What is the solution when the equation is solved for , where is a positive integer?
The initial push of a child on a swing causes the swing to travel a total of 6 feet. Each successive swing travels of the distance of the previous swing. Determine the total distance, to the nearest hundredth of a foot, a child travels in the first five swings.
Determine the total distance, to the nearest hundredth of a foot, a child travels in the first five swings.
Sonja is cutting wire to construct a mobile. She cuts 100 inches for the first piece, 80 inches for the second piece, and 64 inches for the third piece. Assuming this pattern continues, write an explicit equation for , the length in inches of the th piece. Sonja only has 40 feet of wire to use for the project and wants to cut 20 pieces total for the mobile using her pattern. Will she have enough wire? Justify your answer.
Write an explicit equation for , the length in inches of the th piece.
Determine if Sonja will have enough wire to cut 20 pieces total for the mobile using her pattern. Justify your answer.
A Foucault pendulum can be used to demonstrate that the Earth rotates. The time, , in seconds, that it takes for one swing or period of the pendulum can be modeled by the equation where is the length of the pendulum in meters and is a constant of .
The first Foucault pendulum was constructed in 1851 and has a pendulum length of 67 m. Determine, to the nearest tenth of a second, the time it takes this pendulum to complete one swing.
Another Foucault pendulum at the United Nations building takes 9.6 seconds to complete one swing. Determine, to the nearest tenth of a meter, the length of this pendulum.
Determine the time it takes for the first Foucault pendulum to complete one swing.
Determine the length of the pendulum at the United Nations building.
John and Margaret deposit $ into a savings account for their son on his first birthday. They continue to make a deposit of $ on the child's birthday, with the last deposit being made on the child's 21st birthday. If the account pays annual interest, which equation represents the amount of money in the account after the last deposit is made?
While experimenting with her calculator, Candy creates the sequence . Write a recursive formula for Candy's sequence.
Determine the eighth term in Candy's sequence.
Write a recursive formula for Candy's sequence.
Determine the eighth term in Candy's sequence.
Which equation represents a parabola with a focus of and a directrix of ?
Patricia creates a cubic polynomial function, , with a leading coefficient of 1 . The zeros of the function are 2,3 , and -6 . Write an equation for .
Sketch on the set of axes below.
Write the equation for the cubic polynomial with zeros 2, 3, and -6.
Sketch the graph of on the provided axes.
Last year, the total revenue for Home Style, a national restaurant chain, increased over the previous year. If this trend were to continue, which expression could the company's chief financial officer use to approximate their monthly percent increase in revenue? [Let represent months.]
A parabola that has a vertex at and a focus of has an equation of