Expression of a variable from formula - examples
- Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
- Tangent 3
In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
- Simple equations
Solve system of equations: 5x+3y=5 5x+7y=25
- Red balls
In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
- Free fall
How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss?
- Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
Audrey has some guppies in a fish tank. The ration of the oranges guppies to silver guppies is 3:5. She has 12y oranges guppies. Write the number of silver guppies she has in terms of y
- Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
- Boys and girls
There are 28 girls in the hall. 5/7 of all children are boys. How many children and how many boys are there?
- Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
- The ladder
The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
Tomas spent 60% of his savings for his weekly vacation. He was 32 € left. How many euros did he have before vacation?
The weight of the calf meat obtained is 65% of the total weight of live calves. What was the weight of a calf from which 285 kg of meat was obtained?
The cube has area of base 64 mm2. Calculate the edge length, volume and area of its surface.
- MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
The theater has in each row with 11 seats. Ticket to the first 8 rows is for 198 KČ. In next rows is for 84 KČ. The theater was completely sold out. Revenue was 34980 KČ. How many rows are in the theater?
- IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 26 cm, c = |CD| = 5 cm and legs b = d = |BC| = |AD| = 19 cm.
- Arc and segment
Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 49 and corresponding angle is ?.