Expression of a variable from the formula - high school - math problems
- Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
- Slow saving in banks
How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest?
- What is
What is the annual percentage increase in the city when the population has tripled in 20 years?
- Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure?
- Triangle from median
Calculate the perimeter, content, and magnitudes of the remaining angles of triangle ABC, given: a = 8.4; β = 105° 35 '; and median ta = 12.5.
- Closed circuit
In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage.
- Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
- An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
- Compound interest 4
3600 dollars is placed in an account with an annual interest rate of 9%. How much will be in the account after 25 years, to the nearest cent?
- Two groves
Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
- Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
- Hemisphere cut
Calculate the volume of the spherical layer that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.
- Five element
The geometric sequence is given by quotient q = 1/2 and the sum of the first six members S6 = 63. Find the fifth element a5.
- Horses playground
The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
- Sum of the seventeen numbers
The sum of the 17 different natural numbers is 154. Determine the sum of the two largest ones.
- Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
- Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
- Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
- Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
- Tropics and polar zones
What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'