Expression of a variable from formula - examples
- Cube surface and volume
Find the surface of the cube with a volume of 27 dm3.
- On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
- Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together?
- Drying herbs
Herbs lose 75% weight By drying. How many fresh herbs do you have to collect if you want to make 1.5 kg of dried herbs?
- Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
- AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
- Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
- Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
- The tourist
The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone?
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
- Two thirds
Find two-thirds of the number equal to two-thirds of 99
- Two diggers
Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
- Two masters
The two masters will make as many parts as five apprentices at the same time. An eight-hour shift begins at 6 o'clock. When can a master finish the job to produce just as much as an apprentice for the whole shift?
- Spherical tank
The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
- Edges or sides
Calculate the cube volume, if the sum of the lengths of all sides is 276 cm.
- Summer tires
Three tire servants have to change the summer tires on 6 cars in 2 hours. Mark's replacement would take 4.5 hours, Jirka would do it in 3 hours and 10 minutes, and Honza in 4 hours. Will they be able to replace all tires at the desired time?
- Two resistors
Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
- Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?