# Examples for secondary school students - page 19

- Property

The length of the rectangle-shaped property is 8 meters less than three times of the width. If we increase the width 5% of a length and lendth reduce by 14% of the width it will increase the property perimeter by 13 meters. How much will the property cost - Average

What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h. - Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm^{3}. What is it content (surface area)? - Volume from surface area

What is the volume of the cube whose surface area is 96 cm^{2}? - Geometric sequence 3

In geometric sequence is a_{8}= 312500; a_{11}= 39062500; s_{n}=1953124. Calculate the first item a_{1}, quotient q and n - number of members by their sum s_n. - Cubes

Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm^{2}. Determine the length of the edges of this cubes. - Hexagonal pyramid

Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag - Area codes

How many 6 digit area codes are possible if the first number can't be zero? - 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? - 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]. - Cotangent

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

Calculate the coordinates of the circle center: ? - 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. - 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? - Above Earth

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

By introducing a new variable solve biquadratic equation: ?

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