Examples for 9th grade - page 30
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 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 cm3, 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?
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?
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
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?
Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 3 identical plates?
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?
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×?
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?