Answer:
The variable manipulated or controlled by the experimenter is called the independent variable.
Example:
If the flow velocity at the bottom of a tank is measured by varying the height of water in the tank, we are measuring velocity as a function of water height.
Therefore,
water height = independent variable (controlled)
velocity = dependent variable (measured in response to water height).
Mathematically,
v = f(h)
where v = response variable (dependent)
h = controlled variable (independent).
Answer:
b) Betelgeuse would be
times brighter than Sirius
c) Since Betelgeuse brightness from Earth compared to the Sun is
the statement saying that it would be like a second Sun is incorrect
Explanation:
The start brightness is related to it luminosity thought the following equation:
(1)
where
is the brightness,
is the star luminosity and
, the distance from the star to the point where the brightness is calculated (measured). Thus:
b)
and
where
is the Sun luminosity (
) but we don't need to know this value for solving the problem.
is light years.
Finding the ratio between the two brightness we get:

c) we can do the same as in b) but we need to know the distance from the Sun to the Earth, which is
. Then

Notice that since the star luminosities are given with respect to the Sun luminosity we don't need to use any value a simple states the Sun luminosity as the unit, i.e 1. From this result, it is clear that when Betelgeuse explodes it won't be like having a second Sun, it brightness will be 5 orders of magnitude smaller that our Sun brightness.
The answer is D. Sound insulators prevent sound from being transmitted better than elastic solids because sound insulators basically muffle and block the sound waves.
F=9/5C+32 is the formula for Celsius to Fahrenheit.
Answer:
V_{a} - V_{b} = 89.3
Explanation:
The electric potential is defined by
= - ∫ E .ds
In this case the electric field is in the direction and the points (ds) are also in the direction and therefore the angle is zero and the scalar product is reduced to the algebraic product.
V_{b} - V_{a} = - ∫ E ds
We substitute
V_{b} - V_{a} = - ∫ (α + β/ y²) dy
We integrate
V_{b} - V_{a} = - α y + β / y
We evaluate between the lower limit A 2 cm = 0.02 m and the upper limit B 3 cm = 0.03 m
V_{b} - V_{a} = - α (0.03 - 0.02) + β (1 / 0.03 - 1 / 0.02)
V_{b} - V_{a} = - 600 0.01 + 5 (-16.67) = -6 - 83.33
V_{b} - V_{a} = - 89.3 V
As they ask us the reverse case
V_{b} - V_{a} = - V_{b} - V_{a}
V_{a} - V_{b} = 89.3