Quadratic equation + power - practice problems
Number of problems found: 87
- Twice squared
If the square of twice a number is 81, what is the number? Give a positive number x. - Evaluate 37
Evaluate the function K(x) = 2x²+3x-2 what is the value of K(½) - Coordinate 82580
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Quadratic equation - Viets
In the equation 3x²+bx+c=0, one root is x1 = -3/2. Determine the number c so that the number 4 is the root of the equation. Hint - use Viet's formulas.
- Two conductors
Two conductors have resistance Rs=5 ohms when connected in series and Rp=1.2 ohms when connected in parallel. Calculate the value of the resistors. - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Unknown 72884
The square root of an unknown number equals the square of 2. What is the unknown number? - Assembling 63964
Little Pavel was assembling building blocks (a cube is shaped like a cube). He wanted to build a big cube. However, he had 75 dice left, so he increased the edge by one die. Then he was missing 16 dice. How many cubes did he have in the kit? - Two expressions
When x = 3 and y = 5, 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 a rectangular shape; one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original and new garden dimensions if both gardens' areas were the same? - Circumference 40401
Calculate the diameter of a circle whose area in cm² and the circumference in cm are expressed by the same number. - 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.
- Circumference 26651
A rectangle with sides of lengths a, b (cm) has a circumference of 100 cm. The dependence of its area P (in cm2) on the number a can be expressed by the quadratic function P = sa + ta². Find the coefficients s, t. - 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? - Calculate 25111
The quadratic function has the formula y = -2x²-3x + 8. Calculate the function value in points 5, -2, and ½. - 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. - Dimensions 20553
The surface of the block is 558 cm², and its dimensions are in the ratio of 5:3:2. Calculate the volume.
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