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The Clarke family went sailing on a lake. Their boat averaged 6 kilometers per hour. The Rourke family took their outboard runabout for a trip on the lake for the same amount of time. Their boat averaged 14 kilometers per hour. The Rourke family traveled 20 kilometers farther than the Clarke family. How many hours did each family spend on their boat trip?
a plane is heading due west with an airspeed of 306 mph. A wind with a bearing 340 is blowing at 12 mph find the speed and true course of the plane (in bearings)
A 104 inch long piece of wire is cut into two pieces, and two squares are formed. The sum of the areas of the two squares is 388 square inches. If the sides of the squares have integer lengths, what are the lengths of the sides of each square?
A function of two variables f(x,y) is integrated over the square [0,2] x [-1,1]. ex: integral from 0 to 2 , integral from -1 to 1 f(x,y) dx dy. (I wanted to input integral symbols there but didn't know how).
Examples of the product rule of exponents: Sometimes when students see the rule they want to write it as 4^2 + 4^3 = 4^5. Can you explain why this does not work?
Let G be finite abelian group with this property: For each positive integer m such that m | |G|, there are exactly m elements in G with order dividing m. Prove that G is cyclic.
Travelling 260 miles east of a town, John average speed is 60 mph until he came upon an accident site which reduced his speed 20mph. His trip took him 7 hours to complete, how many miles did John travel at the reduce speed.
Write a system of 5 equations in standard form to represent this problem. Write the matrix equation in the form AX=B.
How many dozen of each shirt can this company produce in one week assuming that the machines are used to maximum capacity?
Calculate the probability of rolling dice and obtaining a 3 or a 5 consecutively three times?
Use Gram-Schmidt algorithm to the sequence {x_1,x_2, x_3} to find an orthonormal basis of S. Use the result above to find the QR factorization of the matrix A=(x_1l x_2l x_3).
Is it possible to have a triangle with sides measuring 10ft, 12 ft, and 23 ft.? A mountain road is inclined 30 degrees with the horizontal, if a pick-up truck drives 2 mi. on this road , what change in altitude has been achieved?
If the marble selected is white, then what is the probability that a flip resulted in a head?
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