Real numbers - practice problems - page 7 of 9
Number of problems found: 162
- Euclid1
The right triangle ABC has hypotenuse c = 20 cm. How large sections cut height hc=9 cm on the hypotenuse c? - 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. - 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 - 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? - 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. - Pool
If water flows into the pool through two inlets, it will fill for 5 hours. If the first inlet fills the pool 5 hour longer than the second, how long does it take to fill with two inlets separately? - 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? - 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? - Resistors
Two parallel resistors connected in series give the resulting resistance $R1Ω and $R2Ω. Determine the resistance of these resistors. - 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 - 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 8101 cm³. Determine the length of the edges of a cube. - Gimli Glider
Aircraft Boeing 767 lose both engines at 35000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 2100 feet and maintain constant speed 201 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - When will I be a millionaire?
Barry monthly sends 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months Barry must save to save 1000000 euros. Inflation, interest rate changes, or bank failures are ignored. - Area 4gon
Calculate the area of 4-gon, two, and the two sides are equal and parallel with lengths 18, 9, 18, and 9. Inner angles are 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? - IS triangle
Calculate the interior angles of the isosceles triangle with base 12 cm and legs 19 cm long. - 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. - Angles
Find the interior angles of a rhombus with area 72 cm² and perimeter 48 cm.
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