The area of a rectangle is 48 square meters. The length is twice the width. Find the length and width of the rectangle.
A ball is thrown vertically upward, and its height in meters after ttt seconds is modeled by the equation h(t)=−5t2+20t+15h(t) = -5t^2 + 20t + 15h(t)=−5t2+20t+15.
a. What is the maximum height of the ball?
b. How many seconds does it take to reach the maximum height?
The product of two numbers is 180, and their sum is 27. Find the two numbers.
A garden has an area of 120 square meters. Its length is 4 meters longer than its width. Determine the dimensions of the garden.
A profit function of a business is modeled by P(x)=−3x2+12x−5P(x) = -3x^2 + 12x - 5P(x)=−3x2+12x−5, where xxx represents the number of items produced.
a. What is the maximum profit?
b. How many items should be produced to achieve the maximum profit?
A swimming pool has an area of 90 square meters. The length is 5 meters more than twice the width. Find the dimensions of the pool.
A rocket is launched, and its height h(t)h(t)h(t) in meters after ttt seconds is modeled by the equation h(t)=−4t2+16t+12h(t) = -4t^2 + 16t + 12h(t)=−4t2+16t+12.
a. What is the maximum height of the rocket?
b. How long does it take to reach this height?
The product of two numbers is 72. One number is 3 more than the other. Find the numbers.
A rectangular plot of land has an area of 150 square meters. Its length is 7 meters longer than its width. What are the dimensions of the plot?
The motion of a particle is modeled by the equation s(t)=−2t2+8t+10s(t) = -2t^2 + 8t + 10s(t)=−2t2+8t+10, where s(t)s(t)s(t) is the position of the particle at time ttt.
a. What is the maximum position of the particle?
b. At what time does it reach this position?
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