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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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If a1=7 and an=an-1+5 than find the value of a5<br><br> ​<br> .
Katyanochek1 [597]

Answer:

a₅=27.

Step-by-step explanation:

1) according to the condition the given subsequence is arithmetic sequence. It means, the a₁=7 and d=5, then

2) a₅=a₁+4*d; => a₅=7+4*5=27.

4 0
2 years ago
The ratio of length to width (measured in inches) in a rectangle is 4∶7. find the length of the rectangle if the area is known t
Len [333]
Hey mate
here is your answer

length and width are given in the ratio are ;(4:7)
area of rectangle = (l×b)
therefore,
4x×7x=700
28x^2=700
x^2=700/28
x^2=25
x=5
length =4x=4×5=20, lenght =20 and width =7x so, 7×5=35 width.....
8 0
3 years ago
What is the length of the hypotenuse of the right triangle shown below? If necessary, round your answer to the nearest hundredth
kolezko [41]
It is ten units, as the two sides are of 6 and 8 so you must square them both, add them together (which gives you 100) and then square root that, which gives you 10

8 0
3 years ago
Read 2 more answers
Please help me answer this question.
Alex787 [66]
1. Change x = 4t into x = 3t

4t\cdot\frac{3}{4}=3t so

y=(\frac{3}{4}t)^2-1=\frac{9}{16}t^2-1

Answer A and D are wrong.

2. Change x = 4t into x = 2t

4t\cdot\frac{1}{2}=2t and

y=(\frac{1}{2}t)^2-1=\frac{t^2}{4}-1

Answer b is correct.

3.  Change x = 4t into x = 8t

4t\cdot2=8t and

y=(2t)^2-1=4t^2-1

Answer C. is correct, E. is wrong.

7 0
3 years ago
Identify Like terms : 3y2, 2/3x, -3/4y2, 5x, 12x2
wel
3y^2 and -3/4y^2 
5x and 2/3x
12x^2
4 0
3 years ago
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