Question

The pressure at sea level is 111 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 232323 meters, the pressure around her is 3.33.33, point, 3 atmospheres. The pressure ppp in atmospheres is a function of xxx, the depth in meters.

Answer 1

p=0.1x+1

Explanation:

The pressure increases at a constant rate as depth increases, so we're dealing with a linear relationship.

We could write the desired formula in slope-intercept form: p=\greenD mx+\maroonD bp=mx+bp, equals, start color #1fab54, m, end color #1fab54, x, plus, start color #ca337c, b, end color #ca337c. In this form, \greenD mmstart color #1fab54, m, end color #1fab54 gives us the slope of the graph of the function and \maroonD bbstart color #ca337c, b, end color #ca337c gives us the yyy-intercept. Our goal is to find the values of \greenD mmstart color #1fab54, m, end color #1fab54 and \maroonD bbstart color #ca337c, b, end color #ca337c and substitute them into this formula.

Hint #22 / 3

We know that the pressure at sea level is 111 atmosphere, so the yyy-intercept \maroonD{b}bstart color #ca337c, b, end color #ca337c is \maroonD{1}1start color #ca337c, 1, end color #ca337c, and our function looks like p=\greenD{m}x+\maroonD{1}p=mx+1p, equals, start color #1fab54, m, end color #1fab54, x, plus, start color #ca337c, 1, end color #ca337c.

We also know that at a depth of 232323 meters, the pressure is 3.33.33, point, 3 atmospheres, which means when x=23x=23x, equals, 23, p=3.3p=3.3p, equals, 3, point, 3. We can use this and the yyy-intercept to find \greenD{m}mstart color #1fab54, m, end color #1fab54:

\begin{aligned} \greenD{m}&=\dfrac{p_2-p_1}{x_2-x_1} \\\\ &=\dfrac{3.3-1}{23-0} \\\\ &=\dfrac{2.3}{23} \\\\ &=\greenD{0.1} \end{aligned}

m

​

=

x

2

​

−x

1

​

p

2

​

−p

1

​

​

=

23−0

3.3−1

​

=

23

2.3

​

=0.1

​

This means pressure increases at a rate of 0.10.10, point, 1 atmospheres per meter.

Hint #33 / 3

Since \greenD{m}=\greenD{0.1}m=0.1start color #1fab54, m, end color #1fab54, equals, start color #1fab54, 0, point, 1, end color #1fab54 and \maroonD{b}=\maroonD{1}b=1start color #ca337c, b, end color #ca337c, equals, start color #ca337c, 1, end color #ca337c, the desired formula is:

p=\greenD{0.1} x + \maroonD{1}p=0.1x+1

Answer 2

we have P(x) = mx + 1

Explanation:

Allow me to revise your question for a better understanding:

The pressure at sea level is 1 atmosphere and increases at a constant rate as depth increases. When Sydney dives to a depth of 23 meters, the pressure around her is 3.3 point, 3 atmospheres. The pressure p in atmospheres is a function of x, the depth in meters.

My answer:

Given:

At O meter the the pressure is 1 (0, 1)

At 23 meters the the pressure is 3.3 (23, 3.3)

From that, we can form a linear equation with the standard form:

P(x) = mx + b (1)

The slope of (1) is:

`m=(3.3-1)/(23-0)=(2.3)/(23)=(23)/(230)=0.1`

<=> P(x) = 0.1x + b

Substitute the point (0, 1) into (1) we have:

1 = 0.1*0 + b

<=> b = 1

So we have the equation of this line will be: P(x) = mx + 1