Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. if y = –7 when x = –2, and y = 5 when x = 1, express y in terms of x. show your work.

Step-by-step explanation:

If y is directly proportional to x, then

where, a is constant of proportionality.

If y is inversely proportional to x, then

where, b is constant of proportionality.

It is given that y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x.

           ..... (1)

We have y=-7 at x=-2.

Multiply both sides by 2.

                 .... (2)

We have y=5 at x=1.

                .... (3)

Add equation (2) and (3).

Divide both sides by -3.

The value of a is 3.

Substitute a=3 in equation (3).

The value of b is -2.

Substitute a=3 and b=-2 in equation (1).

Therefore the required equation is .

b = 4 , c = 8

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = , then

sin30° = = = ( cross- multiply )

c = 8

Using Pythagoras' identity in the right triangle

b² + 4² = 8²

b² + 16 = 64 ( subtract 16 from both sides )

b² = 48 ( take the square root of both sides )

b = = = 4