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4 years ago

How to make a word problem with percentage

1 answer:

3 0

Take the numbers out of the problem and then solve and put the decimal place two spaces behind the original place and it is now a percent

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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

What is 3/2 x + 30 degrees

jekas [21]

Sum of internal angles of any triangle = 180∘

∴x + 2x + 3x = 180∘
∴6x = 180∘
∴ x = 30∘

So the angles are: 30∘, 60∘ and 90∘

3 0

3 years ago

1000000 x 0.3=? ready

svlad2 [7]

Answer:

300000

Step-by-step explanation:

Three hundred thousand

3 0

3 years ago

The first term in the expansion of the binomial (3x + y)4

Lelechka [254]

I don't know if i'm right or what because I haven't learned binomial in like almost 4 years. (3x+y)?

5 0

3 years ago

Read 2 more answers

Please help. Is algebra. PLEASE HELP NO LINKS OR FILES. I don't want links.

elena55 [62]

Answer:

question 12 is answer B

question 13 is -8x^3

Step-by-step explanation:

exponent rule $\frac{a^m}{a^n} = a^(^m^-^n^)$

4 0

3 years ago