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7nadin3 [17]
3 years ago
8

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = 4x and y = x2/4 . Find V by slicin

g.
Mathematics
1 answer:
aliya0001 [1]3 years ago
6 0

Answer:

Step-by-step explanation:

Consider the graphs of the y = 4x  and  y = \frac{x^{2} }{4}.

By equating the expressions, the intersection points of the graphs can be found and in this way delimit the area that will rotate around the Y axis.

4x = \frac{x^{2} }{4} \\   x^{2}  = 16x \\ x^{2}  - 16x = 0 \\   x(x-16) = 0 then x=0  o  x=16. Therefore the integration limits are:

y = 4(0) = 0  and  y = 4(16) = 64

The inverse functions are given by:

x = 2 \sqrt{y}  and  x = \frac{y}{4}. Then

The volume of the solid of revolution is given by:

\int\limits^{64}_ {0} \, [2\sqrt{y} - \frac{y}{4}]^{2}  dy = \int\limits^{64}_ {0} \, [4y - y^{3/2} + \frac{y^{2}}{16} ]\  dy = [2y^{2} - \frac{2}{5}y^{5/2} + \frac{y^{3}}{48} ]\limits^{64}_ {0} = 546.133 u^{2}

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answer is 142

Step-by-step explanation:

3 0
3 years ago
Sharon's house, the library, and Lisa's house are all on the same straight road. Sharon has to ride her bike 1 3/5 miles to get
Zigmanuir [339]

Answer:

1.15 miles closer

Step-by-step explanation:

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1 3/5 = 1 12/20

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5 0
3 years ago
The diagram below shows the dimensions of a triangular park built in a new housing development. Two side lengths and one angle m
evablogger [386]
ANSWER

x = 50.5 \degree

EXPLANATION

We use the sine rule for solving triangles.

This is given by the formula,


\frac{ \sin(A) }{a}  =  \frac{ \sin(B) }{b}  = \frac{ \sin(C) }{c}


From the triangle,

\frac{ \sin(x) }{60}  =  \frac{ \sin(40) }{50}

We multiply both sides of the equation by 60 to get,

sin(x)  =  \frac{ 60\sin(40 \degree) }{50}


sin(x)  = 0.7713



We solve for x to obtain,

x = arcsin(0.7713)


x = 50.475

To the nearest tenth, we round to one decimal place to get,

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7 0
3 years ago
Plz don't answer unless you will do all ty
liberstina [14]
The answer would be D
7 0
3 years ago
Never mind i found the answer
stiks02 [169]

Answer:

okieeeeeee also thanks for the points

Step-by-step explanation:

:)))

8 0
2 years ago
Read 2 more answers
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