Examples for 9th grade - page 50
- Quadratic function
It is given a quadratic function y = -5x2+12x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
The value of annual production enterprise is 7.1 million USD. The average annual growth rate is 2.4%. What will be value of production at the end of the fifth year?
- 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
The length of the bases trapezium are in ratio 2:1. Length of midline is 17. How long are the bases of a trapezoid?
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
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.
- Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle.
- 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
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 of the rectangle has length 14 cm. Angle between diagonal and londer sife of rectangle is 37°. Calculate area of the rectangle.
Outer perimeter of silo is 24 m. Concrete wall is 18 cm thick. What is diameter and area of inside floor of silo?
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?
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.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
- Quadratic equation
Determine the numbers b, c that the numbers x1 = -7 and x2 = -4 were roots of quadratic equation: ?