2 years ago