# Grade - examples - page 44

- Cotangent

If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α. - Center

In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z]. - Park

In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m. - Machines

In the workshop are three machines. The first is treated 250 parts for 4.7 hours, the second is treated 300 parts for 1.9 hours and the third is treated 230 parts for 4.6 hours. How long will take to make 3100 parts if worked all three machines at the. - Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle? - The horses

A couple of horses consume 88 kg of oats for 14 days. How many oats consumed 7 horses at the same consumption for 6 days? - School trip

Class has 17 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 1× 3-bed and 2× 4-bed rooms. (Each room has its own unique number) - Numbers

How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6? - Rhombus

Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm. - Statue

On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m. - Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm^{3}. Calculate the surface of the prism. - Semicircle

In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Tank and water

Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in? - Center

Calculate the coordinates of the circle center: ? - Cone

If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Rail turn

The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve. - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - BMI index

Calculate BMI (body mass index, an index indicating obesity, overweight, normal weight, underweight) man weighing m = 71 kg and height h = 170 cm. Index is calculated according to equation (formula): ? With BMI index is possible to compare people of diff - Compare

Compare with characters >, <, =: 85.57 ? 80.83 - Median

In the right triangle are sides a=41 dm b=42 dm. Calculate the length of the medians t_{c}to the hypotenuse.

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