Zoom in to view well Pls and thx!
2 answers:
You might be interested in
Answer:
the equation of the line in slope-intercept form is:
Step-by-step explanation:
First start by finding the slope of the segment that joins those two points using the general formula for the slope of the segments between two points and
on the plane:
Then for our case, calling (-4, 6) = and (-8, 10) =
, we have:
Now, knowing this, we can find the equation of the line by using the "point-slope" form of a line [of slope "m" and going through the point that tells us:
We will be then using the found slope (-1) and for example one of the given points: (-4 , 6), thus:
Answer:
Step-by-step explanation:
I solved this using initial conditions and calculus, so I hope that's what you are doing in math. It's actually NOT calculus, just a concept that is taught in calculus.
The initial condition formula we need is
Filling in our formula with the 2 conditions we are given:
and
With those 2 equations, we have 2 unknowns, the C (initial value) and the k (the constant). We know that the initial value (or starting temp) for both conditions is the same, so we solve for C in one equation, sub it into the other equation and solve for k. If
then
which, by exponential rules is the same as
Since that value of C is the same as the value of C in the other equation, we sub it in:
Divide both sides by 65 and use the rules of exponents again to get
which simplifies down to
Take the natural log of both sides to get
Do the log thing on your calculator to get
.2682639866 = 5k and divide both sides by 5 to find k:
k = .0536527973
Now that we have k, we sub THAT value in to one of the original equations to find C:
which simplifies down to
Raise e to that power on your calculator to get
65 = C(1.710059171) and divide to solve for C:
C = 38.01038064
Now sub in k and C to the final problem when t = 23:
which simplifies a bit to
Raise e to that power on your calculator to get
y = 38.01038064(3.434991111) and
finally, the temp at 23 minutes is
130.565