Optimisation
optimisation problems described by a quadratic function: the largest product, the largest area, the largest revenue, the least sum of squares
Exercises are drawn at random from a large bank - every click gives a different set.
Solved: 0 of 10
Give the time
A ball is thrown vertically upwards. Its height above the ground t seconds after the throw is given by h(t) = −5t² + 20t + 2, where the height h is in metres. How many seconds after the throw does the ball reach its greatest height?
Give the largest possible value
A rectangle has a perimeter of 220 m. What is its largest possible area?
Give the largest possible value
Two numbers add up to 68. What is the largest possible value of their product?
Give the dimensions of the cuboid
The sum of the lengths of all the edges of a cuboid with a square base is 80 cm. For which dimensions is its lateral surface area the greatest? Give first the length x of a base edge, then the height y.
Give the largest possible value
A shop sells 340 items of a product a day at 83 zloty each. Each price cut of 1 zloty increases daily sales by 20 items. What is the greatest possible daily revenue from this product?
Give those two numbers
The difference of two numbers is 10: the second number is subtracted from the first. For which two numbers is their product the least?
Give the price
At a price of c zloty a shop sells 312 - 6c items. At what price is the revenue the largest?
Give the largest possible value
A company's daily profit (in zloty) from selling x items of a product is given by P(x) = −5x² + 580x − 15150. What is the greatest possible daily profit of the company?
Give the dimensions of the rectangle
A rectangular plot is fenced on three sides; the fourth one is a wall. We have 16 m of fencing. What are the dimensions of the plot with the largest area? Give first the length x of each side perpendicular to the wall, then the length y of the side parallel to the wall.
Give those two numbers
Two numbers add up to 40. For which two numbers is their product the largest?
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