Basic functions - math word problems
Number of problems found: 2721
- 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?
On the pedestal high 4 m is a statue 2.7 m high. At what distance from the statue must the observer stand to see it at the maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
- SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer.
- Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current heig
- Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
- The roof
The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste
- Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also
- Coordinates of square vertices
I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C and D. Thanks, Peter.
- Eight blocks
Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
- Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces.
- Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality?
- Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
- Tangents to ellipse
Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1].
- Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
- What percentage
What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
- Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
- Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, c has dimensions in the ratio of 9:3:8. If you know that the diagonal wall AC is 86 cm, and the angle between AC and space diagonal AG is 25 degrees.
- Pyramid - angle
Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees.