Derivation - math problems
Number of problems found: 25
- Ascend vs. descent
Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 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.
- Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m3 to have painted/bricked walls with the least amount of material.
- Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal.
- Paper box
The hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box?
Meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the perimeter of the meadow to allow the goat to eat half of the meadow?
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
- Sphere and cone
Within the sphere of radius G = 33 cm inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
Exists a function whose derivation is the same function?
The body was thrown vertically upward at speed v0 = 79 m/s. Body height versus time describe equation h = v0 * t - (1)/(2) * 10 * t2. What is the maximum height body reach?
On the pedestal high 4 m is a statue 2.7 m high. At what distance from the statue must the observer stand to see it at the maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
- Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diago
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
- Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
- 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?
- The position
The position of a body at any time T is given by the displacement function S=t3-2t2-4t-8. Find its acceleration at each instant time when the velocity is zero.
- Shopping malls
The chain of department stores plans to invest up to 24,000 euros in television advertising. Ads will place all commercials on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers. Durin
- 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.