Find the common difference in the arithmetic sequence, an, in which a3=11 and a12=74.<br><br>

A boat takes 55 hours to go 20 miles upstream. It can go 50 miles downstream in the same time. Find the rate of the current and

sergey [27]

We have two unknowns and two equations so we can solve this question.

The two unknowns are C (speed of current) and B (speed of boat)

Our boat traveled 20 miles in 55 hours going upstream which means it traveled .36 miles in 1 hour; in other words .36mph . Our boat traveled 50 miles in 55 hours going downstream; in other words .909mph .

We can assume that because the boat managed to cover distance in the direction it was headed upstream it must have been going faster than the current so it moved at the speed of the boat minus the speed of the current and when it was going downstream it moved at the speed of the boat plus the speed of the current.

This gives us;

.36mph = B - C

.909mph= B + C

We solve for this system of equations and it simplifies to 1.27mph=2B

and B= .636mph

Plug this into one of the equations and we get that C= .2727mph

This means that the boat moved at .363mph and the current moved at .2727mph.

6 0

3 years ago

A dilation is an enlargement if the scale factor is _____ between 0 and 1. greater than 1. less than 0. equal to 1.

boyakko [2]

Dilation is one of the several means by which we can transform a graph. A function is dilated when is stretched away from an axis or compressed towards an axis. So this means there are 2 types of dilation: a) Stretch (Enlargement) and b) Compression.

Depending on the direction of Dilation, we have Horizontal Dilation and Vertical Dilation.

For a function y = f(x), horizontal dilation is achieved when x is replaced by $\frac{x}{A}$ and vertical dilation is achieved when y is replaced by $\frac{y}{A}$ where A is the scale factor.