# Physical quantity - math word problems

#### Number of problems found: 2706

- The angle of lines

Calculate the angle of two lines y=x-21 and y=-2x+14 - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20) - Decide 2

Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line - Boat

A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight? - Seawater

Seawater has a density of 1025 kg/m^{3}, ice 920 kg/m³. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge. - Ball

The soldier fired the Ball at an angle of 35° at an initial velocity of 292 m/s. Determine the length of the litter. (g = 9.81 m/s^{2}). - Divide an isosceles triangle

How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)? - Freezer

The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, 30 cm. A layer of ice of 23 mm thick was formed on the inner walls (and on the opening) of the freezer. How many liters of water will drain if we dispose the freezer? - Paper box

Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m² of the paper consumed 100 such boxes? - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Scalar dot product

Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120° - Cosine

Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544. - Gold wire

From one gram of gold was pulled wire 1.4 km length. What is its diameter if the density of Au is ρ=19.5 g/cm³? - Space vectors 3D

The vectors u = (1; 3; -4), v = (0; 1; 1) are given. Find the size of these vectors, calculate the angle of the vectors, the distance between the vectors. - Airplane navigation

An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)? - Sphere floating

Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm³. (Instructions: Calculate the average sphere density and compare it with the water density. ) - Eiffel Tower

Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material if it weighs is 2.4 kg? - Climb

Road has climbing 1:27. How big is a angle corresponds to this climbing? - Diagonals of a prism

The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal with the diagonal of the base. - Angle of diagonal

The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.

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