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3 years ago

Question is attached will give brainliest ty !!

Mathematics

1 answer:

creativ13 [48]3 years ago

6 0

Answer:

A. (2x, 2y)

Step-by-step explanation:

<u>Original figure:</u> PQRTS

<u>Dilated figure:</u> P'Q'R'S'T'

<u>Take one of the corresponding sides of the figure and find the scale factor:</u>

SR = 2, S'R' = 4
Scale factor is 4/2 = 2

<u>The dilation rule as per above is:</u>

(x, y) → (2x, 2y)

Correct option is A

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3 years ago

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3 years ago

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3 years ago

Find the moment of inertia about the y-axis of the thin semicirular region of constant density

arlik [135]

The moment of inertia about the y-axis of the thin semicircular region of constant density is given below.

$\rm I_y = \dfrac{1}{8} \times \pi r^4$

<h3>What is rotational inertia?</h3>

Any item that can be turned has rotational inertia as a quality. It's a scalar value that indicates how complex it is to adjust an object's rotational velocity around a certain axis.

Then the moment of inertia about the y-axis of the thin semicircular region of constant density will be

$\rm I_x = \int y^2 dA\\\\I_y = \int x^2 dA$

x = r cos θ

y = r sin θ

dA = r dr dθ

Then the moment of inertia about the x-axis will be

$\rm I_x = \int _0^r \int _0^{\pi} (r\sin \theta )^2 \ r \ dr \ d\theta\\\\\rm I_x = \int _0^r \int _0^{\pi} r^3 \sin ^2\theta \ dr \ d\theta$

On integration, we have

$\rm I_x = \dfrac{1}{8} \times \pi r^4$

Then the moment of inertia about the y-axis will be

$\rm I_y = \int _0^r \int _0^{\pi} (r\cos\theta )^2 \ r \ dr \ d\theta\\\\\rm I_y = \int _0^r \int _0^{\pi} r^3 \cos ^2\theta \ dr \ d\theta$

On integration, we have

$\rm I_y = \dfrac{1}{8} \times \pi r^4$

Then the moment of inertia about O will be

$\rm I_o = I_x + I_y\\\\I_o = \dfrac{1}{8} \times \pi r^4 + \dfrac{1}{8} \times \pi r^4\\\\I_o = \dfrac{1}{4} \times \pi r^4$

More about the rotational inertia link is given below.

brainly.com/question/22513079

#SPJ4

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2 years ago

Ab+bc=<br> this is adding of like terms

stellarik [79]

Answer:

(a+c)b OR it's already on simplified form

Step-by-step explanation:

depending upon what your instructor wants, they may want you to say it's already simplified (which happens sometimes).

HOWEVER, if you know how to factorize (which is essentially un-distributing), you could factor out the b which is common in both.

$ab + bc \\ = b( \frac{ab}{b} + \frac{bc}{b} ) \\ = b(a + c)$

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3 years ago