Let's work through each part step-by-step:

Part (a)

The given equation is: $F = \frac{p_1 - p_2}{r}$

1. Classification: This is a literal equation.
   • Reason: A literal equation is an equation with multiple variables, where no specific numerical values are provided, and it is typically solved for one variable in terms of the others. In this case, $F$, $p_1$, $p_2$, and $r$ are all variables.

Part (b)

We need to calculate the flow rate $F$ using the values:

• $p_1 = 80$
• $p_2 = 60$
• $r = 5$

Substitute these values into the formula: $F = \frac{p_1 - p_2}{r} = \frac{80 - 60}{5} = \frac{20}{5} = 4$

So, the blood flow rate $F$ is: $F = 4$

Part (c)

To solve for $p_1$ in terms of $F$, $p_2$, and $r$, start with the equation: $F = \frac{p_1 - p_2}{r}$

Multiply both sides by $r$ to isolate $p_1 - p_2$: $F \cdot r = p_1 - p_2$

Then, add $p_2$ to both sides: $p_1 = F \cdot r + p_2$

Thus, the formula for $p_1$ is: $p_1 = F \cdot r + p_2$

Part (d)

Using the formula for $p_1$ derived in part (c), find $p_1$ when:

• $F = 5$
• $p_2 = 70$
• $r = 4$

Substitute these values into the formula: $p_1 = F \cdot r + p_2 = 5 \cdot 4 + 70 = 20 + 70 = 90$

So, the value of $p_1$ is: $p_1 = 90$

Part (e)

To solve for $r$ in terms of $F$, $p_1$, and $p_2$, start with the original equation: $F = \frac{p_1 - p_2}{r}$

Multiply both sides by $r$ and then divide by $F$ to isolate $r$: $r = \frac{p_1 - p_2}{F}$

Thus, the formula for $r$ is: $r = \frac{p_1 - p_2}{F}$

Would you like further details on any part?

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Related Questions

1. What are literal equations, and how are they used in real-world applications?
2. How can you classify other types of equations, such as absolute value or quadratic equations?
3. Why does resistance affect blood flow rate, and how does it relate to health?
4. How would changing $p_1$ or $p_2$ impact the blood flow rate?
5. How does this formula relate to Ohm's Law in physics?

Tip:

When rearranging formulas, always perform the same operation on both sides of the equation to keep it balanced.