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10 Nov 2019
Calculus
A potter shapes a lump of clay into a cylinder using a pottery wheel. As it spins, it becomes taller and thinner, so the height, h, is increas- ing and the radius, r, is decreasing. If the height of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 1.5cm and the length is 7cm.
(Hint: What do you know about the total amount of clay?)
Algebra
Consider the linear equation
x + y â 2z = 0.
(a) Find all solutions of this equation in vector form. (b) Give two vectors that span the set of solutions.
(c) Prove that those two vectors are linearly independent and hence give a basis for the set of solutions.
Calculus
A potter shapes a lump of clay into a cylinder using a pottery wheel. As it spins, it becomes taller and thinner, so the height, h, is increas- ing and the radius, r, is decreasing. If the height of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 1.5cm and the length is 7cm.
(Hint: What do you know about the total amount of clay?)
Algebra
Consider the linear equation
x + y â 2z = 0.
(a) Find all solutions of this equation in vector form. (b) Give two vectors that span the set of solutions.
(c) Prove that those two vectors are linearly independent and hence give a basis for the set of solutions.
Trinidad TremblayLv2
4 Feb 2019