Question

I NEED HELP ASAP


Part A: The Grand Prismatic Spring in Yellowstone discharges 8,400 gallons of water at a rate of 560 gallons a minute. Using m for minutes, write an equation that represents this situation.



Part B: video (0:28-0:43) Using the equation you wrote in Part A, how many minutes does it take for 8,400 gallons of water to discharge? Use 1-2 sentences to explain your answer.



Part C: video (0:28-0:43) How many gallons of water are left in the Spring after 7 minutes? Use 1-2 sentences to explain how you determined this amount.



Part D: video (0:44-1:17) Using the Mohs scale of hardness as outlined in the video, if Feldspar is three times as hard as cardboard,c, write an equation and solve to find the hardness scale of cardboard. Use 1-2 sentences to explain the hardness scale of cardboard and how it relates to Feldspar.

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: https://brainly.com/question/17058347