Power + system of equations - practice problems
Number of problems found: 29
- Coordinate 82580
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Together 81521
Pavel and Vojta were planting trees at the forestry brigade. Pavel planted two more trees than Vojta in a six-hour shift. Together, they planted 156 saplings in three such shifts. How many saplings did Pavel and Vojta plant during the brigade? - Distance 69524
The length of the Odra in Moravia is 42% of its length in Poland. The total flow length from the source to the sea is 1165 km. What is the distance in Moravia, and what is the distance in km on the Polish side? - Relative 67684
The boat moves along the river at a speed of v1 = 5km. h-1 and upstream v2 = 2km. h-1. What is the current P's and boat L's speed relative to the water?
- In a GP 72+144
In a GP, the sum of the 2nd and fifth terms is 72, and the sum of the 3rd and 6th terms is 144. Find the common ratio, find the first term, and find the sum of the first six terms - The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers. - Divide 8
Divide 6840 by x, y, and z in such a way that x has twice as much as y, who has half as much as z - The mowers
The mowers were to mow two meadows, one twice as big as the other. They divided into two equal groups in the first half of the day. One continued to mow a larger meadow and cut it all by the end of the day. The second group mowed a smaller meadow but did - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =?
- Divisors 7779
Two numbers are guessing. The second number is five times greater than the first number, and the square of the first number is equal to 3/5 of the second number. Find the sum of the two numbers and all its divisors. - Temperature 7595
Colorless liquid weighing m = 200 g is heated with constant stirring on a stove with power input P0 = 600W. 80% of the supplied energy is used to heat the liquid. Selected measured values of liquid temperature as a function of time are recorded in the t - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7 - AP RT triangle
The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area? - Highway tunnel
The company built the highway tunnel from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" rasters. After 55 business days, both parties me
- Simultaneously 5610
Two cyclists rode towards each other simultaneously from opposite ends of the 28km long route. Each covered the entire route at a constant speed, the fastest being at the finish line 35 minutes earlier. On the route, the cyclists passed each other after 1 - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Time gone
The Square of Richard's age equals the age of his mother. When he is two times older, his mom will be 7/2 times older than he. How old are Richard and his mom? - Parabola 3
Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. f: y=x²+bx+c - Welcomed 3453
The product of two numbers is equal to their sum. One of the numbers is four times larger than the other. Find these numbers. They welcomed that none of them were equal to zero.
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