Physical quantities - math word problems - page 293 of 296

Number of problems found: 5915

Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 30 degrees, |AB| = 15 cm. Calculate the volume of the prism.
An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown.
Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places.
Spherical sector
The spherical sector has axial section has an angle of α = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the surface of this spherical sector.
Sun rays
If the sun's rays are at an angle of 60°, then the famous Great Pyramid of Egypt (which is now 137.3 meters high) has a 79.3 m long shadow. Calculate the current height of the neighboring Chephren pyramid, whose shadow is measured at the same time at 78.8
Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees.
Reflector
The circular reflector throws a light cone with a vertex angle 56° and is on 24 m height tower. The axis of the light beam has the axis of the tower angle 11°. What is the maximum length of the illuminated horizontal plane?
Inclination of a hill
A skier starts down a hill of length l and an angle of inclination of 10˚. It then moves to a horizontal section of the track, which travels the same length l until it stops. Determine the coefficient of sliding friction between the skis and the snow.
Ballistic curve
The soldier fired a ballistic projectile at a 45° angle. The first half of its path it ascended, and the second half it fell. How far and how high did it reach if its average speed was 1,200 km/h and 12 seconds elapsed from the shot to impact?
Angle between lines
Calculate the angle between the following two lines: p: -4x +7y +7 =0 q: -x +4y +7=0
Deviation - slope angle
Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30° from the base plane.
Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees).
Chimney
The lower circumference of the chimney is 12.57 m, and the top circumference is 5.655 m. The slope of the walls is 87°. Find the height of the chimney.
Periodic function
Simplify by using periodicity cos 1125°
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 10 cm. Calculate the body volume.
Isosceles triangle
What are the angles of an isosceles triangle ABC if its base is long a=7 m and has an arm b=9 m?
Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went?
Raindrops
The car runs on a horizontal track at a constant speed of 20 m²-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s. a) How fast is the speed of the drops relative to the car windows? b) What is the angle of the raindro
Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the space diagonal makes an angle of 66° with the base.
Cuboid
Find the dimensions a, b, and c of a cuboid whose space diagonal is d = 6 dm and makes an angle α = 35° with edge a and an angle β = 66° with edge b.

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