# Examples for 9th grade - page 14

- Wire D

Wire length 5 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Tea blend

Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k - 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. - Arm

Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 16 cm and a height v=10 cm. - 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? - Track arc

Two straight tracks is in an angle 99°. They will join with circular arc with radius r=1292 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)? - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 6 so that it is divided into three parts in the ratio 3:2:5. Calculate the circumference of the triangle ABC. - Prism

The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism? - House roof

The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m^{2}is needed to cover roof if roof pitch is 52° and we calculate 9% of waste, connections and overlapping of area roof? - Playing cards

How many possible ways are to shuffle 7 playing cards? - Rotating cone II

Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm. - Cyclists

Cyclist who rides at an average speed 17 km/h travels trip distance 14 min before the cyclist who rides at an average speed 15 km/h. What is the length of this cyclist trip(distance in km)? - Magnification of the square

If we increase the square side, increase the content of the 42 %. About what percentage was increased his sides? - Scouts

The boys from scout group traveled 3 days distance 105 km. Every day walked 1.3 km less than the previous day. How many kilometers scouts walked in the first day? - Perimeter and legs

Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm^{2.} - V-belt

Calculate the length of the belt on pulleys with diameters of 162 mm and 454 mm at shaft distance 425 mm. - Trigonometry

If you know that cos(α) = sin (-968°), what is the angle α? - Q-Exam

If tg α = 3.8, Calculating sin α, cos α, cotg α . - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm. - Tanker

An oil tanker can be emptied by the first pump in 4.4 hours. Second pump can empty an tanker in 7.8 hours. If the first pump started at 8:00 and second 1.4 hour later, at what time will the tanker be empty?

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