Real numbers + triangle - practice problems - last page
Number of problems found: 34
- Gimli Glider
Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - Slope
What is the slope of a line with an inclination 3.96 rad? - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Pyramid roof
1/3 of the area of the roof-shaped regular tetrahedral pyramid with base edge 8 m and height of 4 m is already covered with roofing. How many square meters still need to be covered?
- ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and area 415 cm². Calculate the volume of a cone. - Rectangle
The rectangle is 21 cm long and 38 cm wide. Find the radius of the circle circumscribing the rectangle. - Rotation
The right triangle with legs 11 cm and 18 cm rotates around the longer leg. Calculate the volume and surface area of the formed cone. - Area of RT
Calculate the right triangle area that hypotenuse has length 14, and one hypotenuse segment has length 5.
- Area of RT
The right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of this triangle. - Axial section
The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Regular 5-gon
Calculate the area of the regular pentagon with side 16 cm. - Movement
From the crossing of two perpendicular roads started two cyclists (each on a different road). One runs at an average speed of 28 km/h, and the second 24 km/h. Determine the distance between them after 45 minutes of cycling. - Forces
In point, O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3.
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