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Cosine rules.
Find the side of a regular dodecagon that is inscribed in a circle with radius 4 cm. (A regular dodecagon has 12 equal angles and 12 equal sides.) Show your method of solution. You may use geometric vector.
Heights and distances.
The angle of depression to one side of a lake, measured from the passenger cage of a hot air balloon is 43 degrees. The angle of depression measured to the other side of the lake is 27 degrees. The passenger cage of the balloon is 2500 feet above the lake. Find the width of the lake.
Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data set with a mean of 287 and standard deviation of 14.
Simulate 1000 interactions of the two strategies over the six-year period. Create a histogram of the final fund values. Based on your simulation results, which of the two strategies would you recommend? Why?
Prove that if the orientation on one component of a two-component oriented link L is reversed then its linking number is negated. What is the linking number of the mirror-image link L? Would either of these results still hold if L had three or mor..
Consider a standard deck of playing cards. You randomly select a card from the deck and find that you have drawn a face card.
Suppose that there are two forces acting on a sky diver: gravity at 200 pounds down and air resistance at 180 pounds up and 40 pounds to the right. What is the net force acting on the sky diver?
In R2, let triangle ABC be a right triangle with right angle at angle C. Consider the altitude CH (it meets AB perpendicularly). Prove that |CH|^2 = |AH| * |BH|.
at what time between 5pm and midnight are the most people listening to the station? what percentage of the population is listening at this time?
Discuss examples of administrative decisions that might be made in the managing of performance of professor?
Suppose f and g are functions analytic in a domain D. If z_n is a bounded sequence of distinct points in D and if f(z_n) = g(z_n) for all n, show that f(z) = g(z) for all z in D.
A company installs 5,000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve
Annual profit in thousands of dollars is given by the function, P(x) = 100vx-5 + 3,000, where x is the number of items sold in thousands, x = 5. Describe the meaning of the number 5 in the formula.
tyrone is selling 4 pizzas by the slice to help raise money for the marching band. After lunch, he has 2 1/2 pizas remaining. During dinner he sells 1/4 remaining pizza. Write an expression can be used to find the amount of all 4 pizzas Tyrone sol..
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