Answer:
8
Step-by-step explanation:
sin theta = opposite side/ hypotenuse
sin 30 = 4/x
Multiply each side by x
x sin 30 = 4
Divide each side by sin 30
x sin 30 /sin 30 = 4 sin 30
x = 4 /sin 30
We know that sin 30 = 1/2
x = 4 / 1/2
x = 8
Rather than carrying out IBP several times, let's establish a more general result. Let

One round of IBP, setting


gives


This is called a power-reduction formula. We could try solving for
explicitly, but no need.
is small enough to just expand
as much as we need to.





Finally,

so we end up with


and the antiderivative is

Answer:
The correct options are (1), (3) and (5).
Step-by-step explanation:
The two triangles are shown below.
The measure of ∠F corresponds to ∠F'.
The distance between the points D and origin is of 9 units.
And the distance between the points D' and origin is 3 units.
Thus, the distance from point D' to the origin is One-third the distance of point D to the origin.
Check for similarity:

Thus, the △DEF is similar to △D'E'F'.
Thus, the correct options are (1), (3) and (5).
Answer:
< - 5, 3.5 >
Step-by-step explanation:
A single translation is required to map A onto B
Consider the point (5, 3 ) on A and the corresponding point (0, 6.5) on B
the translation is < 0 - 5, 6.5 - 3 > = < - 5, 3.5 >