Write an equation in slope-intercept form for the line that passes through (-3, 5), and is perpendicular to the graph of 5x - 6y
= 9
2 answers:
Y =-6/5x+7/5 Please vote me as brainliest if you think i helped and i attached a photo with work as well :) Have a great day
Answer:
Equation of line in slope-intercept form:
Step-by-step explanation:
Equation of a line in slope-intercept form is:
y = mx + c
where m is the slope and c is the y-intercept.
Given that (-3,5) passes through the line,hence:
5 = -3m+c ------------1
Also the line is perpendicular to 5x - 6y = 9.
Slope of a line ax+by+c=0 is
Hence slope of 5x - 6y = 9 is
Relation between slopes of two perpendicular lines:
Using above relation, m= .
Substituting m = -6/5 in equation 1, we get:
c = 5 + 3(-6/5)
Putting m = and c =
we get:
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m(x) = p(x) - c(x)
m(x) = 60x -3x^2 -(1800 - 183x)
m(x) = -3x^2 +243x -1800
Then the profit function for the company will be the excess of this per-widget profit multiplied by the number of widgets over the fixed costs.
P(x) = x×m(x) -50,000
P(x) = -3x^3 +243x^2 -1800x -50000
b) The marginal profit function is the derivative of the profit function.
P'(x) = -9x^2 +486x -1800
c) P'(40) = -9(40 -4)(40 -50) = 3240
Yes, more widgets should be built. The positive marginal profit indicates that building another widget will increase profit.
d) P'(50) = -9(50 -4)(50 -50) = 0
No, more widgets should not be built. The zero marginal profit indicates there is no profit to be made by building more widgets.
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On the face of it, this problem seems fairly straightforward, and the above "step-by-step" seems to give fairly reasonable answers. However, if you look at the function p(x), you find the "best price per widget" is negatve for more than 20 widgets. Similarly, the "cost per widget" is negative for more than 9.8 widgets. Thus, the only reason there is any profit at all for any number of widgets is that the negative costs are more negative than the negative revenue. This does not begin to model any real application of these ideas. It is yet another instance of failed math curriculum material.