Real numbers + square (second power, quadratic) - practice problems - page 2 of 3
Number of problems found: 47
- Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Described
Calculate the perimeter of the circle described by a triangle with sides 191, 428, 385. - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r² - Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18
- Hole
We will drill the cylinder shape hole in the cube's center with an edge 14 cm. The volume of the hole must be 27% of the cube. What should drill diameter be chosen? - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the center of the circle S[x0, y0] and the radius of the circle r. - Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately? - Geometric mean
Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines. - Right Δ
A right triangle has the length of one leg 72 cm and the hypotenuse 90 cm size. Calculate the height of the triangle.
- Garden
How many steps of 76 cm circumvent square garden with area 1.8 ha? - Inflation
Once upon a time, the tsar owned a money printer and printed and printed. Printing money prices went up in the first year 2.7 %, in the second 2.1%, in the third 3.6%, and in the fourth 5.4%. Then tsar failed in the election. Calculate the average annual - Short cut
Imagine that you are going to a friend. That path has a length 120 meters. Then turn doprava and go other 630 meters, and you are at a friend's. The question is, how much will the journey be shorter if you go direct across the field? - Cylinders
The area of the side of two cylinders is the same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume, and by how much? - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
- Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - 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.
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