The force of gravity between two objects is given by Fg = −Gm1m2/r2 , where G is the gravitational constant, m1 and m2 are the
2 answers:
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Answer:
Step-by-step explanation:
According to the given information, we have
Sample size : n= 50
Since population standard deviation is unknown, so we use t-test.
Critical value for 95 percent confidence interval :
Confidence interval :
Required 95% confidence interval :
Answer:
Option 4 is correct.
The equation is equivalent to
Step-by-step explanation:'
Given equation:
First group the terms with x and those with y;
Next, we complete the squares.
We can do this by adding a third term such that the x terms and the y terms are perfect squares.
For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.
⇒
or
Add 360 on both sides we get;
Simplify:
Therefore, the given equation is equivalent to
Two figures are similar if one is the scaled version of the other.
This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.
To be more precise, you only need two steps to prove that every two circles are similar:
- Translate one of the two circles so that they have the same center
- Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well
Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.
Recapping, we have:
- Start with circle X and radius r
- Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
- Scale the radius of circle X' until it becomes
. This new circle, say X'', is similar to X' because you only scaled it
So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.