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postnew [5]
3 years ago
5

Find the area lying above the x-axis and below the parabolic curve y = 4x -x2 A. 8 B. 16 C. 10 2/3 D. 8 1/3

Mathematics
1 answer:
dimaraw [331]3 years ago
7 0
To find the area between the x-axis and the parabolic curve, take the integral of the area in which the curve is above the x-axis.
function of the graph is
y = 4x - x²
We can tell by the function (specifically -x²) that the parabola will point downward.
To find the domain in which y>0, let's find the roots (0's) of the function:
0 = 4x - x²
0 = x (4 - x) 
x = 0 or x = 4
Between x=0 and x=4, the curve is above the x-axis. To find the area of the graph, let's take the integral on this range:

First, take the antiderivative of 4x - x²:
2x² - (1/3) x³
Then, plug x=4 into the anti-derivative, and subtract the anti-derivative at x=0:
2(4)² - (1/3)(4³) - (0 - 0)
32 - 64/3
96/3 - 64/3 = 32/3 

Closest Answer is C) 10
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A certain CD-ROM disk can store approximately 6.0 × 102 megabytes of information, where 106 bytes = 1 megabyte. If an average wo
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4 0
3 years ago
Can someone pls help need it ASAP and can you pls explain in full detail how to do it
GenaCL600 [577]

Answer:

x= 1 , y=4

Step-by-step explanation:

x-y= -3 => Equation 1

x+5y= 21 => Equation 2

<u>Substitut</u><u>ion</u><u> </u><u>Method</u><u>:</u>

<u>Substitu</u><u>te</u><u> </u><u>Equation</u><u> </u><u>1</u>=>

x=y-3 <= Equation 3

Put x=y-3 in Equation 2:

x+5y=21

( y-3)+5y=21

y-3+5y=21

6y-3=21

6y=21+3

6y=24

y=24÷6

y=4

Put y=4 in Equation 1:

x-y= -3

x-4=-3

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