Examples for 9th grade - page 65
In the park is marked diamond shaped line connecting locations A, D, S, C, B, A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m.
How many mm of water rained the roof space 75 m2 if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-)
- Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
The largest angle at which the lift rises is 16°31'. Give climb angle in permille.
- Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
- Password dalibor
Kamila wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes this two changes. How many opportunities have a choice?
- Rectangular triangles
The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c
- Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
- Motion 2
At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet?
- Chord 4
I need to calculate the circumference of a circle, I know the chord length c=19 cm and the distance from the center d=33 cm chord to the circle.
- Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 51 cm. Its mass is 5 kg, length 56 cm. What is the pipe wall thickness?
- Blackjack TU160
Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At
- Giant coin
From coinage metal was produced giant coin and was applied so much metal, such as production of 10 million actual coins. What has this giant coin diameter and thickness, if the ratio of diameter to thickness is the same as a real coin, which has a diameter
- Trapezoid v3
The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ?
- High wall
I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
- Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
- Juice box 2
Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of the
- Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
- Triangle midpoints
Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
- Concentric circles
In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord.