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gayaneshka [121]
3 years ago
11

17) 16-81 +10 > 22 -6-4-2 0 2 4 6 8 10 12 14 16 18 20 22 24

Mathematics
1 answer:
dlinn [17]3 years ago
6 0

Answer: I'm not totally sure what the question is because of the lack of detail but i believe the answer is  g(x - 8) + 4

Step-by-step explanation:

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The first and last terms of a 10-term arithmetic series are listed in the table. What is the sum of the series?
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The arithmetic sequence general formula is an = a1 + d *(n-1) where d is the arithmetic difference and n is an integer. In this case, upon derivation, the formula that represents the sum of the series is S = (a1  + an)*(n/2). Substituting, S = (3+75)*(10/2) equal to 390
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Mitchell walked 5/12 of a mile in 1/2 of an hour. At this rate, how far could Mitchell walk in 1 hour?
vovangra [49]

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2 \times  \frac{1}{2} hour = 1hour \\

Thus ;

2 \times  \frac{5}{12}  \:  \: miles =  \frac{10}{12}  \:  \: miles = \frac{5}{6}  \:  \: miles  \\

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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 <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.

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3 years ago
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Vikki [24]
I believe the answer would be C

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