# Examples for 9th grade - page 30

- Reflector

Circular reflector throws light cone with a vertex angle 60° and is on 22 m height tower. The axis of the light beam has with the axis of the tower angle 24°. What is the maximum length of the illuminated horizontal plane? - Four-digit number

Find also a four-digit number, which quadrupled written backwards is the same number. - Maple

Maple peak is visible from a distance 4 m from the trunk from a height of 1.7 m at angle 50°. Determine the height of the maple. - Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism! - Loans, loan ...

In Slovakia, launched a short-term non-bank loans, of which few people have their "take" are considered unfavorable. Often, the borrower ends up in a spiral of debt, which takes more and more onerous loan used to repay earlier loans. Calculate how many 4- - Mushrooms from the forest

Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda? - Cube 6

Volume of the cube is 216 cm^{3,}calculate its surface area. - Katy MO

Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY? - Permill

How many permill is 1931 from 166456? - Cone and cube

About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r? - Snowman

In a circle with a diameter 41 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman. - The angle of lines

Calculate the angle of two lines y=-3x+25 and y=x-3 - Peleton

Cycling race was run at an average speed of 33 km/h. One cyclist lost with defect 6 minutes. How long and how far he must go at speed 38 km/h to catch peleton again? - Ray

Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 3 identical plates? - Pipeline

How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter? - 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? - Automaker

The automaker now produces daily 4 new cars more than last year so the production of 360 cars will save just one full working day. How many working days to produce 360 vehicles needed last year? - Sphere fall

How many percent fall volume of sphere if diameter fall 5×? - Vectors

Vector a has coordinates (7; 16) and vector b has coordinates (15; -7). If the vector c = b - a, what is the magnitude of the vector c? - angles in quadrilateral

What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?

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