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3 years ago

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Find the range of f(x)=-3x+1 if the domain is (x=-2,7(

1 answer:

tigry1 [53]3 years ago

8 0

<span>To find the range of this function, simply plug each of the end values into the original equation. In this case, with x of -2, the function becomes f(x) = 6+1 or 7, and with x of 7, the function becomes f(x) = -21+1 or -20. As such, the range of the function is -21 <= f(x) <= 7.</span>

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A basketball player made 77 out of 100 attempted free throws. What percentage of free throws was made?

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Answer:

77%

Step-by-step explanation:

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2 years ago

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Pls help for Algebra 11b = 143

ziro4ka [17]

Answer:

b = 13

Step-by-step explanation:

Divide 143 by 11

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3 years ago

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The equation 3x + 2 = 29 is modeled below.

DanielleElmas [232]

Answer:

Subtract 2 from both sides.

Step-by-step explanation:

Remember to do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:

Parenthesis

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Division

Addition

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> Also, note the equal sign, what you do to one side, you do to the other side of the equation.

First step is to subtract 2 from both sides of the equation:

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The second step is to divide 3 from both sides of the equation:

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7 0

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.

4 0

2 years ago

−6 + 2n = 3n − ( 6 + 5 )<br> Please provide the answer along with how you got the answer!

pickupchik [31]

Answer:

5

Step-by-step explanation:

-6+2n=3n-(6+5)

-6+2n=3n-11

-6+2n-3n=-11

-6-n=-11

n=-6-(-11)

n=-6+11

n=5

5 0

2 years ago