Real numbers - practice problems - page 6 of 9

Number of problems found: 165

Marlon
Marlon drew a scale drawing of a summer camp. In real life, the sand volleyball court is 8 meters wide. It is 4 centimeters wide in the picture. What is the drawing's scale factor? Simplify your answer and write it as a ratio, using a colon.
Crystal
The crystal grows every month at 1.2 permille of its mass. How many months does it take to develop from weight 177 g to 384 g?
On the number line
What number is exactly in the middle between 9.8 and -2.4 on the number line?
An aquarium
An aquarium tank that measures 2.4 m high, 6 m long, and 1.5 m wide and is filled with water. The density of water is 1,000 kg/m³. What is the mass of the water in the tank?
Number distant equally
Which number is also distant from the numbers 5.3 and 7.7 on the number line?
2x cone
A circular cone of height 36 cm is cut by a plane parallel to the base, dividing it into two smaller cones of equal volume. Calculate the height of the smaller cone.
Scientific notation
Approximately 7.5x10⁵ gallons of water flow over a waterfall each second. There are 8.6x10⁴ seconds in 1 day. Select the approximate amount of water flowing over the waterfall in 1 day.
Sea
How far can you see from the top of a ship's mast that is 9 metres above sea level? (The Earth's radius is 6370 km km.)
Trigonometric functions
In a right triangle, it holds that: tg α= frac(4) 2 Find the values of s and k: sin α= (s)/(√ 20) cos α= (k)/(√ 20)
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
Building
How high is the building that throws horizontal shadow 85.6 m long at angle 34°12'?
Described
Calculate the circumference of the circle circumscribed about a triangle with sides 82, 495, and 438.
Rectangle
In rectangle ABCD with sides |AB|=19, |AD|=19, a perpendicular is drawn from point A to diagonal BD, meeting it at point P. Determine the ratio r = (|PB|)/(|DP|).
Pumps
A tank is filled by two pumps working together in 23 minutes. The first pump alone fills the tank 37 minutes faster than the second pump alone. How long does it take the first pump to fill the tank on its own?
Tinsmith
A tinsmith constructs a chimney pipe 186 cm long and 16 cm in diameter. The pipe is made from a flat sheet with an overlap of $x cm at the seam. What dimensions must the sheet have?
Square 2
Points D[10,-8] and B[1,-10] are opposite vertices of square ABCD. Calculate the area of square ABCD.
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
Integer part system
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.)
Hypotenuse and height
In a right triangle is length of the hypotenuse c = 195 cm and height h_c = 70 cm. Determine the length of both triangle legs.

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