The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased? A. 2^1/3. B. 2^1/2. C. 2^2/3. D. 2^3/2

Answers

Answer 1
Answer: The given equation for the relationship between a planet's orbital period, T and the planet's mean distance from the sun, A is T^2 = A^3. Let the orbital period of planet X be T(X) and that of planet Y = T(Y) and let the mean distance of planet X from the sun be A(X) and that of planet Y = A(Y), then A(Y) = 2A(X) [T(Y)]^2 = [A(Y)]^3 = [2A(X)]^3 But [T(X)]^2 = [A(X)]^3 Thus [T(Y)]^2 = 2^3[T(X)]^2 [T(Y)]^2 / [T(X)]^2 = 2^3 T(Y) / T(X) = 2^3/2 Therefore, the orbital period increased by a factor of 2^3/2
Answer 2
Answer:

Answer:

The orbital increased by factor 2^{(3)/(2)}.Hence, correctander is option D.

Step-by-step explanation:

Given;T^2=A^3

Distance of the planet X from the sun = d

Time-period of the planet X:

T^2=d^3..(1)

Distance of the planet Y from the sun = d'= 2d

T'^2=d'^2=(2d)^3=8d^3..(2)

On dividing (1)and (2).

(T')/(T)=(8d^3)/(d^3)=8=2√(2)=2^1* 2^{(1)/(2)}=2^{(3)/(2)}

The orbital increased by factor 2^{(3)/(2)}.Hence, correctander is option D.


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Answers

80, and to check 80*0.35=28
35% of what is 28

To do this, convert 35% to a decimal by dividing it by 100

You get 0.35

Divide28 by 0.35 and you get 80

So. 35% of 80 is 28

Hope this helped!


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Scrooge-Oh! But he was a tight-fisted hand at the grindstone! Scrooge! a
squeezing, wrenching, grasping, scraping, clutching, covetous old
sinner! Hard and sharp as flint, from which no steel had ever struck out
generous fire; secret, and self-contained, and solitary as an oyster. The
cold within him froze his old features, nipped his pointed nose, shrivelled
his cheek, stiffened his gait; made his eyes red, his thin lips blue; and
spoke out shrewdly in his grating voice. A frosty rime' was on his head,
and on his eyebrows, and his wiry chin. He carried his own low
temperature always about with him; he iced his office in the dog-days;
and didn't thaw it one degree at Christmas.
a stone for sharpening knives
2-wanting what someone else owns
3- frost
1. How is language used in this extract to describe Scrooge?
2. Write a description of an unusual character-real or
imagined

Answers

Answer:

Step-by-step explanation:

2|x+8|=20
Plz show work

Answers

Answer: x=2, or x=-18

Step-by-step explanation:

Since anything in an absolute value can be positive or negative (since in an absolute value, everything has to be positive since absolute value measures distance and distance cannot be a negative), so |x+8| can become either (x+8) or [-(x+8)].

Our first equation: (after I've removed absolute value)

2(x+8)=20

2x+16=20

2x=4

x=2

And our second equation: (after I've removed absolute value):

-2(x+8)=20

-2x-16=20

-2x=36

x=-18

A principal of $4900 is invested at 8.5% interest, compounded annually. how much will the investment be worth after 7 years? Round to the nearest dollar

Answers

The investment will be worth $8,674 after 7 years.