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2 years ago

PLEASE HELP I NEED QUALITY ANSWERS AS WELL WILL MARK BRAINLIEST!!!

Mathematics

1 answer:

hammer [34]2 years ago

4 0

Answer:

True

Step-by-step explanation:

So the radius would be 5 (as you times it by 2 to get 10)

Therefore

2a=10 is the same as what the circle with diameter d=2r=10

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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.

4 0

2 years ago

48 is what percent of 120?

Nataliya [291]

Answer:

Step-by-step explanation:

57.6

8 0

1 year ago

Read 2 more answers

Consider these three squares with known area 25, 144,169

hram777 [196]

Answer:

Step-by-step explanation:

three squares with known area 25, 144,169...

1) area of the square =25

Side ×side=25

Side^2=25

Side=√25

Side =5.

Answer is 5.

2) area of the square =144

Side ×side=144

Side^2=144

Side=√144

Side =12

Answer is 12.

3)area of the square =169

Side ×side=169

Side^2=169

Side=√169

Side =13

Answer is 13.

6 0

2 years ago

Find the arc length of the partial circle.

ElenaW [278]

Answer:

38.485(correct to 5 significant figure)/ 12.25π

Step-by-step explanation:

$\pi(7 {}^{2} )( \frac{90degree}{360deree} )$

$= \pi(49)( \frac{1}{4} )$

=38.485(cor. to 5 sig.fig.)/ 12.25π

to find arc length of sector,we need to π(radius²)(sector's degree divided by 360 degree)

8 0

2 years ago

Which of these choices show a pair of equivalent expressions?

NISA [10]

Answer:

A. 6^2/7 and (√6)^7

Step-by-step explanation:

Because we can't get 6 out of root as a whole we need to use the power to show its value when we do so.

The power of (√6)^7 has is seven and degree of the root is 2 so we have to put 2/7 over 6 when we take it out of root.

6 0

2 years ago