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09.12.2019 •

Mathematics

Find the distance between the origin and (8,15)

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Ответ:

swordnewsnetwork

25.06.2022

Mathematics

Part a) The equation in point slope form is y-11.2=-0.025(x-37)

Part b) $6.1\ in$

Step-by-step explanation:

Part a) Determine the equation of the line in point slope form

Let

x -----> the time in minutes

y -----> the height of the candle in inches

we know that

After 37 minutes, the candle was 11.2 inches tall

we have the point

(37,11.2)

Eighteen minutes later, it was 10.75 inches tall

we have the point

(37+18,10.75) -----> (55,10.75)

Find the slope of the linear equation

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{10.75-11.2}{55-37}$

$m=\frac{-0.45}{18}$

$m=-0.025\frac{in}{min}$ ----> is negative because is a decreasing function

The equation of the line in point slope form is equal to

y-y1=m(x-x1)

we have

m=-0.025

(x1,y1)=(37,11.2)

substitute

y-11.2=-0.025(x-37)

Part b) Determine the height of the candle after 4 hours

Remember that

$1\ h=60\ min$

$4\ h=4(60)=240\ min$

For x=240 min

substitute in the linear equation

y-11.2=-0.025(240-37)

y-11.2=-5.075

y=-5.075+11.2

$y=6.125\ in$

Round to the tenth place

$y=6.1\ in$

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