# Examples for 9th grade - page 22

- Perpendicular

What is the slope of the perpendicular bisector of line segment AB if A[-4,-5] and B[1,-1]? - Cable car 2

Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car? - Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm. - Triangular prism

Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm. - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3.}Calculate the volume, surface and diameter of the sphere. - Right triangle

Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC. - Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum - Salary

Calculate equivalent annual salary to hourly salary $ 19. Assume a 42-hour work week. - Circle

Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes? - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 14 cm and u_{2}= 15 cm. Prism height is twice base edge length. - Perpendicular

Determine the slope of the line perpendicular to the line p: y = -x +4. - Segments

Line segments 67 cm and 3.1 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide? - Chord

In a circle with radius r=70 cm is chord 10× longer than its distance from the center. What is the length of the chord? - Column

Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke? - The car

The car has traveled the distance between A and B for four hour. If we increased the average by 17 km/h the car travel this distance an hour earlier. Determine the initial speed of the car and the distance between A and B. - Certificate

There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2? - Salary

Lawyer got to pay 840 Euros in banknotes of 20 and 50 Eur. Total got 18 banknotes. How many was which? - Circle

On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN. - Truck

In 7 hours started from town Krnov truck at speed 40 km/h. Passenger car started against it in 8 hours 30 minutes from the city of Jihlava at speed 70 km/h. Distance between this two cities is 225 km. At what time and at what distance from Krnov this two. - Commitee

A class consists of 6 males and 7 females. How many committees of 7 are possible if the committee must consist of 2 males and 5 females?

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