Question

B. Translate each statement to an equation using k as the constant of variation.

Answer 1

Answer:

See Explanation

Step-by-step explanation:

To do this, we will make use of the following rules:

Direct Variation: $a\ \alpha\ b$ => $a = kb$

Inverse Variation: $a\ \alpha\ \frac{1}{b}$ ==> $a = k/b$

Joint Variation: $a\ \alpha\ bc$ ==> $a= kbc$

Direct, then inverse variation: $a\ \alpha\ b\ \alpha\ \frac{1}{c}$ ==> $a= kb/c$

Having highlighted the rules, the solution is as follows:

1. m varies directly to a

$m\ \alpha\ a$

$m =ka$

2. p varies inversely as q.

$p\ \alpha\ \frac{1}{q}$

$p\ = k\frac{1}{q}$

3. $r\ varies$ directly as s and inversely as t.

$r\ \alpha\ s\ \alpha\ \frac{1}{t}$

$r = k\frac{s}{t}$

4. z varies jointly as $e\ and\ f.$

$z\ \alpha \ ef$

$z = kef$

5. F varies directly as the $square\ of\ t.$

$F\ \alpha\ t^2$

$F = kt^2$

6. d varies jointly r and t

$d\ \alpha\ rt$

$d = krt$

7. P is inversely proportional to h.

$P\ \alpha\ \frac{1}{h}$

$P= \frac{k}{h}$

8. P varies directly as V

$P\ \alpha\ V$

$P=kV$

9. d varies directly as the square of  t

$d\ \alpha\ t^2$

$d = kt^2$

10. s varies jointly as  b and d and inversely as the  square L

$s\ \alpha\ bd\ \alpha\ \frac{1}{L^2}$

$s = k\frac{bd}{L^2}$