Square (second power, quadratic) - math word problems
Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
- Triangular pyramid
A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
- The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
- Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
- The schoolyard
The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m2 and has a square shape again. How many meters was each side of the yard enlarged?
- Evaluate 5
Evaluate expression x2−7x+12x−4 when x=−1
- The parabolic segment
The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
- The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
Simplify powers multiplication: (3+22)(5-42)
- The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
- Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long?
- Completing square
Solve the quadratic equation: m2=4m+20 using completing the square method
- Cube surface and volume
The surface of the cube is 500 cm2, how much cm3 will be its volume?
- Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
- Area to volume
If the surface area of a cube is 486, find its volume.
- Substitution method
Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
- A tile
A tile setter is covering 5ft by 5ft square shower wall. Each tile covers 4 5/8in by 4 5/8in square. How many rows of tile are needed to reach 5ft? How many tiles are needed to cover 5ft by 5ft square
- Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
- A car
A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case!