Real numbers - practice problems - page 7 of 9
Number of problems found: 165
- Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the centre S[x₀, y₀] and the radius r of the circle. - Euclid1
The right triangle ABC has hypotenuse c = 20 cm. How large sections cut height hc=9 cm on the hypotenuse c? - Rail turn
The curve radius on a railway line is 532 m. The length of the rail track along this curve is 818 m. What is the angle ASB in degrees, where A and B are the endpoints of the curve and S is the centre of the arc? - Inequality proof
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 - Geometric mean
Calculate the geometric mean of 15.2 and 25.6. Also determine the mean by geometric construction, treating 15.2 and 25.6 as lengths of line segments. - 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. - Garden
How many steps of 64 cm each are needed to walk around the perimeter of a square garden with an area of 1.5 ha? - Pool
Water flows into a pool through two inlets and fills it in 5 hours. If the first inlet alone takes 5 hours longer than the second inlet alone, how long does each inlet take to fill the pool on its own? - 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. - Resistors
Two resistors connected in parallel give a combined resistance of $R1 Ω, and connected in series give a combined resistance of $R2 Ω. Determine the resistance of each resistor. - Short cut
Imagine that you are going to a friend. That path has a length of 120 meter. 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 directly across the field? - Inflation
Once upon a time, a ruler had a printing press and printed money endlessly. As a result, prices rose by 2.7% in the first year, 2.1% in the second, 3.6% in the third, and 5.4% in the fourth. The ruler then lost an election. Calculate the average annual in - 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? - Cube in a sphere
A cube is inscribed in a sphere with volume 8101 cm³. Determine the edge length of the cube. - Gimli Glider
A Boeing 767 loses both engines at an altitude of 35000 feet. The captain maintains optimal gliding conditions, losing 2100 feet per minute while maintaining a constant airspeed of 201 knots. Calculate how long it takes for the plane to reach the ground f - Square
Points A[9,9] and B[-4,1] are adjacent vertices of square ABCD. Calculate the area of square ABCD. - When will I be a millionaire?
Peter sends 220 euros to the bank each month, which bears interest at 2.9% p.a. Calculate how many months Peter must save to accumulate 33000 euros. Ignore inflation, changes in interest rates, and bank failures. - Area 4gon
Calculate the area of a parallelogram with two pairs of equal parallel sides of lengths 18 and 9, and interior angles of 45°, 135°,45°, 135°. - Hole
We will drill the cylinder shape hole in the cube's center with an edge 16 cm. The volume of the hole must be 10% of the cube. What should drill diameter be chosen?
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