Math Answers

Using the Chain Rule, find the 𝑑𝑦/𝑑𝑥 and express the final answer in term of x.

𝑦 = 2𝑢/𝑢²−1 , u=x²

The volume, V cm3, of a metallic cube of side length x cm, is increasing at the constant rate of 0.216 cm3 s– 1 .

(a) Determine the rate at which the side of the cube is increasing when the side length reaches 6 cm.

(b) Find the rate at which the surface area of the cube, A cm2, is increasing when the side length reaches 6 cm.

Consider the function, f x( ) = 2x3 −24x2 −7. Find the intervals of x where f(x) is increasing or decreasing.

Find the coordinates of the points on the curve 𝑦 = 3𝑥3 − 2𝑥2 − 12𝑥 + 2 where the normal is parallel to the line 𝑦 = −𝑥 + 1.

The tangent to the curve 𝑦 = 2𝑥2 − 5𝑥 + 6 at the point (2,1) intersects the normal to the same curve at the point (1,4) at point 𝑄. Find the coordinates of 𝑄

5. What is the negation of each of these propositions? a) Mei has an MP3 player. b) There is no pollution in New Jersey. c) 2 + 1 = 3. d) The summer in Maine is hot and sunny.

find the mean of the probability distribution of the random variable x, which can take only the values if P(x)= 1/10 , for x= 1,2,3...., 10

Two balls are drawn in succession without replacement from an urn containing 4 red balls and 5 blue balls. Let R be the random variable representing the number of red balls. Find the values of the random variable R

 Find the mean of the following probability of a random variable X. P(1) = 1/8 , P(2) = 3/8, P(4) = 3/8, P(4) = 1/8

Find the first and second derivative of the following:

1. y=cos x²

2.y=sinx cos x²

3.y=xsin x²

4.y=x cos x²