# Examples for 9th grade - page 26

1. Loan
Apply for a \$ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.
2. Diagonals in the diamond
The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m2. Determine the sizes of the diagonals.
3. Triangle SAA
The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
4. Fire tank
Whole fire tank was discharged once in 5 days by first out by second in \$n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
5. Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
6. Chemical parison
The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
7. Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
8. Circle arc
Calculate the area of the circular arc in m2 where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.
9. Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express
10. Forth and back
Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B?
11. Pedestrian
Pedestrian came started at 8h in the morning with speed 4.4 km/h. At half-past eleven cyclist started at 26 km/h same way. How many minutes take cyclist to catch up pedestrian?
12. Parallelogram
The perimeter of the parallelogram is 417 cm. The length of one side is 1.7-times longer than the length of the shorter side. What is the length of sides of a parallelogram?
13. Tetrahedron
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
14. Trapezoid RT
The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio
15. Exp
If ?, then n is:
16. Sequence
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
17. Earth's diameter
The Earth's diameter on the equator is approximately 12750 km. How long does the Gripen flyover the Earth above the equator at 10 km if it is at an average speed of 1500 km / h?
18. Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
19. Metal alloy
What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
20. Cuboid
The volume of the cuboid is 245 cm3. Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid?

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