Homework Answers

4. Which has the higher annual yield, 6% compounded quarterly or 6.25% compounded semiannually?

2. To help pay your college expenses, you borrow P7000 and agree to repay the loan at the end of 5

years at 8% interest, compounded quarterly.

(a) What is the maturity value of the loan?

(b) How much interest are you paying on the loan?

(D^3+2D^2D'-DD'^2-2D'^3)z=(y+2)e^x

Part I. Differentiation Rules on Algebraic Functions

Apply the appropriate differentiation technique/s to determine the derivative of the following algebraic functions.

1. f(x)=x^(-6)+4x^3-10
2. f(x)=5x^3-4/x^2
3. y=√(5-2x)
4. g(x)=(x^2-5x-7)(x^2-5)
5. g(x)=(3x^2-4x+1)(2x-3)
6. h(x)=(4x^3-2x+1)/(2x-3)
7. h(x)=(4x+3)/(5x^2-3x+6 )
8. y=(3x^2+2x-3)^3
9. y=(5x+3)^2 (2x-1)
10. y=(3x-2)^2/(4x+1)

Part II. Differentiation Rules on Trigonometric Functions and Higher-Order Derivatives

Apply the appropriate differentiation technique/s to determine the derivative of the following trigonometric functions.

1. y=cos〗⁡(x^2+3)
2. y=sin⁡〖(5x^2-7)〗
3. y=cot⁡(6x)
4. y=tan⁡(cos⁡x )
5. y=csc⁡(5x^3 )

Find the first derivative, second derivative, and third derivative for each of the following functions.

1. y=6x^4+3x^3-4x^2-1
2. f(x)=(2x+3)^4

The leader of the association of jeepney drivers claims that the average daily take home pay of all jeepney drivers in a particular city is php 450. A random sample of 100 jeepney drivers in the city was interviewed and the average daily take home pay of these drivers is found to be php 500. Use a 0.05 significance level to find out if the average daily take home pay of all jeepney drivers in the city is greater than php 450. Assume that the population variance is php 8644.

The diameters of washers are normally distributed with mean 50mm and variance

4mm. A washer is considered non-defective if its diameter lies between 46mm and

53mm. If one washer is randomly selected, what is the probability that:

4.2.1 its diameter less than 45mm? (6)

4.2.2 itis defective?

There is a claim that on daily average students spend 5.5 hours on social media with standard deviation of 1.25 .A resercher wants to test the claim at 5% level significance.

1.formulate the null and alternatuve hyphothesis

2.Determine the test statistic to be used

3.Find the corresponding z value

4. Identify the rejection region