Answer:
When radius of star increase by 6 factor then area of star will increase by a factor of 36.
Explanation:
As we know that
Area of star A given as

Where R is the radius of star.
Area of star when radius become 6 times


So

We can say that when radius of star increase by 6 factor then area of star will increase by a factor of 36.
Answer:
C The launcher will fall off the platform and land D/2 to the left of the platform because the launcher is twice the mass of the ball.
Explanation:
The figure is missing: you can find it in attachment.
We can apply the law of conservation of momentum to check that the launcher will leave the platform with a speed which is half the speed of the ball. In fact, the total initial momentum is zero:

while the total final momentum is:

where
is the mass of the launcher
is the mass of the ball
is the velocity of the launcher
is the velocity of the ball
Since the total momentum must be conserved,
, so

Therefore we find

which means that the launcher leaves the platform with a velocity which is half that of the ball, and in the opposite direction (to the left).
Since the distance covered by both the ball and the launcher only depends on their horizontal velocity, this also means that the launcher will cover half the distance covered by the ball before reaching the ground: therefore, since the ball covers a distance of D, the launcher will cover a distance of D/2.
To solve this problem we will apply the concepts related to the wavelength of its third harmonic.
It describes that the wavelength is equivalent to

Here,

The wavelength is in turn described as a function that depends on the change of the speed as a function of the frequency, that is to say

In this case the speed is equivalent to the speed of sound and the frequency was previously given, therefore


Finally the length of the pipe would be


The answer is B. It is locked up in glaciers and ice caps.
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