Real numbers - practice problems - page 6 of 9
Number of problems found: 161
- Cubes
Cube, which consists of 8 small cubes with edge 1 dm, has volume: - Triangle ABC
Calculate the sides of the triangle ABC with an area of 725 cm², and if sides are in a ratio a: b: c = 9:19:11 - Tinsmith
Tinsmith constructs chimney pipe 186 cm long and 16 cm wide. A pipe is made from the plate overlap at the joint and needs to add $x cm width of the plate. What dimensions of the sheet will have to be prepared for the construction? - Described
Calculate the perimeter of the circle described by a triangle with sides 82, 495, 438. - 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 - 3N on the number axis
The line represents the number axis, and the marked points correspond to the numbers a, - a, and a + 1, but in no particular order. Construct the points that correspond to the numbers 0 and 1. Discuss all the possibilities. - Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Inequality 7320
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - 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. - Rail turn
The curve radius on the railway line is 532 m. The length of the rail track on it is 818 m. How many degrees is the angle ASB if A and B are boundary points and S is the center of the arc curve? - Pumps
The tank is filled with two pumps in 23 minutes. The first pump is filled in 37 minutes earlier than the second one. How many minutes is filled with the first pump? - 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. - Garden
The square garden area is 2/9 of a triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing are needed to fence a square garden? - Garden
How many steps of 64 cm circumvent the square garden with area 1.5 ha? - Open intervals
Open intervals A = (x-2; 2x-1) and B = (3x-4; 4) are given. Find the largest real number for which A ⊂ B applies. - 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 - Cylinders
The area of the side of two cylinders is the same rectangle of 48 cm × 38 cm. Which cylinder has a larger volume, and by how much? - Rhombus ABCD
Rhombus ABCD, |AC| = 63 cm, |BD| = 50 cm. Calculate the perimeter of the rhombus ABCD. - Diagonals of the rhombus
Calculate the height of the rhombus whose diagonals are 18 cm and 6 cm. - Resistors
Two parallel resistors connected in series give the resulting resistance $R1Ω and $R2Ω. Determine the resistance of these resistors.
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