Examples for 9th grade - page 58
- Percentage of waste
In a square plate with side 42 cm we cut 4 same circles. Calculate the percentage of waste.
- The chord
Calculate a chord length which the distance from the center of the circle (S, 20 cm) equals 7 cm.
The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
- Train from Brno
First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
- Trapezoid - diagonal
Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
- Garden pond
Concrete garden pond has bottom shape of a semicircle with a diameter 1.1 m and is 47 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 22 cm?
- Tourist Jirka
Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
- 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.
- Mystery of stereometrie
Two regular tetrahedrons have surfaces 48 cm2 and 108 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
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?
In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
- Vector - basic operations
There are given points A [13; 11] B [23; -4] C [9; -1] and D [-11; 25] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w
- 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.
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.
We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then
- 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″.
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?