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2 years ago

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Mathematics

1 answer:

faltersainse [42]2 years ago

3 0

Answer:

V = 34,13*π cubic units

Step-by-step explanation: See Annex

We find the common points of the two curves, solving the system of equations:

y² = 2*x x = 2*y ⇒ y = x/2

(x/2)² = 2*x

x²/4 = 2*x

x = 2*4 x = 8 and y = 8/2 y = 4

Then point P ( 8 ; 4 )

The other point Q is Q ( 0; 0)

From these two points, we get the integration limits for dy ( 0 , 4 )are the integration limits.

Now with the help of geogebra we have: In the annex segment ABCD is dy then

V = π *∫₀⁴ (R² - r² ) *dy = π *∫₀⁴ (2*y)² - (y²/2)² dy = π * ∫₀⁴ [(4y²) - y⁴/4 ] dy

V = π * [(4/3)y³ - (1/20)y⁵] |₀⁴

V = π * [ (4/3)*4³ - 0 - 1/20)*1024 + 0 )

V = π * [256/3 - 51,20]

V = 34,13*π cubic units

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An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. The company has set

jeyben [28]

The best firm for the Appliance manufacturer for the repair work is Firm 2 .

In the question ,

it is given that ,

An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .

The acceptable range of the repair time is 50 minutes to 90 minutes.

the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .

the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .

the range is calculated using the formula

Range = Mean ± Standard Deviation

So , for firm 1 ,

the Range = 74 ± 4

= 74 $+$ 4 and 74 - 4

= 78 and 70

the range for firm 2 is

= 72 ± 5.1

= 72 $+$ 5.1 and 72 - 5.1

= 7.1 and 66.9

The second company has a lower range and it should be preferred .

Therefore , The best firm for the Appliance manufacturer for the repair work is Firm 2 .

Learn more about Standard Deviation here

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8 0

2 months ago

The area of a parallelogram is 6 ft' and the height is 3 ft. Find the length of the corresponding base.

Reil [10]

Just do 6/3 because you have the area and one length, just divide the area by the height you have.

6 0

2 years ago

Please help me by showing how to do it

Margaret [11]

20 x 10 = 200
45 - 10 = 35 - 8 = 27
8 x 8 = 64
20 - 8 = 22
22 x 45 = 990
The area of the shape is 990 square feet.

Hope I could help!

8 0

2 years ago

Read 2 more answers

Write a polynomial in factored form that has the given zeros:

wlad13 [49]

Answer:

f(x) = (x + 4)^2*(x - 5)^3

Step-by-step explanation:

For a polynomial P(x) with zeros (or roots):

x₁, x₂, ..., xₙ

And a leading coefficient (the one that multiplies the term of highest degree) A, we can write the polynomial as:

P(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)

Now, some of these roots can be repeated.

For example if x₁ = x₂

Then we say that the root x₁ has a multiplicity of two.

And we write the polynomial as:

P(x) = A*(x - x₁)^2*(x - x₃)*....*(x - xₙ)

Now, if we have a polynomial with the roots (or zeros):

Zero at -4 with a multiplicity of 2 (we have the root x = -4 two times)

Zero at 5 with a multiplicity of 3 (we have the root x = 5 3 times)

(And a leading coefficient A = 1, I assume)

This polynomial will be written as:

f(x) = (x - (-4))*(x - (-4))*(x - 5)*(x - 5)*(x - 5)

f(x) = (x + 4)*(x + 4)*(x - 5)*(x - 5)*(x - 5)

f(x) = (x + 4)^2*(x - 5)^3

The correct option is the third one:

4 0

2 years ago

Find the measures of the numbered angles in the isosceles triangle

Damm [24]

Answer:

As you noted, ∠PRS=80°. Take the triangle △TRS: we know two angles out of three, so that ∠TSR=45°. Now take the isosceles triangle △PTS: the two angles adjacent to the base PT are equal to 35°, so the third angle ∠PST=110° and then ∠PSR=65°. This is one of the two angles adjacent to the base of an isosceles trapezoid: knowing it, you can easily complete the solution.

8 0

2 years ago

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