Bill is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool, he will complete a 250-yard warmup and then swim laps in a lane that is 25 yards long. If Bill swims at the indoor pool at his gym, he will complete a 300-yard warmup, plus a main set that consists of 20 yards per lap. If Bill swims the correct number of laps, he can complete the same distance in either pool. How long will Bill's workout be in total?

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

a ≈ 172.05

step-by-step explanation:

the pictures.