Answer:
y=cotx
Step-by-step explanation:
Use the binomial theorem:

The <em>x</em> ³ terms occurs for 5 - <em>k</em> = 3, or <em>k</em> = 2, and its coefficient would be

Answer:
The volume of the ball with the drilled hole is:

Step-by-step explanation:
See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

Then we set the integral for the volume by using shell method:

That can be solved by substitution:

The limits of integration also change:
For x=5: 
For x=15: 
So the integral becomes:

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

Then applying the basic rule we get:

Since that is just half of the solid, we multiply by 2 to get the complete volume:


7. Loan amount = $12000
Monthly payment = $380
Duration of the repayment = 3 years = 3(12) = 36 months.
Total amount Jason repaid = 36 × 380 = 13680
Interest on loan amount = amount repaid - loan amount
= 13680 - 12000
= 1680
Hence, total amount Jason paid in interest on loan = $1680 and the correct option is (D).
8. Loan amount = $35000
Monthly payment = $315
Duration of the repayment = 10 years = 10(12) = 120 months.
Total amount Gerald repaid = 120 × 315 = 37800
Interest on loan amount = amount repaid - loan amount
= 37800 - 35000
= 2800
Hence, total amount Gerald paid in interest on loan = $2800 and the correct option is (B).
a[n] = 7n - 16
The fifth term is a[5]
a[5] = 7(5) - 16 = 35 - 16 = 19
Answer: C. 19