Real numbers - practice problems - page 8 of 9
Number of problems found: 161
- Spherical cap
From the sphere with a radius of 26 was a truncated spherical cap. Its height is 2. What part of the volume is a spherical cap from the whole sphere? - 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. - Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 119 m. How far is it from the other end of the fence? - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Rectangle
The rectangle is 21 cm long and 38 cm wide. Find the radius of the circle circumscribing the rectangle. - Pyramid roof
3/5 of the area of the roof-shaped regular tetrahedral pyramid with base edge 9 m and height of 6 m is already covered with roofing. How many square meters still need to be covered? - Gutter
How much metal is needed to produce 60 pieces of gutter pipes with the diameter 17 cm and length of 6 m? The plate bends add 6% of the material.
- 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 an area of 415 cm². Calculate the volume of a cone. - Area of RT
Calculate the right triangle area in which the hypotenuse has length 14 and one hypotenuse segment has length 5. - IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long. - Movement
Two cyclists (each on a different road) started from the crossing of two perpendicular roads. One runs at an average speed of 16 km/h, and the second 25 km/h. Determine the distance between them after 20 minutes of cycling. - Regular 5-gon
Calculate the area of the regular pentagon with side 16 cm. - 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. - Axial section
The axial section of the cone is an equilateral triangle with an area 208 km². Calculate the volume of the cone.
- 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. - Triangle TBC
TBC is an isosceles triangle with base TB with base angle 75° and legs length |TC| = |BC| = 35. How long is the base TB? - Pump
What power does a pump output to move 1060 hl of water to a height of 43 m for 8 hours? - Slope
What is the slope of a line with an inclination -325°? - Copper winding
Calculate the current flowing through the copper winding at an operating temperature of 70°C Celsius if the winding diameter is 1.128 mm and the coiled length is 40 m. The winding is connected to 8V.
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