Answer:
The length of the two pieces are 41 in and 24 in
Step-by-step explanation:
Let
x -----> the length of one piece
y ----> the length of the other piece
we know that
-----> equation A
-----> equation B
Solve the system of equations by substitution
Substitute equation B in equation A and solve for y

Find the value of x

therefore
The length of the two pieces are 41 in and 24 in
Answer:
D. 50
Step-by-step explanation:
Multiply the top and bottom number by 10. The bottom number comes out to be 70 and the top number comes out to be 50.
Answer:
The imaginary part is 0
Step-by-step explanation:
The number given is:

First, we can expand this power using the binomial theorem:

After that, we can apply De Moivre's theorem to expand each summand:
The final step is to find the common factor of i in the last expansion. Now:



The last part is to multiply these factors and extract the imaginary part. This computation gives:


(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)
A calculator simplifies the imaginary part Im(x⁶) to 0