Posted: June 1st, 2024

MATH V2010-One of the most exciting plays in basketball

I.One of the most exciting plays in basketball is the dunk shot. The amount of timeT that passes from the moment a player leaves the ground, goes up, makes theshot, and arrives back on the ground is called the hang time. A function relatingan athlete's vertical leap V, in inches, to hang time T, in seconds, is given by: V(T) = 48T2 a) Hall-of-Famer Michael Jordan has a hang time of about 0.889 sec. What is Michael Jordan's vertical leap? (T = hang time) b) The record for the greatest vertical leap in the NBA is held by Darryl Griffith of the Utah Jazz. It was 48 in. What was Darryl Griffith's hang time? (V is the vertical leap) Source: Peter Brancazi, "The Mechanics of a Slam Dunk" Popular Mechanics, Nov 1991.II.Suppose that you invested $16,000 in a high-risk growth fund that after 2 yearswas worth $25,000. Your broker used the following equation to find theaverage annual rate of return, r 16,000(1 + r)2 = 25,000 What is the annual rate of return? Hint: Rewrite the equation in standard form, then solve by factoring. Write your final answer as a %. (there is no negative rate of return so the answer will be positive)III.If sailcloth costs $10 per square foot, what is the cost of a new mainsail? Before solving this problem let's review the Pythagorean Theorem. This theorem relatesthe lengths of the three sides of a right triangle. A right triangle has a 90º angle. The side opposite the 90º angle is called the hypotenuse and the other sides are called legs. The Pythagorean theorem states that for every right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. a2 + b2 = c2 Now solve the problem: The mainsail on the sailboat shown below is a right triangle in which the hypotenuse is called the leech. If sailcloth costs $10 per square foot, what is the cost of a new mainsail? Hint: To find the cost of the sail, you need to know the area of the sail. You must first find the base (x) of the mainsail using the Pythagorean Theorem. Once you have found the value of x then find the area of the sail by using the formula for the area of a triangle: 1/2 base times height; A= ½bh .xLeech13 ft12 ftPlease show what work you can. You can use the Equation Editor in MS Word to write your math equations. To access the equation editor, click on Insert on the menu bar, select Object, and select Microsoft Equation. If you do not have MS Word, you will need to use parenthesis and other symbols to create the equations. For example use the ^ (above the 6) to represent a value to the power and * for multiplication. You can also do the work in your own handwriting, but will need to scan a legible document to post to the dropbox.

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