Swimming Function

[marshall1432]

I have 2 questions i would like help with and I am including my work:

Given r(x)= x/x + 4, find r(10,000)

I then substituted 10,000 in for x and got:

r(x)= 10,000/10,000 + 4
r(x)= 10,000/10,004
i then tried to get it smaller but I ended up with:
r(x)= .997

Is this right or is there a fraction?

The second part:


The question states:

An athlete swims from point A to point B at a rate of 2 mph and runs from point B to point C at a rate of 8mph. Use the dimensions in the figure to write the time t required to reach point C as a function of x.

The picture is not showing up so ill do my best to explain.

Point A to Point C =3 miles.
Point B lies in between A and C, so that the swimmer in the pool is swimming to get out at a diagonal to start running. The distance from A to the shore is 1 mile. The distance between A and B is x and the distance between B and C is unknown.
my work:

t(x)=sqrt(2^2)+ (8^2)=C^2
t(x)=sqrt(4) + (64)= C^2
t(x)=sqrt(70)=c^2
t(x)=sqrt(70) or 8.366.

It would take the swimmer 8 minutes and 37 seconds to reach point C.

 

[jwpaine]

I have 2 questions i would like help with and I am including my work:

Given r(x)= x/x + 4, find r(10,000)

I then substituted 10,000 in for x and got:

r(x)= 10,000/10,000 + 4
r(x)= 10,000/10,004
i then tried to get it smaller but I ended up with:
r(x)= .997

Is this right or is there a fraction?

10,000/10,004 = (10,000(1/2))/(10,004(1/2)) = (5000/5002)
divide the numerator and denominator by 2 again to get it down to it's simplest form.

 

[skeeter]

The question states:

An athlete swims from point A to point B at a rate of 2 mph and runs from point B to point C at a rate of 8mph. Use the dimensions in the figure to write the time t required to reach point C as a function of x.

The picture is not showing up so ill do my best to explain.

Point A to Point C =3 miles.
Point B lies in between A and C, so that the swimmer in the pool is swimming to get out at a diagonal to start running. The distance from A to the shore is 1 mile. The distance between A and B is x and the distance between B and C is unknown.

you are not solving for a specific time ... you have been asked to write the total time to travel from A to C as a function of the distance x.

A to C = 3 miles
A to B = x miles
A to shoreline's closest point, call it point D = 1 mile

using Pythagoras ...

D to B = sqrt(x² - 1)

B to C = sqrt(8) - sqrt(x² - 1)

the basic equation is ... time in hours = (distance in miles)/(speed in mph), and you have two different legs for the trip.

t(x) = x/2 + [sqrt(8) - sqrt(x² - 1)]/8

 

[marshall1432]

Answers

Ok, so the answer to the 1st question is: 5000/5002= 2500/2501

The 2nd answer is the function you gave me. That is the final function value?

 

[skeeter]

Re: Answers

Ok, so the answer to the 1st question is: 5000/5002= 2500/2501

The 2nd answer is the function you gave me. That is the final function value?

what do you mean by "final" function value? this function has an infinite number of values since x can be any value between 1 and 3.