Calculus Answers

(Section 13.3 and Chapter 14) Let D be the region in R 3 p that lies inside the cone z = x 2 + y 2 above the plane z = 1 and below the hemisphere z = p 4 − x 2 − y 2 . (a) Sketch the region D in R 3 .(b) Express the volume of D as a sum of triple integrals, using cylindrical coordinates.

Determine the slope-intercept form of a linear equation, given the listed attributes: a) Slope = -2 and y-intercept = (0,10) b) Slope = -3 and (4, -2) lies on line c) Slope = 0 and (2,4) lies on line d) (3, -2) and (-12,1) lies on line e) (20, 240) and (15,450) lies on line

A. Find the slope, x-intercept and y-intercept form of the following equations a) 5x + 2y =-10 b) 13y -2x = 3 c) 25𝑦 + 31𝑥 − 18 = 10𝑦 d) −3𝑥 + 4𝑦 − 10 = 7𝑥 − 2𝑦 + 50

Q3

Insurance Premiums An insurance company has a simplified method for determining the annual premium for a term life insurance policy. A flat annual fee of $ 150 is charged for all policies plus $2.50 for each thousand dollars of the amount of the policy. For example, a $20,000 policy cost $150 for the fixed fee plus $50, which corresponds to the face value of the policy. ( stated in thousands of dollars ) , determine the function which can be used to compute annual premiums. 

Q1

Membership Drive A small health club is trying to stimulate new memberships. For a limited time, the normal annual fee of $300 per year will be reduced to $200. As an additional incentive, for each new member in excess of 60, the annual charge for each new member will be further reduced by $2. Determine the function p = f(n), where p equals the memberships fee for new members and n equals the number of new members.

Given that y = x is a particular solution of the differential

equation y''-x2y'

+ xy = 0. Find its general solution.

"x^2-xy+y^2=3" is the equation of an ellipse. By implicit differentiation determine the equation of the normal of the given equation at (-1,1)

The equation of the ellipse is given as "(x\/a)^2+(y\/b)^2 =1"

find the equation of the tangent at (x₀, y₀)

Calculate all second order derivatives of g(x,y)= xsin(x+y)+e^y

Use a triple integral to determine the volume of the region bounded by z =

p

x

2 + y

2 and z = x

2 + y

2

In 1st octant