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Vaselesa [24]
3 years ago
5

Please find the answer !

Mathematics
1 answer:
algol133 years ago
4 0

Answer:

ring volume is 12cm3

Step-by-step explanation:

Lr ccm=volume of water and ring - Volume of water

ring cubic centimeters =x

x=9.2cm*4.5cm*7cm - 8.8cm*4.5cm*7cm

x=289.2cm3 - 277.2cm3

x=12cm3

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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 <em>f</em> :

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 <em>g</em> :

\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 <em>n</em> 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 <em>f</em> has a minimum of -7 and a maximum of 299.

4 0
3 years ago
What are these answers?
murzikaleks [220]
The first one is 25/9
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\text{Used de.finition of the logarithm:}\ \ \ \log_ab=c\iff a^c=b



8 0
3 years ago
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Express 8 sin^2x - 10sinxcosx in the form a+b sin(2x+c).
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Compare. Write <br> 1/8 6/10
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The  difference between 1/8 and 6/10 = 0.475 , does this help? 
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