# Examples for 9th grade - page 53

- Total displacement

Calculate total displacement of the 12-cylinder engine with the diameter of the piston bore B = 6.8 cm and stroke S=2 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back t - Slope form

Find the equation of a line given the point X(10, -2) and slope -1.2. Arrange your answer in the form y = ax + b, where a, b are the constants. - Trains

From station 130 km away started passenger train and after 2.8 hours after the express train, which travels 24 km an hour more. Express train finish journey 14 minutes early. Calculate the average speed of this two trains. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees. - Three workers

Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 25 days, B together with C for 16 days, A together with C for 10 days. How long it would take to complete the task every one of them alone? How long it would. - 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. - Price of state

Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 1121 (super-gross wage).Then tax him 35.2% employer contribution - 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. - 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.} - Quadratic equation

Determine the numbers b, c that the numbers x_{1}= -7 and x_{2}= -4 were roots of quadratic equation: ? - Cable car

Cable car rises at an angle 21° and connects the upper and lower station with an altitude difference of 1030 m. How long is "endless" tow rope? - 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. - 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 - Jewel

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

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