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Travka [436]
3 years ago
6

Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 a

nd x = -1 about the x-axis.
Mathematics
1 answer:
Marysya12 [62]3 years ago
8 0

Answer:

Let's define A as the area given by the integral:

\int\limits^1_{-1} {3x^4} \, dx

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536

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Please help with 11c!?
Contact [7]

Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

11c)

This is compound growth problem. It goes by the formula:

F=P(1+r)^t

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t

To solve exponentials, we can take Natural Log (Ln) of both sides:

2=(1.08)^t\\Ln(2)=Ln((1.08)^t)

Using the rule shown below we can simplify and solve:

Ln(a^b)=bLn(a)

We can write:

Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064

To the nearest year, that would be about 9 years

5 0
3 years ago
Mr. Douglas drove 2,482 miles. He spent 42.5 hours in the car driving. What was his average speed for the trip?
riadik2000 [5.3K]

I think you just divide the number of miles by the number of hours he spent driving.

2,482/42.5= 58.4

58mph

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Jesse earns $12.62 an hour, plus she earns overtime for hours exceeding 40 hours per week. What is her gross weekly pay for work
san4es73 [151]
40(12.62) + 7(12.62(1.5)) = 504.80 + 7(18.93) = 504.80 + 132.51 =
637.31 <===
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