Because of the high heat and low humidity in the summer in Death Valley, California, a visitor requires about one quart of water for every two miles traveled on foot. If the density of water is 0.990 g/mL at 45°C, how many kilograms of water are required for a person to walk 30 kilometers in Death Valley?

The answer to your question is   mass = 8.73 kg

Step-by-step explanation:

Data

1 quart 2 mi

density = 0.99 g/ml

total distance = 30 km

Process

1.- Convert 2 mi to km

                  1 mi 1.61 km

                  2 mi  x

                  x = (2 x 1.61)/1

                  x = 3.22 km

2.- Calculate the quarts drank

                   1 quart 3.22 km

                   x           30 km

                   x = (30 x 1)/3.22

                   x = 9.32 quarts

3.- Convert quarts to milliliters

                   1 quart 946.35 ml

                 9.32 quart x

                  x = (9.32 x 946.35) / 1

                  x = 8817 ml

4.- Calculate the grams of water

     density = mass / volume

     mass = volume x density

-Substitution

     mass = 8817 x 0.99 g/ml

-Result

     mass = 8729 g

5.- Convert to kg

     mass = 8729/1000 kg

     mass = 8.73 kg

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!