Examples for 9th grade - page 62
- Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 9 cm, height v = 14 cm and |CAB| = 29°. Calculate area of the trapezoid.
Pyramid has a base a = 9cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
- Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 14 cm and central angle 66 degrees.
Calculate the area of what may vary rectangular, if it focused by surveyor and found the dimensions 14 x 12 m while in each of the four joint points can be position deviation 8 cm?
Calculate the area of the triangle ABC if b = c = 20 cm, R = 21 cm (R is the circumradius).
Calculate area of the parallelogram ABCD as shown if |AB| = 45 cm, |BC| = 23 cm and angle BAD = 30°
- Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=13 cm, vb=17 cm and side b is 5 cm shorter than side a.
- Gimli Glider
Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2080 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60°
How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
- Secret number
Determine the secret number n, which reversed decrease by 8.6 if the number increase by 8.6.
- Black building
Jordan built building with a rectangular shape 5 m × 5.1 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenching
- Loans, loan ...
In Slovakia, launched a short-term non-bank loans, of which few people have their "take" are considered unfavorable. Often, the borrower ends up in a spiral of debt, which takes more and more onerous loan used to repay earlier loans. Calculate how many 4-
- Golden ratio
Divide line of length 526 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line.
- Wind drift
The plane flies at 450 km/h, passing distance 2100 kilometers with the wind and once again against the wind for 9 h 29 min. What is the wind speed?
- Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
The pharmacy add to 3 liters of 95-percent alcohol 5 liters of 38.04 percent alcohol. How many percent pharmacy got?
- Collecting day
At collecting day at school pupils of three classes took total of 1063 kg of paper. Class B collected half more than A Class and class C 55 kg more than B. How many kg of paper collected each class?
Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .