Quadratic equation + system of equations - math problems
- Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
- The tourist
The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. After a 4 km walk, however, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re
- TV competition
In the competition, 10 contestants answer five questions, one question per round. Anyone who answers correctly will receive as many points as the number of competitors answered incorrectly in that round. One of the contestants after the contest said: We
- Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
- Rectangle field
The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
- Three parallels
The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
- Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
- Faces diagonals
If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
- Two chords
Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
- Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
- GP - three members
The second and third of a geometric progression are 24 and 12(c+1) respectively, given that the sum of the first three terms of progression is 76 determine value of c
- Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
- Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
- Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
- Two cyclists 2
At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,
- Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
- MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
- Two resistors
Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
- Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
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