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Dimas [21]
3 years ago
9

Beth wants to plant a garden at the back of her house. She has 32m of fencing. The area that can be enclosed is modelled by the

function A(x) = -2x2 + 32x, where x is the width of the garden in metres and A(x) is the area in square metres. What is the maximum area that can be enclosed?
Please help :(
Mathematics
1 answer:
Maksim231197 [3]3 years ago
8 0

Answer:

The maximum area that can be obtained by the garden is 128 meters squared.

Step-by-step explanation:

A represents area and we want to know the maximum.

A(x)=-2x^2+32x is a parabola.  To find the maximum of a parabola, you need to find it's vertex.  The y-coordinate of the vertex will give us the maximum area.

To do this we will need to first find the x-coordinate of our vertex.

x=\frac{-b}{2a}{/tex] will give us the x-coordinate of the vertex.Compare [tex]-2x^2+32x to ax^2+bx+c then a=-2,b=32,c=0[tex].So the x-coordinate is [tex]\frac{-(32)}{2(-2)}=\frac{-32}{-4}=8.

To find the y that corresponds use the equation that relates y and x.

y=-2x^2+32x

y=-2(8)^2+32(8)

y=-2(64)+32(8)

y=-128+256

y=128

The maximum area that can be obtained by the garden is 128 meters squared.

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Hope this helps

8 0
3 years ago
a line that includes the point (3,4) has a slope of 2. what is the equation in the slope-intercept form?
Andreas93 [3]

Answer:

y=2x-2

Step-by-step explanation:

<em>the slope is y/x</em>

the slope is 2 or 2/1

<em>subtract 2 from the y value and 1 from the x value</em>

(3-1,4-2) = (2,2)

<em>keep doing this until you get a 0 in the x value</em>

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<em>1 is your x-intercept</em>

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So now you know your y-intercept and your slope so you can now write your equation.

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8 0
3 years ago
Click on the value for m that makes this inequality true
Stolb23 [73]

Answer:

To solve this inequality you need to get m by itself

3m+10<30 (First subtract 10 from each side)

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5

Hope this helps ;)

8 0
3 years ago
Read 2 more answers
CAN SOMEONE HELP ME UNDERSTAND THIS PLEASE
ICE Princess25 [194]

YEAH OFC SHAWTY!

  • so for A its -4^11 because if the powers have the same base and they are being multiplied you add the powers
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  • for D you pretend like the denominator has a power of 1 and subtract. So its -24^5-24^1 which hopefully puts it into perspective of being -24^4 becuase we subtracted the powers

I cant do 2 right now, but i will in a minute

<u>And for 3 his mistake is that they arent the same bases so he cant add the powers, he should have converted them to the same base first. </u>

7 0
3 years ago
What value of c makes the equation -3c/4=24 true ?
Sonbull [250]
Creo que C es igual a -6
4 0
3 years ago
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