Expression of a variable from the formula - high school - math problems
Number of problems found: 401
By what percentage does the sound intensity increase if the sound intensity level increases by 1 dB?
- Sphere cut
A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the volume of the segment. What is the distance of the cutting plane from the center of the sphere?
- Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?
- Cuboid diagonals
The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
- Coils of transformer
The primary coil of the transformer has 400 turns, a current of 1.5 A passes through it and is connected to a voltage of 220 V. For the secondary coil, find the voltage, current, and a number of turns if the transformation ratio k = 0.1.
- Equilateral cone
We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?
- On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
- Calculate 7
Calculate the height of the trapezoid ABCD, where coordinates of vertices are: A[2, 1], B[8, 5], C[5, 5] and D[2, 3]
- Five circles
On the line segment CD = 6 there are 5 circles with radius one at regular intervals. Find the lengths of the lines AD, AF, AG, BD, and CE
- What are
What are the four terms between 4 and 19?
- Insert 3
Insert five arithmetic progression members between -7 and 3/2.
- Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
- Growth of wood
The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
- Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m3 of soil were excavated when digging the pit?
- 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?
- Lookout tower
How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
- The cylinder
The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder.
- 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.
- Dimensions of the trapezoid
One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2