Square root + expression of a variable from formula - examples
- Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
The cuboid has a surface area 7705 cm2, the length of its edges are in the ratio 1:4:5. Calculate the volume of the cuboid.
- Square diagonal
Calculate length of the square diagonal if the perimeter is 476 cm.
- IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
- R Trapezium
Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
- Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m.
If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
- Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
- Trapezoid 15
Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
- Body diagonal
Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base,
- Cube 8
The surface of the cube is 0.54 m2. Calculate the length of the cube edge.
- Triangle KLM
In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
- Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
- Gasoline tank cylindrical
What is the inner diameter of the tank, which is 8 m long and contains 40 cubic cubic meters of gasoline?