Consider the following trigonometric function. h(x) = 3 sin (2x - pi) + 2. Graph h(x) in the interactive widget.

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

During summer, when the snow melts, the water level of the Yukon River increases. If the water level of the river increased by 7

kondaur [170]

Answer:

13 centimeters per day.

Step-by-step explanation:

We have been given that during summer, the water level of the river increased by 78 centimeters in 6 days. We are asked to find the water level increase rate in centimeters per day.

To find the water level increase rate per day, we will divide total increase by total days as:

$\text{Water level increase rate per day}=\frac{78\text{ cm}}{6\text{ days}}$

$\text{Water level increase rate per day}=\frac{13\text{ cm}}{\text{ day}}$

Therefore, the water level increase rate is 13 centimeters per day.

5 0

3 years ago

SO CONFUSED PLEASE SOMEONE EXPLAIN! DUE SOON AND NEED HELP!!!!!!!! QUESTION IN PICTURE BELOW

jeka57 [31]

Answer:

=> Apply law of cosine

$c^2=a^2+b^2-2abcos\left(C\right)$

=> input value

$z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)$

=> simplify

$z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}$

=> calulcation

$z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}$

=> apply rule: Distance must be greater than 0

which is about 14.51828

4 0

2 years ago

Plz Help! I will mark brainliest

blondinia [14]

Answer:

the answer is C

(5+3i)-(2+9i) = 3-6i

5 0

2 years ago

Read 2 more answers

which set of numbers can represent the side lengths, in centimeters, of a right triangle?a. 8,12,15b. 10,24,26c. 12,20,25d. 15,1

Mama L [17]

Answer:

B

Step-by-step explanation:

Pythagorean theorem (applicable on right triangles only) says:

$a^{2}+b^{2}=c^{2}$

Where $a$ and $b$ are the two legs of the triangle and $c$ is the length of the hypotenuse [THE LONGEST SIDE].

<u>We can square each leg on the triangle and take the sum, if that is equal to the square of the longest side, we have a right triangle. Let's check for all of these.</u>

A.

$8^{2}+12^{2}\\=64+144\\=208$