Answer:
The manager of a furniture factory finds that it costs $2400 to manufacture 50 chairs in one day and $4800 to produce 250 chairs in one day.
(a) First we will find m, that represents the rate of change of cost with respect to number of chairs:
so, m = 12 dollars per chair.
Let C be the cost and X be the number of chairs, the function can be written as (assuming that it is linear):
(b) Slope of the graph is m =12
Here slope represents that for every unit increase in number of chairs produced (X), the overall cost (C) will increase by 12 dollars.
Option - the cost (in dollars) of producing each additional chair.
(c) Y intercept is a dependent variable. It is $1800, when the value of independent variable (X) is 0. Also we can say that $1800 is the fixed cost that has to be paid irrespective of any chairs produced. If there is 0 production, still $1800 has to be paid.
Option - the cost (in dollars) of operating the factory daily.
8x^2 + 2x - 3 = 0
(4x )(2x )
(4x + 3)(2x - 1) = 0
Surprise: that might actually work.
4x + 3 =0
4x = - 3
x = - 3/4 That would be between 90 and 180 because the cos(x) is minus in quad 2.
2x - 1 = 0
2x = 1
x = 1/2 This one is actually only in quad 1.
cos(y) = 1/2
y = 60 degrees.
cos(y) = - 3/4
y = 138.6 degrees. You could do this by
cos(y) = 3/4
cos(y) = 41.4 degrees. Because the 3/4 is minus, the angle is in quad 2
180 - 41.4 = 138.6. Same answer.
The calculator does in the following way.
2nd F
Cos-1(
- 0.75
)
=
which will give you 138.6 immediately.
(a)
R(p) = -8p² + 1328p
R(50) = -8(50)² + 1328(50)
= -8(2500) + 66,400
= -20,000 + 66,400
= 46,400
R(70) = -8(70)² + 1328(70)
= -8(4900) + 92,960
= -39,200 + 92,960
= 53,760
R(90) = -8(90)² + 1328(90)
= -8(8100) + 119,520
= -64,800 + 119,520
= 54,720
(b) R(p) = -8p² + 1328p NOTE: maximum is the vertex
<em>a=-8, b=1328</em>
p = = 83
(c)
R(83) = -8(83)² + 1328(83)
= -8(6889) + 110,224
= -55,112 + 110,224
= 55,112
<em>range=(7</em><em>,</em><em>3</em><em>2</em><em>,</em><em>5</em><em>7</em><em>)</em><em>.</em>
<em>Hope</em><em> </em><em>this</em><em> </em><em>will</em><em> </em><em>help</em><em> </em><em>u</em><em>.</em><em>.</em><em>.</em><em>.</em>