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2 years ago

What is the vertex of f(x)=x^2+12x=31

Mathematics

1 answer:

Ket [755]2 years ago

3 0

Answer:

√

−

Decimal Form:

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3.76393202

…

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8.23606797

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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.

4 0

2 years ago

Please help these are not easy for me

Pavel [41]

Answer:

12a^2 - 9a + 5

Step-by-step explanation:

(5a^2 - 6a - 4) - (-7a^2 + 3a - 9)

5a^2 + 7a^2 = 12a^2

-6a - 3a = -9a

-4 + 9 = 5

12a^2 - 9a + 5

7 0

2 years ago

Write a verbal expression for 3n-8

lisabon 2012 [21]

Answer: Pick anyone that suits you

8 is subtracted from 3 times a number
Thrice a number minus 8

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogra

marissa [1.9K]

Answer: 12.32 for 5 day week or 8.8 for a seven day week

Step-by-step explanation:

2.2 x 28 = 61.6

61.6 divided by 5 is 12.32

divide by seven if its a full week and the answer is 8.8

7 0

3 years ago

will give brainliest The polygons are similar, but not necessarily drawn to scale. Find the value of x.

Serggg [28]

Answer:

I'm in eight grade so don't assume i'm right. But from looking at this. It looks like x-1=8 and y+1= 28. I'm only doing High School Math 1 in eight grade tho. So if i'm wrong i'm sorry

Step-by-step explanation:

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2 years ago