Find the total area of the composite figure below. SHOW ALL WORK.

Mathematics

1 answer:

Leviafan [203]2 years ago

5 0

Answer:

358.5 sq-in

Step-by-step explanation:

This is the answer.

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Question 8 Find the unit vector in the direction of (2,-3). Write your answer in component form. Do not approximate any numbers

slamgirl [31]

Answer:

The unit vector in component form is $\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$ or $\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j$ .

Step-by-step explanation:

Let be $\vec u = (2,-3)$ , its unit vector is determined by following expression:

$\hat {u} = \frac{\vec u}{\|\vec u \|}$

Where $\|\vec u \|$ is the norm of $\vec u$ , which is found by Pythagorean Theorem:

$\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}$

$\|\vec u\| = \sqrt{13}$

Then, the unit vector is:

$\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)$

$\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$

The unit vector in component form is $\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)$ or $\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j$ .

6 0

3 years ago

The height, h, in feet of a piece of cloth tied to a waterwheel in relation to sea level as a function of time, t, in seconds ca

BartSMP [9]

Answer:

20 seconds

Step-by-step explanation:

I assume you mean $h(t)=8\cos(\frac{\pi}{10}t)$ for your function.

As the given function is in the form of $f(t)=a\cos(bt+c)+d$ (some textbooks may write this formula differently), the period is equal to $\frac{2\pi}{|b|}$ . Hence, the period of the given function is $\frac{2\pi}{|\frac{\pi}{10}|}=\frac{2\pi}{1}*\frac{10}{\pi}=\frac{20\pi}{\pi}=20$ , or 20 seconds.