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2 years ago

Calculate the length of the third side of this triangle. 6 cm, 8 cm

Mathematics

1 answer:

stiv31 [10]2 years ago

7 0

<h2>By pythagoras theoram </h2>

 $c = \sqrt{a2 + b2}$ 

6²-- 8²

18--16

2 

Hence the third value 2 

Step-by-step explanation:

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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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3 years ago

Please help will give brainliest

Anarel [89]

Answer: A. 12^2

Step-by-step explanation: Follow PEMDAS

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2 years ago

Solve the equation R-3=28/R R=

geniusboy [140]

Remember that it's against our guidelines to copy content from other websites, books or any other material to which you don't own the rights to. We know you have the power to solve these problems on your own

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2 years ago

(cos6x+6cos4x+15cos2x+10)/(cos5x+5cos3x+10cosx)=?

Tasya [4]

Do you mean cos6x+6cos4x+15cos2x+10cos5x+5cos3x+10cosx ? or cos6x+6cos4x+15cos2x+10cos5x+5cos3x+10cosx ? or cos6x+6cos4x+15cos2x+10cos5x+5cos3x+10cosx ? or cos6x+6cos4x+15cos2x+10cos5x+5cos3x+10cosx ?

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3 years ago

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Lina20 [59]

Answer:

Step-by-step explanation:

Each 90° clockwise turn takes a point (x,y) and transforms it to (y,-x). For a 180° turn you would do this process twice in a row; for a 270° turn, three times in a row.

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2 years ago

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