Real numbers - high school - practice problems - page 2 of 4
Number of problems found: 73
- Exponential equation
Solve exponential equation (in real numbers): 23x-6=9 - Wire D
Wire length 1 m is bent to form a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Permutations with repetitions
How many times can the input of 1.2.2.3.3.3.4 be permutated into four digits, three digits, and two digits without repetition? Ex: 4 digits = 1223, 2213, 3122, 2313, 4321. . etc 3 digits = 122.212.213.432. . etc 2 digits = 12, 21, 31, 23 I have tried the - Determine 80662
Given the function y = x² - 4x + 3. Determine all real numbers z such that g(x) = g(-2).
- Crystal
The crystal grows every month 1.2 permille of its mass. How many months to develop a crystal from weight 177 g to 384 g? - Sequentially 35731
There are 6 different tickets marked with numbers 1 to 6 in the pocket. In how many different ways can we sequentially, taking into account the order, choose three of them, if the chosen tickets return to the pocket? - Trigonometric functions
In the right triangle is: tg α= frac(4) 2 Find the value of s and k: sin α= (s)/(√ 20) cos α= (k)/(√ 20) - Sea
How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Building
How high is the building that throws horizontal shadow 85.6 m long at angle 34°12'?
- Described
Calculate the perimeter of the circle described by a triangle with sides 191, 428, 385. - Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Triangle TBC
TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB? - 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 - Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence?
- Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18 - Rectangle
In rectangle ABCD with sides, |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio (|PB|)/(|DP|). - 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? - 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.) - 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.
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