B varies inversely with C. When B is 2, C is 8. Find the value of C when B is 5.
2 answers:
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Integrate both sides with respect to <em>t</em> :
∫ d<em>y</em>/d<em>t</em> d<em>t</em> = ∫ -12<em>t</em> ² d<em>t</em>
<em>y(t)</em> = -4<em>t</em> ³ + <em>C</em>
Use the initial condition to solve for <em>C</em> :
5 = -4•0³+ <em>C</em>
<em>C</em> = 5
So
<em>y(t)</em> = -4<em>t</em> ³ + 5
and the answer is D.
Alternatively, you can directly apply the fundamental theorem of calculus:
Answer:
a)
b)
c) They'd have lost $1000 if they had sold no calendars.
Step-by-step explanation:
a) The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
In this case we know that "y" represents the profit of loss and "x" the number of calendars sold.
Then, according to the exercise, the line passes through these two points:
and
Then, we can find the slope of the line with the formula
Now, we can substitute the slope and one of those points into and solve for "b":
Then, subtituting values, we get that the equation that describes the relation between the profit of loss and the number of calendars sold, is:
b) The slope of the line is the profit they made from selling each calendar
c) The y-intercept is the amount they would have lost if they had sold no calendars:
They'd have lost $1000 if they had sold no calendars.