Question

Suppose the line y = 2.8333x - 22.4967 describes the relation between the​ club-head speed​ (in miles per​ hour), x and the distance a golf ball travels​ (in yards), y.

(a) Predict the distance a golf ball will travel if the club-head speed is 100 mph.

(b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual?

(c) The golf ball will travel 260.8 yards. (Round to the nearest tenth as needed.)

(d) The residual is:_________ (Round to the nearest tenth as needed.)

Answer 1

a)
`y=260.8333~yd`

b)
`\Delta d=4.1667~yd`

c)
`y=260~yd`

d)
`\Delta y'=0.8333~yd`

Explanation:

Given:

equation of line,
`y=2.8333x-22.4967`

x = club-head speed​ (in miles per​ hour)

y = the distance a golf ball travels​ (in yards)

a)

x = 100 mph

Then the distance travelled by the ball:

(put the given value of x in the above eq.)

`y=2.8333* 100-22.4967`

`y=260.8333~yd`

b)

If the observed distance in the above case comes out to be 265 yards then the residual value will be:

`\Delta d=265-260.8333`

`\Delta d=4.1667~yd`

c)

From the calculated value when rounding it to the nearest tenth:

`y=260~yd`

d)

The residual on rounding the calculated value to the nearest tenth:

`\Delta y'=260.8333-260`

`\Delta y'=0.8333~yd`

Answer 2

c) The golf ball will travel 260.8 yards.

d) Hence the residual is 4.2 yards.

Explanation:

c) y' = 2.8333x - 22.4967

Now the golf ball will travel
`= 2.8333*100 - 22.4967`= 260.8 yards

here y'= 260.8 yards.

d) The residual is : y - y' = 265 - 260.8 = 4.2 yards.