Max/Min
A ball is thrown off a building from 200 feet above the ground. Its starting velocity is -10 feet per second.The equation h=-16t2-10t+200 can be used to model the height of the ball after t seconds. About how long does it take for the ball to hit the ground?
t= -3.86 or t=3.24
We disregard negative time. Therefore t=3.24
A rectangular piece of sheet metal is 7 inches shorter than is wide. From each corner, a 3 × 3 inch square is cut out and the flaps are then folded up to form an open box. If the volume of the box is 1620 inch, find the length and width of the original piece of sheet metal.
The width of the sheet of metal is 𝟑𝟑 inches, and the length of the sheet of metal is 𝟐𝟔 inches
The product of two consecutive negative integers is 1122. What are the numbers?
The two negative numbers are –33 and –34.
A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?
The width of the pathway will be 1.5 meters
A ball is thrown upward from the top of a 40 foot high building at a speed of 80 feet per second. The ball’s height above ground can be modeled by the equation h=-16t2+80t+40.When does the ball hit the ground?
t=5.485
A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?
The enlargement will be 12 inches by 16 inches.
If six times the sum of twice a number and 1 is equal to −6 times its square, then find the number(s).
-1
A rectangular piece of cardboard measuring 40 in. by 30 in. is to be made into an open box with a base (bottom) of 900 in2by cutting equal squares from the four corners and then bending up the sides. Find, to the nearest tenth of an inch, the length of the side of the square that must be cut from each corner.
x=32.7 or x=2.3
A rock is thrown upward from the top of a 112-foot high cliff overlooking the ocean at a speed of 96 feet per second. The rock’s height above ocean can be modeled by the equation h=-16t2+96t+112.What is the maximum height of the rock?
256 feet
You have a 500-foot roll of fencing and a large field. You want to construct a rectangular playground area. What are the dimensions of the largest such yard? What is the largest area
The largest area will have dimensions of 125' by 125', for a total area of 15 625 square feet.
The sum of a number and its square is 272. Find the number.
n=16 or n=-17
The local park has a rectangular flower bed that measures 10 feet by 15 feet. The caretaker plans on doubling its area by adding a strip of uniform width around the flower bed. Determine the width of the strip
The width of the strip that is to be added to the flower bed is 2.5 feet.
A water balloon is catapulted into the air so that its height h, in metres, after t seconds is h = −4.9t2?? + 27?t + 2.4. For how long is the balloon more than 30 m high?
x=2 or x=-15
ou have a 1200-foot roll of fencing and a large field. You want to make two paddocks by splitting a rectangular enclosure in half. What are the dimensions of the largest such enclosure
The paddock should be 300' by 200', with the divider running parallel to the 200-foot-long side.
Find two numbers x and y whose difference is 100 and whose product is a minimum.
x=-50 and y=50
Bob made a quilt that is 4 ft x 5 ft. He has 10 sq. ft. of fabric he can use to add a border around the quilt. How wide should he make the border to use all the fabric?
The width of the border should be 0.5 ft.
A rock is thrown directly upward with an initial velocity of 96 feet per second from a cliff 200 feet above a beach. The height of the rock above the beach (h) after 𝑡 seconds is given by the equation h = −16𝑡2 + 96𝑡 + 200. When will the rock be 328 feet above the beach?
t=2,4
Two trains leave a station at 11:00am. One train travels north at a rate of 45 mph and another travels east at a rate of 60 mph. Assuming they do not stop, at what time will the trains be 200 miles apart?
𝟏: 𝟒𝟎𝐩𝐦
One integer is 4 less than twice another integer, and their product is 96. Set up an algebraic equation and solve it to find the two integers
{8,12} and {-6,-16}
A box can be made by cutting out the corners and folding up the edges of a sheet of cardboard. A template for a cardboard box with a height of 2 inches is given. What is the length of each side of the cardboard sheet if the volume of the box is to be 50 cubic inches?
9 inches