Quadratic Word ProblemsQuadratic Word Problems

• I didn’t have time to solve all of them today. I will do that tomorrow and post them.

• If you have a question on one, E-MAIL MEShauna.Hedgepeth@lamarcountyschools.orgI will give you hints and will tell you if your answer is

right.

1. The formula h = vt - 5t2 is used to determine the height, h, at t seconds of a cannon ball that was launched at an

initial velocity of v meters per second. What is the height of a cannon ball 10 seconds after a launch at an initial velocity

of 150 meters per second?

2. Simpon's back yard measures 50 ft by 75 ft. He wants to put a border of plants on all 4 sides of the yard with walkways in the borders. Since Simon wants to be sure that his kids have room to play, he has decided to leave 2100 square feet of the yard planted only in grass. Which equation could simon use to determine the width of the plant/walkway border?a) 2100 = (2x)(2x)b) 2100 = (50)(75) - (2x)(2x)

c) 2100 = (50 - 2x)(75 - 2x) d) 2100 = (50 - x)(75 - x) e) (50)(75) = (50 - 2x)(75 - 2x)

• Solve the previous problem: 2100 = (50 - 2x)(75 - 2x)

3. Dennis has decided to double-mat a landscape he had painted in artclass at the senior citizen center. The original painting has dimensions of14 inches by 11 inches. The inside mat is 2x inches wide on each side.The outside mat is x inches wide on each of the inside mat. Which equation will solve for the area covered by the matted painting?

a) A = 2x(x)14 + 2x(x)(11)b) A = 14(x + 2x) + 11(x + 2x)c) A = (6x + 14)(6x + 11)d) A = (3x + 14)(3x + 14)e) A = 4x(x + 14)(x + 11)

4. Mr. Hedgepeth is tired of animals (or sneaky neighbors) stealing histomato plants at night. He has decided to put up an electric fence allthe way around the garden and then place a movable screen on topof the fence at night. Mr. H's rectangular tomato garden is twice aswide as it is long. He plans to put the electric fence 4 feet from the edge of the garden on each side. The area on the inside of the fenceis 154 square feet. What is the width of the garden?

5. A rectangle has a perimeter of 40 meters. Find the dimensions of the rectangle with the maximum area

6. The circulation of the Charlotte Arts Council Newsletter is 50,000. Due to increased production costs, the council must increase the current price of 40 cents per copy. According to a recent survey, the circulation of the newsletter will decrease 5000 for each 10 cent increase in price. What price per copy will maximize the Arts Council’s income from the newsletter?

7. A tour bus carries tourists through the historic district of Savannah, GA, serving 300 customers a day. The charge is $8 per person. The owner estimates that the company would lose 20 passengers a day for every $1 increase in the fare. What charge would be the most profitable for the tour bus company?

8. The population of the United States from 1800 to 1809 can be approximated by the model: POPULATION = 0.6942t2 + 6.183 where the population is given in millions of people and the time (t) represents the calendar year with t = 0 corresponding to 1800. If this model had continued to be valid up through present time, when would the population of the US have reached 250 million?

9. An object is fired upwards from the top of a 200 ft tower at a velocity of 80 ft/sec. The height of the object t seconds after firing is given by the formula h(t) = -16t2 + 80t + 200. Find the maximum height reached by the object and the time that it takes for that height to be reached.

10. The Empire State Building is 1250 feet high. If an object is thrown upwards from the top of the building at an initial velocity of 35 feet per second, it’s height t seconds after it is thrown is given by the function h(t) = -16t2 + 35t + 1250. How long will it be before the object hits the ground?

(Mary Kate, this is NOT me.)

11. h = -16t2 - v0t + h0h = current heightv0 = initial velocityh0 = initial height

120 ft120 ftAfter being forced to do word problemsfor two days, Hedge's students revolt anddecide to drop her off of the top of thenearest water tower. She falls at an initial velocity of 25 ft/second. Howlong until she hits the ground?

11. h = -16t2 - v0t + h0h = current heightv0 = initial velocityh0 = initial height

bomberbomberThe water tower didn't kill her. :(The government lets you rent a bomber to try and kill her that way. If the pilot is flying at 32,000 feet over level terrain drops Hedge like a bomb at 35 ft/sec, how long will it take for Hedge to splat on the ground?

HedgeHedge

13. The CN Tower in Toronto, Ontario is 1820 feet tall. An "object" (HEDGE) is dropped from the tower. How long with it take for it to hit the ground?