Real numbers - practice problems - page 8 of 9
Number of problems found: 162
- Euclid1
The right triangle ABC has hypotenuse c = 20 cm. How large sections cut height hc=9 cm on the hypotenuse c?
- Events
Event W has the probability of 0.57. What is the probability that the event W occurs in 2, 6, 5 try?
- Hypotenuse and height
In a right triangle is length of the hypotenuse c = 54 cm and height hc = 25 cm. Determine the length of both triangle legs.
- 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.
- Pyramid roof
1/3 of the area of the roof-shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still need to be covered?
- The www server
Calculate how many average minutes the web server is unavailable a year if the availability is 99.9999%.
- Rectangle
The rectangle is 21 cm long and 38 cm wide. Find the radius of the circle circumscribing the rectangle.
- Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface?
- Area of RT
Calculate the right triangle area in which the hypotenuse has length 14 and one hypotenuse segment has length 5.
- 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
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.
- Spherical cap
From the sphere with a radius of 21 was a truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
- Regular 5-gon
Calculate the area of the regular pentagon with side 16 cm.
- 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.
- IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long.
- 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.
- 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?
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