Equation + power - practice problems - page 3 of 7
Number of problems found: 125
- 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 - Three members GP
The sum of three numbers in GP (geometric progression) is 21, and the sum of their squares is 189. Find the numbers. - 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 - Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to the done work in 12 days?
- Block-shaped 7976
A block-shaped pool with a volume of 200m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Completing square
Solve the quadratic equation: m2=4m+20 using completing the square method - 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. - Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours long and the second pipe 9 hours longer than both pipes open simultaneously?
- 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 - Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and was then replaced by Martin. The whole work was done in 6.5 hours. Calculate how long Peter worked before being replaced by Martin. - Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Non linear eqs
Solve the system of non-linear equations: 3x²-3x-y=-2 -6x²-x-y=-7 - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament.
- Powers 3
2 to the power of n divided by 4 to the power of -3 equal 4. What is the value of n? - 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? - Domains of functions
F(x)=x²-7x and g(x)=5-x² Domain of (fg)(x) is. .. . . The domain of (f/g)(x). .. - Ellipse
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the ellipse's center. - Solve: 6632
For n ϵ N solve: 100 = (0.01n)²
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