# Expression of a variable from formula - examples - page 21

1. Exponential equation Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625
2. The tourist The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
3. The coil How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
4. The pond We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
5. Area of garden If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
6. Cube surface and volume Find the surface of the cube with a volume of 27 dm3.
7. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
8. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
9. The painter In order for the painter to get the desired color, he must mix green and yellow in a ratio of 4: 7. If it has 28 l of green color, how many liters of yellow color should he add? How many liters of mixed color does he get?
10. Cuboid walls If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
11. Rectangles The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
12. Workers Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send?
13. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
14. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
15. Triangle perimeter Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
16. Soldier 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?
17. Car driver The car driver is in town A and is scheduled to be in town B at a specified hour. If it travels at an average speed of 50km/h, it will arrive in city B 30 minutes later. But if he travels at an average speed of 70km/h, he would arrive half an hour earlier
18. Two pipes How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
19. Diagonals of a rhombus 2 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
20. Peroxide How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?

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