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2 years ago

Question 2 of 43

Mathematics

1 answer:

BartSMP [9]2 years ago

3 0

Answer:

Step-by-step explanation:
I just think that

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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

I NEED THIS IMMEDIATELY!!

wariber [46]

Answer:

sloths 2:6 meerkats

simplified

sloths 1:3 meerkats

1 s = 3 m

2 s = 6 m

42/3 = 14

14 s = 42 m

16 X 3 = 48

16 s = 48 m

72/3 = 24

24 s = 72 m

m = s X 3

s= m/3

4 0

3 years ago

Read 2 more answers

Show algebriacally that the sum of two consecutive numbers is always odd

egoroff_w [7]

X + (x+1) = 2x+1
Here, 2x+1 is always odd
For example the value of x is 2 then we can say that,
x=2; x+1=3; 2x+1 = 5 [odd number(5)]
= 2 + 3 = 5

Please note that the bolded words are only for your better understanding

HOPE IT HELPS!

3 0

4 years ago

Simplify. 17 _ 6 _ 10 Ÿ 2 + 12 A. 27.8 B. 59 C. 67 D. _1

Evgesh-ka [11]

17 - 6 x 10 ÷ 2 + 12 = 17 - 60 ÷ 2 + 12 = 17 - 30 + 12 = -13 + 12 = -1

7 0

3 years ago

Read 2 more answers

Ella has a points card for a movie theater.

MAXImum [283]

Answer:

175<=12.5x+40

Step-by-step explanation:

She starts with 40 points already so you add in those 40 then since she gets 12.5 points per visit that is your x, so you set that as greater than or equal to 175

7 0

3 years ago