Begin6°. The edges a, b, c of a right parallelepiped are given. Find the volume V = a·b·c and the surface area S = 2·(a·b + b·c + a·c) of the right parallelepiped.

Begin7°. Given the radius R of a circle, find the length L of the circumference and the area S of the circle:

L = 2·π·R, S = π·R².

Use 3.14 for a value of π.

Begin8°. Given two numbers a and b, find their average: (a + b)/2.

Begin9°. Given two nonnegative numbers a and b, find their geometrical mean (a square root of their product): (a·b)^1/2.

Begin10°. Two nonzero numbers are given. Find the sum, the difference, the product, and the quotient of their squares.

Begin11°. Two nonzero numbers are given. Find the sum, the difference, the product, and the quotient of their absolute values.

Begin12°. The legs a and b of a right triangle are given. Find the hypotenuse c and the perimeter P of the triangle:

c = (a² + b²)^1/2, P = a + b + c.

Begin13°. Given the radiuses R₁ and R₂ of two concentric circles (R₁ > R₂), find the areas S₁ and S₂ of the circles and the area S₃ of the ring bounded by the circles:

S₁ = π·(R₁)², S₂ = π·(R₂)², S₃ = S₁ − S₂.

Use 3.14 for a value of π.

Begin14°. Given the length L of a circumference, find the radius R and the area S of the circle. Take into account that L = 2·π·R, S = π·R². Use 3.14 for a value of π.

Begin15°. Given the area S of a circle, find the diameter D and the length L of the circumference. Take into account that L = π·D, S = π·D²/4. Use 3.14 for a value of π.

Begin16°. Two points with the coordinates x₁ and x₂ are given on the real axis. Find the distance between these points: |x₂ − x₁|.

Begin17°. Three points A, B, C are given on the real axis. Find the length of AC, the length of BC, and the sum of these lengths.

Begin18°. Three points A, B, C are given on the real axis, the point C is located between the points A and B. Find the product of the length of AC and the length of BC.

Begin19°. The coordinates (x₁, y₁) and (x₂, y₂) of two opposite vertices of a rectangle are given. Sides of the rectangle are parallel to coordinate axes. Find the perimeter and the area of the rectangle.

Begin20°. The coordinates (x₁, y₁) and (x₂, y₂) of two points are given. Find the distance between the points:

((x₂ − x₁)² + (y₂ − y₁)²)^1/2.

Begin21°. The coordinates (x₁, y₁), (x₂, y₂), (x₃, y₃) of the triangle vertices are given. Find the perimeter and the area of the triangle using the formula for distance between two points in the plane (see Begin20). The area of a triangle with sides a, b, c can be found by Heron formula:

S = (p·(p − a)·(p − b)·(p − c))^1/2,

where p = (a + b + c)/2 is the half-perimeter.

Begin22°. Exchange the values of two given variables A and B. Output the new values of A and B.

Begin23°. Variables A, B, C are given. Change values of the variables by moving the given value of A into the variable B, the given value of B into the variable C, and the given value of C into the variable A. Output the new values of A, B, C.

Begin24°. Variables A, B, C are given. Change values of the variables by moving the given value of A into the variable C, the given value of C into the variable B, and the given value of B into the variable A. Output the new values of A, B, C.

Begin25°. Given an independent variable x, find the value of a function y = 3x⁶ − 6x² − 7.

Begin26°. Given an independent variable x, find the value of a function y = 4(x−3)⁶ − 7(x−3)³ + 2.

Begin27°. Given a number A, compute a power A⁸ using three multiplying operators for computing A², A⁴, A⁸ sequentially. Output all obtained powers of the number A.

Begin28°. Given a number A, compute a power A¹⁵ using five multiplying operators for computing A², A³, A⁵, A¹⁰, A¹⁵ sequentially. Output all obtained powers of the number A.

Begin29°. The angle value α in degrees (0 ≤ α < 360) is given. Convert this value into radians. Take into account that 180° = π radians. Use 3.14 for a value of π.

Begin30°. The angle value α in radians (0 ≤ α < 2·π) is given. Convert this value into degrees. Take into account that 180° = π radians. Use 3.14 for a value of π.

Begin31°. A Fahrenheit temperature T is given. Convert it into a centigrade temperature. The centigrade temperature T_C and the Fahrenheit temperature T_F are connected as:

T_C = (T_F − 32)·5/9.

Begin32°. A centigrade temperature T is given. Convert it into a Fahrenheit temperature. The centigrade temperature T_C and the Fahrenheit temperature T_F are connected as:

T_C = (T_F − 32)·5/9.

Begin33°. X kg of sweet cost A euro. Find the cost of 1 kg and Y kg of the sweets (positive numbers X, A, Y are given).

Begin34°. X kg of chocolates cost A euro and Y kg of sugar candies cost B euro (positive numbers X, A, Y, B are given). Find the cost of 1 kg of the chocolates and the cost of 1 kg of the sugar candies. Also determine how many times the chocolates are more expensive than the sugar candies.

Begin35°. A boat velocity in still water is V km/h, river flow velocity is U km/h (U < V). The boat goes along the lake during T₁ h and then goes against stream of the river during T₂ h. Positive numbers V, U, T₁, T₂ are given. Find the distance S covered by the boat (distance = time · velocity).

Begin36°. The velocity of the first car is V₁ km/h, the velocity of the second car is V₂ km/h, the initial distance between the cars is S km. Find the distance between the cars after T hours provided that the distance is increasing. The required distance is equal to a sum of the initial distance and the total distance covered by the both cars (total distance = time · total velocity).

Begin37°. The velocity of the first car is V₁ km/h, the velocity of the second car is V₂ km/h, the initial distance between the cars is S km. Find the distance between the cars after T hours provided that at the start time the distance is decreasing. This distance is equal to an absolute value of a difference between the initial distance and the total distance covered by the both cars.

Begin38°. Solve a linear equation A·x + B = 0 with given coefficients A and B (A is not equal to 0).

Begin39°. Solve a quadratic equation A·x² + B·x + C = 0 with given coefficients A, B, C (A and the discriminant of the equation are positive). Output the smaller equation root and then the larger one. Roots of the quadratic equation may be found by formula

x_1, 2 = (−B ± (D)^1/2)/(2·A),

where D = B² − 4·A·C is a discriminant.

Begin40°. Solve a system of linear equations

A₁·x + B₁·y = C₁,
A₂·x + B₂·y = C₂

with given coefficients A₁, B₁, C₁, A₂, B₂, C₂ provided that the system has the only solution. Use the following formulas:

x = (C₁·B₂ − C₂·B₁)/D, y = (A₁·C₂ − A₂·C₁)/D,
where D = A₁·B₂ − A₂·B₁.

Last revised:
01.01.2024