Quadratic equation + third power - practice problems
Number of problems found: 53
- Two expressions
When x = 3 and y = 5, by how much does the value of 3x² – 2y exceed the value of 2x² – 3y?
- Given 2
Given g(x)=x2+x+1 where x=t². What is g(t²)?
- Two gardens
The flower garden has a square shape. The new garden has the shape of a rectangle, and one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original garden dimensions and the new garden if both gardens' area i
- The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.
- Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
- 1 page
One page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?
- Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube.
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?
- Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
- 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. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
- Three members GP
The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
- Completing square
Solve the quadratic equation: m2=4m+20 using completing the square method
- 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?
- Substitution method
Solve goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2
- Non linear eqs
Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
- AP RT triangle
The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area?
- Domains of functions
F(x)=x2-7x and g(x)=5-x² Domain of (fg)(x) is. .. . . Domain of (f/g)(x). ..
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
- Find the
Find the number x, which if it increases by 2, then its square increases by 21 percent.
- Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
Looking for help with calculating roots of a quadratic equation? Quadratic Equations Problems. Third power - practice problems.