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Find the angle between the diagonal of a cube of side length 3 and the diagonal of one of its faces. The angle should be measured in radians.
From the top of a building 70 meters high, the angles of depression of two objects that are directly east of the observation position are 38° and 25° respectively. find the distance between the objects.
What is the probability that the mean annual snowfall during 40 randomly picked years will be between 105 inches and 112 inches?
suppose a function f is conjugate to a function g by the homeomorphism h. show that g is conjugate to f by the homeomorphism h-inverse. Use the fact that h-inverse is a homeomorphism whenever h is.
Let A be an n × n matrix with eigen values 1, 2, · · · , n. Prove there are (2 n )n! Different matrix S with the property that the length of each column vector of S is 2 such that (S -1 )AS is diagonal.
How many days would the company have to operate each factory in order to fill an order for exactly 500 baseline and 325 GT cars?
Suppose that the simultaneous equations F(x,y,z)=0 and G(x,y,z)=0 define x=f(z) and y=g(z) implicitly, Determine expressions for dx/dz and dy/dz in terms of partial derivatives of F and G
A tent for a family of 6 is on sale for $109.99. Find the volume of space inside the tent (w= 8ft, l=12ft, h=6ft) for the family to sleep.
The perimeter of a triangle ABC is 54. If the triangle has side lengths AB=3x,BC=4x, and AC=5x, find the lengths of each side.
Describe objects that have each of the following types of symmetry.
Find the probabilities that the sample, drawn without replacement, contains the following, All blue balls, Exactly 2 black balls
Name at least one situation in real life where you measure slope? What is the range of the slopes you encounter for this measurement?
use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown and Using simulation estimate the loss of revenue due to copier breakdown for one year
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