Functions - examples
- Diagonals at right angle
In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
If you know that cos(γ) = sin (806°), what is the angle γ?
- Election mathematics
In elections, 12 political parties received this shares of voters: party A 56.2 %party B 8.5 %party C 8.2 %party D 6.2 %party E 6.1 %party F 5.5 %party G 3.2 %party H 2.1 %party I 2 %party J 1 %party K 1 % Calculate what the shares acquired in the parlia
- Newton's task
Grass grows in the meadow equally fast and evenly. It is known that 99 cows graze meadow for 14 days and 95 cows by 22 days. How many cows graze meadow for 77 days?
The aircraft has in a fuel tank 68 hl of aviation fuel and flight consumes 3.6 liters of fuel. Identify the function, which expresses the dependence of the volume of fuel in tank on the track distance plane flew by. How many hectolites of fuel is still in
- Electrics - conductor
The wire is 106 meters long at 0 °C and at every temperature increase of 1 °C the length increases by 0.15 mm per 1 m length of wire. Determine a function which represents the overall length of the wire as a function of temperature. What is the length of t
For linear function f(x) = ax + b is f(14)=179; f(15)=154. Calculate m, if f(m) = 2019 .
- Car rent
Rental cars are paid a fixed daily fee plus 16 cents for each kilometer traveled. Samuel want to rent a car for a day and worked out that will pay 175 euros. When paying he got a 20% discount on the daily fee, the cost per kilometer is unchanged. Samuel th
Exists a function whose derivation is the same function?
Tatra's tachometer shows the initial state 886123 km this morning. Tatra today travel at an average speed of 44 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4 hours?
- Lie/do not lie
The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer.
Eequation f(x) = 0 has roots x1 = 64, x2 = 100, x3 = 25, x4 = 49. How many roots have equation f(x2) = 0 ?
Suzanne helped write out diplomas. Issuance its first took 3 minutes, each next 2.3 minutes. How much time it will take to write out n=16 diplomas (including the first), write out this pace?
- Square ABCD
Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
Straight streets is long x = 1425 meters. At the beginning and at the end of the street are poles. The poles are spaced 25 m. How many poles are on the street?
- Quadratic function
It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week?
What is the vertical asymptote of ?
- Owner of the company
The owner of the company with extensive administrative activity wants to sell the obsolete 3 machines at the price of CZK 1000 per 1 machine with a six-month warranty period. If the machine breaks down during this period, the owner will return the employe
- Quadratic function
Write the equation of the quadratic function which includes points A (-1, 10), B (2, 19), C (1,4)