# Units - examples - page 28

1. Vertical prism
The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
2. Mushrooms
Fresh mushrooms contain 94% water, dried 14%. How many kg of fresh mushrooms is needed to collect to get 10 kg dried?
3. Segments
Which of the pairs of numbers on the number line encloses the longest segment: ?
4. Rhombus diagonal
Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
5. 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.
6. 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.
7. 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?
8. Chemical parison
The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
9. 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.
10. Rectangular trapezoid
How many inner right angles has a rectangular trapezoid?
11. Circular motion
Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
12. 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?
13. 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?
14. Segment
Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
15. 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?
16. 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?
17. 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?
18. Goniometric form
Determine goniometric form of a complex number ?.
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. 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.

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