# Examples for 8th grade - page 63

- Two runners

Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute - VAT

In the country XYZ car Daewoo Leganza costs 3779 Euros including VAT; 3325.52 Eur without VAT. a) Determine the rate of VAT. b) How much is Euro VAT paid on the purchase? c) How many % of the total price of the goods is VAT? VAT = value added tax. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″. - Diagonal

Diagonal of the rectangle has length 14 cm. Angle between diagonal and londer sife of rectangle is 37°. Calculate area of the rectangle. - Triangle

For how many integer values of x can 8, 11 and x be the lengths of the sides of triangle? - Cone

If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Cylinders

Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much? - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 50 km, with regular train leave at 6:05 and arrive at 7:20, but train is late and has departure at 9:52 and arrive at 11:05. - Square 2

Points D[9,-1] and B[3,3] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Circumscription

Calculate radius of the Circumscribed circle in the rectangle with sides 17 and 16. It can be rectangle inscribed by circle? - Chord MN

Chord MN of circle has distance from the center circle S 118 cm. Angle MSN is 41°. Determine the radius of the circle. - Carbon dioxide

Calculate how many grams of oxygen are in 126 g of carbon dioxide CO_{2}. Relative atomic mass of oxygen is 16 and of carbon is 12. - Extreme temperatures

USA hit extreme heat wave. Calculate percentage of the air temperature change from normal summer temperature 24 °C to 37 °C. - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 17 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - Cone in cube

The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage. - Jewel

Rhombus-shaped jewel have area of 86 mm^{2}and the edge in long 10 mm. Calculate the size of rhombus acute angle. - Triangle SAA

The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle. - Bomber

Bomber flies 5 km at 1400 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s^{2.} - Temperature calculus

Calculate percentage of temperature increase if changed from -6 °C to 2 °C?

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