Question

write the equation of a function h(t) that represents the amount of heat in joules required to heat the bar to a temp of t degrees Celsius

Answer 1

@jdoe0001 @Nnesha

Answer 2

hmm what did the table give you?

Answer 3

usually the Joules and Celsius made

could just be used as an "x" and "y" table with each pair being a coordinate of the graph

so you'd do the same as before to get the equation, pick 2 points, get their slope
and then plug in the point-slope form

Answer 4

hmmm well... the gold bar was 25 degrees warm from the getgo
to raise it to 26
you'd just need 7Joules so would be more like

\( \bf \begin{array}{ccllll}
Joules&Celsius
\\\hline\\\
x&y
\\\hline\\
7&26\\
{\color{red}{ 14}}&{\color{blue}{ 27}}\\
21&28\\
{\color{red}{ 28}}&{\color{blue}{ 29}}\\
35&30
\end{array}
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 14}}\quad ,&{\color{blue}{ 27}})\quad &({\color{red}{ 28}}\quad ,&{\color{blue}{ 29}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 5

slope is 7 y=7x-168

Answer 6

o nevermind, you used joules as x not y give me a sec

Answer 7

keep in mind that Joules is the INPUT, and the Celsius is the OUTPUT

Answer 8

wait your graph is wrong

Answer 9

hmm.... where is it off?

Answer 10

x is 14 and y is 26 not x is 7

Answer 11

hmmm ok...... x = 14 means 2 Celsius or 7 + 7 Joules

starting off at 25 degrees warm, the gold bar will go up to 27

Answer 12

o ok, i see. so it doesnt start with 7, 25 because nothings been heated its just 0,25

Answer 13

yeap

Answer 14

so slope is still 7

Answer 15

y=7x-175?

Answer 16

how do i put that in the h(t) thing?

Answer 17

hmm site is getting laggy

Answer 18

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 14}}\quad ,&{\color{blue}{ 27}})\quad &({\color{red}{ 28}}\quad ,&{\color{blue}{ 29}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ 29}}-{\color{blue}{ 27}}}{{\color{red}{ 28}}-{\color{red}{ 14}}}\implies ?\)

Answer 19

2/14 or 1/7

Answer 20

yeap thus \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 14}}\quad ,&{\color{blue}{ 27}})\quad &({\color{red}{ 28}}\quad ,&{\color{blue}{ 29}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{1}{7}
\\ \quad \\

y-{\color{blue}{ 27}}={\color{green}{ \cfrac{1}{7}}}(x-{\color{red}{ 14}})\qquad \textit{plug in the values }\\
\qquad \uparrow\\
\textit{point-slope form} \)

Answer 21

it doesn't need it in any specific form... so I gather point-slope form is just as good

Answer 22

ok, what about #12?

Answer 23

he/she 's buying cases of balls, each case has 24 cans, each can 24 balls

the INPUT here is how many cases? the OUTPUT is how many balls?

well... in 1 case there are 24* 3 balls

so there \(\large \begin{array}{rrrllll}
cases&balls
\\\hline\\
1&24\cdot 3\to 72\\
2&144\\
3&288\\
4&576\\
...&...
\end{array}\) pick any 2 points, get the "x" and "y" and get their slope and same as before

plug in the point-slope form

Answer 24

woops
he/she 's buying cases of balls, each case has 24 cans, each can 3 balls thus 24 * 3

Answer 25

slope is 72

Answer 26

y=72x?

Answer 27

hmmm right my table is a bit off there.... but yes... that's correct should be \(\begin{array}{rrrllll}
cases&balls
\\\hline\\
1&24\cdot 3\to 72\\
2&144\\
3&288\\
4&360\\
...&...
\end{array}\)

anyhow

Answer 28

yeap

Answer 29

so how would i graph that with no y-intercept

Answer 30

you forgot about our good fellow Mr Zero \(\large \begin{array}{llll}
y=&{\color{brown}{ 72}}x&{\color{blue}{ +0}}\\
&\uparrow &\uparrow \\
&{\color{brown}{ slope}}&{\color{blue}{ y-intercept}}
\end{array}\)

Answer 31

o ok :) what does the slope represent in the function? the number of cans in a case?

Answer 32

slope is a rate of change

how much is "y" changing on every change in "x"

Answer 33

so.... in this case... "y" is how many balls in each "x" cases

Answer 34

that would mean there are 7 balls in each case :/

Answer 35

yes IF the slope were 7, yes

Answer 36

well if our slope is 1/7 and you say x is the case and y is the number of balls... so it would be 7 balls per case

Answer 37

hmmm you're referring to the Joules and Celsius slope, yes, that was 1/7

Answer 38

o crap.. sorry i got confused

Answer 39

but if the slope in this case were 1/7 on the cases and balls...yes, it'd be 1/7 ball per case =)

Answer 40

kinda no easy to play tennis with 1/7 of a ball though

Answer 41

xD

Answer 42

what about number 10? i dont really understand what the question is asking

Answer 43

sorry i mean 11

Answer 44

well.. you know the equation from Joules and Celsius

so to know how much it'd take to get 260 degrees.... .solve it like so
the degrees are the OUTPUT so set y = 260 and solve for "x"

Answer 45

i got 126.38 repeating for 10 but i meant 11

Answer 46

a negative value of the function... means a negative Degree

so the gold bar was 25 from the getgo

y = 25 means 0 joules into it

24, 23, 22, 21, 20 ...... 3, 2, 1 , -1, -2 ,-3, -4? what do you think that means for the gold bar?

Answer 47

its temperature decreases?

Answer 48

well.... yes..... it's

think about say... you're the gold bar, and you're sitting at the tv watching the weather forecast and the newscast say
"well folks it was 25 degrees yesterday BUT today is going to be -4 degrees"

how would you feel?

Answer 49

shocked? there was a dramatic decrease in temperature from 1 day to another

Answer 50

well... surely... besides that, you'd be wearing thicker clothes

so you're really no "warm" anymore...you're getting "colder"

Answer 51

ok so a negative value of h(t) means the gold bar is getting colder

Answer 52

yeap