Question

help please

Answer 1

Temp of 92 is recorded at 1200 feet
At 2400 feet temp is 32
given that there is a linear relation between temp t and height h
Do you agree with this?

Answer 2

@jairo330 ??

Answer 3

i dont understand. is there an equation i can use?

Answer 4

We'll find an equation, it's given there is a linear relation between temp t and height h so
\[t=ah+b\]
here a and b are constants, we need to find them
Do you get this part?

Answer 5

yes

Answer 6

ok, we know that
Temp of 92 is recorded at 1200 feet
t=92 and h=1200
so
\[\large92=1200a+b \text{.............equation 1}\]
and other info we have is "At 2400 feet temp is 32"
so
\[\large32=2400a+b\text{.............equation2}\]
Canyou solve equation 1 and 2 for a and b?

Answer 7

how? it's just a line

Answer 8

do you know how to solve simultaneous linear equations?

Answer 9

no

Answer 10

We have two equations
\[92=1200a+b\]
\[32=2400a+b\]
I'll subtract the second from the first
\[92-32=(1200a+b)-(2400a+b)\]
We'll get
\[60=1200a+b-2400a-b\]
\[60=1200a\cancel {+b}-2400a\cancel{-b}\]
\[60=1200a-2400a\]
\[60=-1200a\]
Do you understand this?
can you find "a" now?

Answer 11

a=-1/20

Answer 12

that makes sense

Answer 13

good, now we'll find b
We already have
\[92=1200a+b\]
put a=-1/20 in this
\[92=1200\times \frac{-1}{20}+b\]
\[92=-60+b\]
can you find b from this?

Answer 14

yes 152

Answer 15

so our linear relation is
\[t=\frac{-h}{20}+152\]
this is the relation between temp t and height h :)
dis you understand?

Answer 16

yes that makes sense

Answer 17

thanks a lot

Answer 18

:D