How do you solve it?

Question

asked Dec 22, 2019 47.0k views

1 Answer

Nataliya · Answer 1 · 2019-12-27T16:50:53+0000

At heart we're being asked for a line through two points,

$(40^\circ \textrm{ C}, 355 \textrm { m/s}) \quad \textrm{and} \quad (49^\circ \textrm{ C}, 360 \textrm { m/s})$

In general the line through (a,b) and (c,d) is

(y-b)(c-a)=(x-a)(d-b)

Check that you understand why both (a,b) and (c,d) are on this line.

Here our indepedent variable, instead of x, is T, temperature. Our dependent variable is v, velocity. Substituting,

(v - 355)(49 - 40) = (T - 40)(360 - 355)

9(v - 355) = 5(T - 40)

$v-355 = \frac 5 9 T - (200)/(9)$

$v= \frac 5 9 T - (200)/(9) + 355$

$v= \frac 5 9 T + (2995)/(9)$

That's our answer; let's check it.

When T=40, v = (5/9)40 + (2995/9) = 355 good

When T=49, v= (5/9)49 + (2995/9) = 360 good