Questions from General Calculus

Q: A sample of tritium-3 decayed to 94.5%

A sample of tritium-3 decayed to 94.5% of its original amount after a year. (a) What is the half-life of tritium-3? (b) How long would it take the sample to decay to 20% of its original amount?

Q: Identify and sketch the graph of each surface. x =

Identify and sketch the graph of each surface. x = y2 + z2 - 2y - 4z + 5

Q: A surface consists of all points P such that the distance from

A surface consists of all points P such that the distance from P to the plane y = 1 is twice the distance from P to the point (0, -1, 0). Find an equation for this surface and identify it.

Q: Find two unit vectors that are orthogonal to both j + 2k

Find two unit vectors that are orthogonal to both j + 2k and i - 2j + 3k.

Q: Differentiate. y = x / 2 - tan x

Differentiate. y = x / 2 - tan x

Q: Find the cross product a × b and verify that it is

Find the cross product a × b and verify that it is orthogonal to both a and b. a = 2, 3, 0 , b = 1, 0,5

Q: Sketch the points (1, 5, 3), (0

Sketch the points (1, 5, 3), (0, 2, -3), (-3, 0, 2), and (2, -2, -1) on a single set of coordinate axes.

Q: Name all the equal vectors in the parallelogram shown.

Name all the equal vectors in the parallelogram shown.

Q: What are the projections of the point (2, 3,

What are the projections of the point (2, 3, 5) on the xy-, yz-, and xz-planes? Draw a rectangular box with the origin and (2, 3, 5) as opposite vertices and with its faces parallel to the coordinate...

Q: Copy the vectors in the figure and use them to draw the

Copy the vectors in the figure and use them to draw the following vectors. (a). u + v (b). u + w (c) v + w (d). u - v (e). v + u + w (f). - w - v