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
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 16 cm and a height v=10 cm.
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.
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 m2 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.
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?
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 cm2.
Calculate the length of the belt on pulleys with diameters of 162 mm and 454 mm at shaft distance 425 mm.
If you know that cos(α) = sin (-968°), what is the angle α?
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.
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?