Calculus Answers

A box with an open top is to be constructed from a square piece of cardboard, 10 in wide, by cutting out a square from each of the four corners and bending up the sides.
A. What is the length of the side of the square cut out from the corners of the box. Let x = the length of the side of the square cut out of the corners
B. What is the maximum volume of such a box?

consider the function F=
x^2 | x+2| for x<-2
(2/x)+1 for -2 <or= x < 0
3 for x=o
(sinx/x) for x>0

describe all asymptotes of F (vertical and horizontal)

4) The position function s of a particle moving along a coordinate line is given by

s(t)=4t^3 +15t^2-18t+1

, where time t is measured in minutes, and

s(t) is
measured in feet. Assume that
the positive direction extends to the right, and the negative direction extends to the
left.

a) Determine the velocity function [rule] v(t) .

b) Determine the time intervals in which the particle moves to the right.
Use a sign chart.

c) Determine the time intervals in which the particle moves to the left.
Use a sign chart.

d) Draw a schematic representing the motion of the particle in the time interval
(-6, 3)

find the slope of the tangent line to y=2/3x^2-x/6 at (-1,5/6)

The average mass of 4 boys is 36.5kg.When one boy left,the average mass of the remaining boys is 36kg.What is the mass of the boy who has left?

Jasmine has 24 erasers and Muthu has 20 erasers.How many erasers must Muthu give to Jasmine so that she will have thrice the number of erasers that Muthu has?

Mrs Tan mixed 5ooml of orange squash with 4.5 litres of water.She poured the mixture equally into 100 glasses.What was the amount of mixture in each glass?

Tom read a book from page 1 to page 59 without skipping any page.What is the sum of all the page number?

Let x = Integral (squ root (sec(t))^4 -1) (dt) from -pi/4 to pi/4

Hello,
When the dr/dt for sphere is constant and r=at + b, how does dV/dt change over time?

This is my work so far:

dr/dt = a
V=(4/3)(pi)r^3
dV/dt = 4(pi)r^2 (dr/dt)
dV/dt = 4(pi)(at + b)^2 (a)

Well, if radius is steadily decreasing, is change in volume decreasing constantly.
I know in my work, since there is a variable t, volume would not change at a constant rate. But am I thinking about it correctly?