A river flows due south at 1.4 mi/h. In what direction should the swimmer head, at a velocity of 3 mi/h, in order to arrive at a landing point due east of his starting point? (Round your answer to one decimal place.)

Solution:

It is that a river is flowing in the south direction with a speed of 1.4 mi/h.

A swimmer wishes to cross the river in a horizontal direction so that he lands at a point which is due east of his starting point.

The speed of the swimmer is = 3 mi/h

Therefore he has to swim in such a direction that his resultant is in the direction east to his starting point.

Let this angle be θ.

Therefore, from the figure,

Therefore, the swimmer has to swim in the northeast direction making an angle of (90+27.4) = 117.4° with the direction of flow of river (i.e. south).  

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions