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2 years ago

Help pls ! find the angle measure given extended triangles

Mathematics

1 answer:

Serhud [2]2 years ago

8 0

First, determine which inverse trigonometric function to use based on which two side lengths are provided. Then, create an equation that uses the value of the inverse trigonometric function of the ratio of the given sides, set it equal to the unknown angle, and simplify.

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Its a math problem Please help me !!! For the data sets below, which of the following statements is FALSE?

Evgesh-ka [11]

Answer:

fist bubble i am pretty sure

Step-by-step explanation:

7 0

2 years ago

Combine the like terms.<br> 7W-W+3

Bess [88]

The like terms are 7w and -w, so we can collect them to get:

6w+3

Hope this helps!! :)

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3 years ago

What is the median of 7, 12, 13, 40, 88, 95, 95 HURRY!!

bija089 [108]

To find the median you have to put all the numbers in order from smallest to largest and find the one that's in the middle.
All of the numbers listed are already in order, and the one that lies in the middle is 40. So the answer is 40.

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2 years ago

Please Help me with this question

Olegator [25]

Answer:

look up mixed numbers calculator by calculator soup, and then you can find all of your answers! Its an amazing website! good luck (:

Step-by-step explanation:

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2 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago