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solong [7]
2 years ago
6

Region R is bounded by the curves y = 4x^2 and y = 4. A solid has base R, and cross sections perpendicular to the y-axis are sem

icircles with the diameter lying in R. The volume of this solid is
A. pi/4
B. pi/2
C. pi
D. 2pi

Mathematics
1 answer:
vlada-n [284]2 years ago
6 0

Each cross section has a diameter equal the horizontal distance between the two "halves" of the parabola. We have

y = 4x²   ⇒   x = ±√y/2

so the diameter for some given y would be √y/2 - (-√y/2) = √y.

The volume of a cross section with thickness ∆y is then

π/2 (√y/2)² ∆y = π/8 y ∆y

The total volume of the solid would then be

\displaystyle \int_0^4 \frac\pi8 y \, dy = \frac\pi8 \times \frac12 y^2 \bigg|_{y=0}^{y=4} = \boxed{\pi}

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3 years ago
I want to plant 45 sunflower plants and 81 rose plants in my garden. If I put the same number of plants in each row and each row
Minchanka [31]

Answer:

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3 0
3 years ago
Write an equation of the line that passes through point p and is perpendicular to the line with the given equation
goldenfox [79]
Do you have the specific point??

Remember, if 2 lines are perpendicular, their slopes are opposite reciprocals. So if one line has a slope of 4, the other line should have a slope of -1/4.

Hopefully your equation is in y=mx+b form. If so,

make sure you know slope (m) and the y-intercept. After this is done, plug in the points from p for y and x, and make sure to turn m into -1/m. Solve for b, and your new equation should be y=(new slope)x+(new y-intercept)
5 0
3 years ago
The sum of a number and 6 is greater than or equal to –4 =
Vinvika [58]

Answer:

x is greater than or = to 8

8 0
3 years ago
Evaluate x(y+3)/(3+y)z for x=12, y=1, and z=6.<br><br> A) 2<br><br> B) 5<br><br> C) 8<br><br> D) 6
fgiga [73]

Answer:

2

Step-by-step explanation:

We take the equation

x(y+3)/(3+y)z

and substitute the values for each individual variable in the problem. It looks like this:

12(1+3)/(3+1)6

Now we can solve the equation.

When solved, it equals 2.

5 0
3 years ago
Read 2 more answers
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