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3 years ago

Set a = 3 and k = 1. Use the slider to manipulate M. What happens to the graph when M is negative?

Mathematics

1 answer:

ANEK [815]3 years ago

5 0

Answer:

C (reflection across the x access)

Step-by-step explanation:

I got it right on edge

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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

3 years ago

Solve the following inequality algebraically: look at the picture

seraphim [82]

The answer is b -9 < x < 12

8 0

2 years ago

Answers for all questions

abruzzese [7]

Answer:

3 and dived 30 multy is 182 is your answer

Step-by-step explanation:

1+1=2

8 0

3 years ago

A candy company has orders for chocolate bars feom 5 different stores. Each order dontains 45 chocolate bars. Use he distrubutiv

LenKa [72]

Answer:

CANDY diabeatise sgdigduejsdid

5 0

3 years ago

Read 2 more answers

What is the value of t?

inna [77]

Answer:

4.56

Step-by-step explanation:

After this equation is simplified, it is solved the way any 1-step linear equation is solved.

1.4t -0.4(t -3.1) = 5.8 . . . . . . given

1.4t -0.4t +1.24 = 5.8 . . . . . eliminate parentheses

t +1.24 = 5.8 . . . . . . . . . collect terms (now you have a 1-step equation)

t = 4.56 . . . . . . . . . .subtract 1.24

4 0

2 years ago