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A rectangular piece of metal is 10cm longer than it is wide. Squares with sides 2 cm long are cut from the four corners of the piece of metal, and the flaps are folded upward to form an open box. If the volume of the box is 832cm^3, what were the dimensions of the original piece of metal?
FIND and PROVE a formula for the inverse hyperbolic tangent, arctanh(x). The formula should involve a natural logarithm. Also, check the answer by substituting the definition of tanh x into your inverse formula and simplify. Show all work please.
Algebraic expression by addition rule.
Apply the factor theorem.
Use mathematical induction to show that a rectangular checkerboard with an even number of cells and two cells missing, one white and one black, can be covered by dominoes.
Objective questions
Find the slope of the line that is (a) parallel and (b) perpendicular to the line through each pair of points:
on a recent trip to a local orchard the nomial family picked four different kinds of apples - braeburn cortland fuji
Explain how Euler concludes from 1) that pi^2/6=1+1/4+1/9+1/16 ... . Compare the formula in 2) to Archimedes' calculation for pi. Which of these methods is more efficient and why?
Make a graph of the relationship.
Suppose K is a Galois extension of Q whose degree is a power of 2, and such that K is included in R (the reals). Show that the elements of K can be constructed by ruler and compass.
Use the given information to find the exact value of each of the following.
Write the equation of a line that intersects the negative x-axis and the positive y-axis at points not equidistant from the origin (0, 0). Draw the line. Draw the line that is the reflection of your line across the line y=x.
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