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2 years ago

Verify the identity and explain how cot(x- pi/2)= -tan x

Mathematics

1 answer:

pav-90 [236]2 years ago

8 0

Answer:

First, let's recall some usefull information:

- cot(x) = 1/tg(x) = cos(x)/sin(x)

- tan(x) = sin(x)/cos(x)

We also know that:

- cos(x - pi/2) = sin(x)

- sin(x - pi/2) = -cos(x)

Now we can use those relationships and get:

cot(x - pi/2) = cos(x - pi/2)/sin(x -pi/2) = sin(x)/-cos(x) = -tan(x)

So we have verified the identity, and explained step by step why the identity is true.

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WHY IS EDGENUITY SO HARD?!?!??!?!

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because you have to work, and i'm doing edinuity

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3 years ago

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What is the value of x when h(x)=-3? -7

Pachacha [2.7K]

Answer:

○ -1

Step-by-step explanation:

Looking closely at this piecewise function, when the line on the left-hand side intersects at -3 = y, x is -1.

I hope this helps, and as always, I am joyous to assist anyone at any time.

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2 years ago

Mary can read 22 pages in 30 minutes how long would it take her to read a 100 page book? Right your answer in hours and minutes

mario62 [17]

30 divided by 22= 1.36
1.36 minutes for each page, to check 1.36x22= 29.92
1.36x100= 136 minutes.
Mary would need about 2 hours and 16 minutes to read a 100 page book.

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2 years ago

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

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2 years ago

6 times the sum of 12 and 8

White raven [17]

12 * 8 = 96 * 6 = 576

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3 years ago

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