Question

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Answer 1

a) The equation $V(m) = 8400 - 560\cdot m$ represents the discharge of the Grand Prismatic Spring.

b) The discharge of the Grand Prismatic Spring takes 15 minutes.

c) The remaining quantity after 7 minutes is 4480 gallons.

d) The hardness of cardboard is 2.

How to apply concepts of linear functions

a) In this case, the volume of water ($V$), in gallons, decreases linearly in time ($m$), in minutes. Then, we could model the situation by using the following expression:

$V(m) = V_{o} - \dot V \cdot m$ (1)

Where:

• $V_{o}$ - Initial volume, in gallons.
• $\dot V$ - Discharge rate, in gallons per minute.

If we know that $V_{o} = 8400\,gal$ and $\dot V = 560\,\frac{gal}{min}$, then the volume of the Grand Prismatic Spring is represented by this expression:

$V(m) = 8400 - 560\cdot m$ (2)

The equation $V(m) = 8400 - 560\cdot m$ represents the discharge of the Grand Prismatic Spring. $\blacksquare$

b) By (1) and $V(m) = 0$ we find the time required for discharge:

$m = \frac{0 - 8400}{-560}$

$m = 15\,min$

The discharge of the Grand Prismatic Spring takes 15 minutes. $\blacksquare$

c) The quantity of gallons remaining is found by evaluating the function for $m = 7$:

$V(7) = 8400 - 560\cdot (7)$

$V(7) = 4480\,gal$

The remaining quantity after 7 minutes is 4480 gallons. $\blacksquare$

d) According to Mohs scale, the hardness of feldspar is 6. The statement indicates the following relationship, as there is a constant relationship between both hardnesses:

$y = 3\cdot x$ (3)

Where:

• $x$ - Hardness of cardboard.
• $y$ - Hardness of feldspar.

If we know that $y = 6$, then the hardness of cardboard is:

$x = \frac{6}{3}$

$x = 2$

The hardness of cardboard is 2. $\blacksquare$

To learn more on linear functions, we kindly invite to check this verified question: brainly.com/question/17058347