Minimum - high school - practice problems
Number of problems found: 41
- Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal. - 5-number summary
Given the following 5-number summary: 11, 19, 24, 30, 48, which of the statistics cannot be determined? - Summands 4213
Divide the number 28 into two summands so that their product is maximal. - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder. - Closest 82051
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Prove 2
Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - Summands
We want to split the number 110 into three summands so that the first and the second summand are in ratio 4:5, and the third with the first are in ratio 7:3. Calculate the smallest summands. - 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? - 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. - Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divided by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Statue
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. - Frequencies 81136
In grouped data classes such as 10-15, 16-20, 21-25, 26-30 with the respective frequencies of each class as 3, 5, 4, 3, then the range (range of variation) is: a. 15 b. 6 c. 20 d. 5 - 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. - Equilateral triangle
How long should the minimum radius of the circular plate be cut into an equilateral triangle with side 21 cm from it? - Half-planes 36831
The line p and the two inner points of one of the half-planes determined by the line p are given. Find point X on the line p so that the sum of its distances from points A and B is the smallest. - Dogde Caliber
The petrol kilometers M (unit: kilometers per liter) of the Dodge Caliber car is modeled by the function: M(s) = - 1/28s² + 3s- 31 What is the car's best petrol kilometers, and what speed is attained? - Function x*tanx
Functions: f(x)=xtanx f(x)=(e^x)/((e^x)+1) Find; i)vertical and horizontal asymptotes iii)the interval of decrease and increase iii)Local maxima and local minima iv)interval of concavity and inflection. And sketch the graph. - 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? - Seedcake
Seedcake costs 44 cents. How many minimum seedcakes must we buy that we can pay in cash, only whole euros?
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