# Quadratic equation + system of equations - problems

- 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 - Pool

If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately? - Cuboid

Cuboid with edge a=24 cm and body diagonal u=50 cm has volume V=17280 cm^{3.}Calculate the length of the other edges. - Right triangle Alef

The area of a right triangle is 294 cm^{2,}the hypotenuse is 35 cm long. Determine the lengths of the legs. - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Rectangle SS

Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle. - Trains

From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains. - Pumps

The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? - RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments? - Circle

Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Euler problem

Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels? - Sequence

In the arithmetic sequence is given: S_{n}=2304, d=2, a_{n}=95 Calculate a_{1}and n. - Sum-log

The sum of two numbers is 32, the sum of their logarithms (base 10) is 2.2. Determine these numbers. - The hall

The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m^{2.}What were the original dimensions of the hall? - Golden ratio

Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line. - Diagonal 20

Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be? - Rectangle vs square

One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle. - Garden

The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m^{2.}Calculate the dimensions of the garden.

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