HELP ME PLEASE!!!

A lamina with constant density rho(x, y) = rho occupies the given region. Find the moments of inertia Ix and Iy and the radii of

jenyasd209 [6]

Answer:

Ix = Iy = $\frac{ρπR^{4} }{16}$

Radius of gyration x = y = $\frac{R}{4}$

Step-by-step explanation:

Given: A lamina with constant density ρ(x, y) = ρ occupies the given region x2 + y2 ≤ a2 in the first quadrant.

Mass of disk = ρπR2

Moment of inertia about its perpendicular axis is $\frac{MR^{2} }{2}$ . Moment of inertia of quarter disk about its perpendicular is $\frac{MR^{2} }{8}$ .

Now using perpendicular axis theorem, Ix = Iy = $\frac{MR^{2} }{16}$ = $\frac{ρπR^{4} }{16}$ .

For Radius of gyration K, equate MK2 = MR2/16, K= R/4.

3 0

3 years ago

Emilio owns a bakery. The number of boxes of cookies he has left on a Monday is represented by the function x + y = 42, where y

Katarina [22]

Answer:

y=42-x

x=42-y

Step-by-step explanation:

x=42-y

Subtract y from both sides of the equation

y=42-x

Subtract x from both sides of the equation

3 0

2 years ago

Q # 20 please help to solve

spin [16.1K]

If submarine is at the surface (the initial position) and then dives 375 ft, the coordinate of submarine becomes -375 ft <span>relatively to the initial position. When the submarine dives another 175 ft down, the coordinate of submarine becomes -375-175=-550 ft relatively to the initial position.
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Answer: Correct choice is A.
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8 0

3 years ago

The product of x and the sum of 6 and 8 times the square of x

Vaselesa [24]

Answer:

x(6 + 8x²) or 6x + 8x³.

Step-by-step explanation:

"The square of x" can be represented by x² and 8 times that would be 8 * x² or 8x². The sum of 6 and 8x² can be represented by 6 + x² and the product of x and 6 + x² can be represented by x * (6 + 8x²) or x(6 + 8x²) which simplifies to 6x + 8x³.

7 0

2 years ago

Read 2 more answers

From data gathered in the period 2008−2012, the yearly value of U.S. exports can be modeled by the function E(x) = −228x3 + 2,25

vredina [299]

Answer:

The total value the U.S. imported and exported is 19364 billion dollars

Step-by-step explanation:

* Lets explain how to solve the problem

- The yearly value of U.S. exports can be modeled by the function

E(x) = −228 x³ + 2,252.8 x² − 6,098.5 x + 11,425.8

# x is the number of years after 2008

# E(x) is the value of exports in billions of dollars

- The yearly value of U.S. imports can be modeled by the function

I(x) = −400.4 x³ + 3,954.4 x² − 11,128.8 x + 17,749.6

# x is the number of years after 2008

# I(x) is the value of imports in billions of dollars

* We need to calculate the total value the U.S. imported and

exported in 2012

∵ x is the number of years after 2008

∴ At 2012 x = 4 years

- Lets calculate the value of the exports in 2012

∴ E(x) = -228(4)³ + 2,252.8(4)² - 6,098.5(4) + 11,425.8

∴ E(x) = 8484.6 billion dollars

- Lets calculate the value of the imports in 2012

∴ I(x) = -400.4(4)³ + 3,954.4(4)² - 11,128.8(4) + 17,749.6

∴ I(x) = 10879.2 billion dollar

∵ The total value the U.S. imported and exported = E(x) + (I(x)

∴ The total value = 8484.6 + 10879.2 = 19363.8

∴ The total value = 19364 billion dollars

* The total value the U.S. imported and exported is 19364 billion dollars

7 0

3 years ago