Equation + maximum - practice problems
Number of problems found: 25
- Parabolic 79764
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - A construction 2
A construction company will be penalized for its bridge construction delays. The penalty is set at 4,000 for the first day and shall be subjected to a 1,000 increase for each succeeding day. The company can afford a maximum payment of 165,000 for a penalt - A missile
A missile is fired with a speed of 100 fps in a direction 30° above the horizontal. Determine the maximum height to which it rises. Fps foot per second. - A cheetah
A cheetah was separated from his brothers on a hunting mission. The brothers were at the watering hole 120 km away. The lost cheetah knew that he had to make it back before sundown, which was 1.5 hours away. His brothers had planned to leave the wateri
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - The bridge
A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force pushes the car onto the bridge as it passes through the center? What maximum speed can it cross over the center of the bridge, so it does not fly - TV competition
In the competition, ten contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors who answered incorrectly in that round. After the contest, one of the contestants said - The percent 2
The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5%, respectively. Suppose you have 3200 to invest and want to put twice as much in the growth fund as in the money market to maximize your return. How should you inve
- Two integers
Two integers, a, and b, have a product of 36. What is the least possible sum of a and b? - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - Block-shaped 7976
A block-shaped pool with a volume of 200m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament.
- Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C? - Equations 4781
Determine the smaller root of the root pair of the system of equations. 5a + 4b = 11 3a - 2b = 11 - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Summands 4213
Divide the number 28 into two summands so that their product is maximal. - Manufacturer 4212
How many electronic scooters should the manufacturer sell to maximize their income if the income function is given by the equation TR (Q) = -4Q2 + 1280 Q + 350?
Do you have homework that you need help solving? Ask a question, and we will try to solve it.