Equation + power - practice problems - page 2 of 7
Number of problems found: 125
- In a GP 72+144
In a GP, the sum of the 2nd and fifth terms is 72, and the sum of the 3rd and 6th terms is 144. Find the common ratio, find the first term, and find the sum of the first six terms - Supported 61914
A person lifts a stone weighing 285 kg with the help of a lever that is supported at a distance of 30 cm from the stone. A person acts on the lever at a distance of 90 cm from the support. How much force does a person have to use to lift a stone? - Jointly and cube power
If y varies jointly as x and the cube of z and y=16 when x=4 and z=2, find an equation representing this relationship. a. y=xz b. y = 2xz³ c.y = 2kx/z³ d.y = xz³/2 - 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. - Find x 2
Find x, y, and z such that x³+y³+z³=k for each k from 1 to 100. Write down the number of solutions.
- 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. - Cuboid and ratio
A cuboid has a volume of 810 cm³. The lengths of edges from the same vertex are in a ratio of 2:3:5. Find the dimensions of a cuboid. - Suppose
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? - One third power
Which equation justifies why ten to the one-third power equals the cube root of ten? - Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
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