# 9th grade (14y) + expression of a variable from formula - examples - page 11

The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
2. RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
3. Trapezoid - central median
The central median divides the trapezoid into two smaller trapezoids. Determines the ratio of their contents.
4. Fifth member
Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
5. Rectangle 35
Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
6. Regular n-gon
In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
7. Arithmetic progression
In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ?
8. Cylindrical tank
Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
9. A mast
A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
10. Rectangular triangle PQR
In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
11. Determine AP
Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
12. Diagonals
Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
13. 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%?
14. Quotient
Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
15. Coach
Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach?
16. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
17. Chord
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.
18. Q of GP
Calculate quotient of geometric progression if a1=5 a a1+a2=12.
19. The gardener
The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
20. Coefficient
Determine the coefficient of this sequence: 7.2; 2.4; 0.8

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