All categories

3 years ago

Find the volume of the solid by rotating the region bounded by y=x^3, y=8, and x=0 about the y axis.

Mathematics

1 answer:

dimulka [17.4K]3 years ago

7 0

Answer:

Solution : Volume = 96/5π

Step-by-step explanation:

If we slice at an arbitrary height y, we get a circular disk with radius x, where x = y^(1/3). So the area of a cross section through y should be:

A(y) = πx^2 = π(y^(1/3))^2 = πy^(2/3)

And now since the solid lies between y = 0, and y = 8, it's volume should be:

V = ∫⁸₀ A(y)dy (in other words ∫ A(y)dy on the interval [0 to 8])

=> π ∫⁸₀ y^(2/3)dy

=> π[3/5 * y^(5/3)]⁸₀

=> 3/5π(³√8)⁵

=> 3/5π2^5

=> 96/5π ✓

You might be interested in

Find the domain of

ch4aika [34]

Answer:

C (x ≥ -6)

Step-by-step explanation:

Algebraic:

The domain of $\sqrt{x}$ is $x\geq 0$ . When transformed 6 units to the left, it becomes $x\geq -6$

Graphically:

As shown in the attached graph, $x\geq -6$ .

6 0

3 years ago

In a bolt factory, machines 1,2, and 3 respectively produce 20%, 30% and 50% of the total output. of their respective outputs 5%

lorasvet [3.4K]

Answer:

a. 1/10 or 10%

b. 1/2 or 50%

Step-by-step explanation:

Since the combination of machines 1, 2 and 3 produce 100% of the total output when added together, then the probability of choosing a bolt at random that is defective is: 5 + 2 + 3 = 10% out of 100% or 10/100, which is 1/10 or 10%.

If the bolt that is choosen at random is defective, than the probability that it came from machine 1 is 5/10 or 1/2 which is also 50%.

3 0

3 years ago

Put these numbers in order from greatest to least. 1 6/8,-10/25,-18/25,1

goldenfox [79]

$\textsf{Hey there!}$

$\textsf{Put these numbers in order from GREATEST to LEAST}$

$\bullet{\mathsf{ \ 1\dfrac{6}{8}}}$

$\bullet\mathsf{\ -\dfrac{10}{25}}$

$\bullet{\mathsf{\ -\dfrac{18}{25}}}$

$\bullet{\textsf{ 1}}$

$\star\textsf{ We know that fractions, decimals, negatives are BELOW 0 (on the left}$ $\textsf{of 0)}$

$\star\textsf{ \& we also know that positives and real numbers is/are ABOVE 0 (to the right}$ $\textsf{of 0)}$

$\textsf{Now we can answer your question}$

$\blacksquare \ \mathsf{1\dfrac{6}{8} = \dfrac{14}{8} = 1.75}$

$\blacksquare\ \mathsf{-\dfrac{10}{25} = -0.40}$

$\blacksquare\ \mathsf{- \dfrac{18}{25} = -0.72}$

$\blacksquare \ \mathsf{1 = 1}$

$\textsf{Look carefully at the stuff converted to the decimal or regular number \& }$ $\textsf{you will have your answer from \underline{greatest} to \underline{least}}$