# Examples for 8th grade - page 7

- Kites

Boys run kite on a cable of 86 meters long. What is the kite altitude, if the angle from the horizontal plane is 77°? - Phone numbers

How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? - Friends in cinema

5 friends went to the cinema. How many possible ways can sit in a row, if one of them wants to sit in the middle and the remaining's place does not matter? - Pentagon

Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 10 cm. - New refrigerator

New refrigerator sells for 878 USD, Monday will be 25% discount. How much USD will save, and what will be the price? - Intersections

How many intersections have circles with radius 12 dm and 17 dm, if the distance of their centers is 20 dm. - Estate

Semicircle estate must be fence. The straight section has 44 meters long fence. How many meters of fence should buy? - Climb in percentage

The height difference between points A and B is 442 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 6.8 km. - Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Reciprocal

It is true (prove it) that if a> b> 0: ? - Lie/do not lie

The function is given by the rule f(x) = -x-12. Determine whether point D[-4; 2] lies on this function. Solve graphically or numerically and give reasons for the your answer. - Octahedron - sum

On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also. - Daily average

Calculate the average temperature during the day, when 14 hours was 20 °C and 10 hours was 15 °C. - Rhombus HP

Calculate area of the rhombus with height 98 mm and perimeter 20 mm. - Sphere growth

How many times grow volume of sphere if radius rises 3×? - Similarity of squares

The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? - Division

Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 1:6:3. How many candies should each get if in bag were 210? - Air mass

What is the weight of the air in a classroom with dimensions 5 m × 2 m × 3.1 m ? The air density is 1.293 kg/m^{3.} - Lines

Five bus lines runs at intervals 3, 5, 10, 11, 13 minutes. In the morning, suddenly start at 7:00. After how many minutes the bus lines meet again?

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