# Algebra - examples

- Height as diameter of base

The rotary cylinder has a height equal to the base diameter and the surface of 471 cm^{2.}Calculate the volume of a cylinder. - Cross road

From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes? - Isosceles triangle

The circumference of the isosceles triangle is 32.5 dm. Base length is 153 cm. How long is the leg of this triangle? - Tractors

5 tractors will plow the field for 8 hours. In 2 hours, 1 tractor broke down. How long do the remaining tractors complete the plow? - Rectangle - area, perimeter

The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle. - Two buses

The first bus runs 15 minutes the second bus runs after 21 minutes. Together they both leave at 7:00 on Monday. When and what day will they meet? - Budget plan

In the construction of the building, the planned budget exceeded 13%, which was 32,500 euros. How many euros cost built the building? - Container

The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have? - Barrel with water

The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel. - Bricklayers

Seven bricklayers will build the house in 630 days. How many bricklayers do we need to take after 150 days to complete the building for (additional) 336 days? - Equations - simple

Solve system of linear equations: x-2y=6 3x+2y=4 - Integer

Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6. - Slant height

The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone - Eq with reciprocal

Solve given equation with reciprocal member: a-6/a+10=4/8 - A perineum

A perineum string is 10% shorter than its original string. The first string is 24, what is the 9th string or term? - Together 3

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together? - Nineteenth member

Find the nineteenth member of the arithmetic sequence: a1=33 d=5 find a19 - Equatiom

Solve equation with negatives: X/(-5) + 2 = -9 - Minimum surface

Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed. - 3d printer

3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm^{3.}Find the length of m = 5 kg spool filament. (how to calculate length)

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