Equation + minimum - math problems
Number of problems found: 16
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
- Test scores
Jo's test scores on the first four 100 point exams are as follows: 96,90,76, and 88. If all exams are worth the same percent, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)?
- 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 co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Three numbers
Create from digits 1-9 three-digit numbers with their sum the smallest. What value is the sum of these numbers? (Use each digit only once)
We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
Cherries in the bowl can be divided equally among 19 or 13 or 28 children. How many are the minimum cherries in the bowl?
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
- 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?
- 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.
- Rotaty motion
What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
- Paper box
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 be side of the squares to be the largest volume of the box?
- 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. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
- 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 you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i
- TV competition
In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We g
- Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?