Answer:
a) 
b) 
c)
Step-by-step explanation:
a)
We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:
P(x) = R(x) - C(x)
Finding Profit Function (P(x)):
This is the profit function.
b)
The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.
Remember the power rule for differentiation shown below:
Now, we differentiate the profit function to get the marginal profit function (P'):
This is the marginal profit function , P'.
c)
We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:
and
5x-13=15+7x
-13=15+2x
-28=2x
-14=x
Answer:
51 m^2
Step-by-step explanation:
The shaded area is the difference between the area of the overall figure and that of the rectangular cutout.
The applicable formulas are ...
area of a triangle:
A = (1/2)bh
area of a rectangle:
A = bh
area of a trapezoid:
A = (1/2)(b1 +b2)h
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We note that the area of a triangle depends only on the length of its base and its height. The actual shape does not matter. Thus, we can shift the peak of the triangular portion of the shape (that portion above the top horizontal line) so that it lines up with one vertical side or the other of the figure. That makes the overall shape a trapezoid with bases 16 m and 10 m. The area of that trapezoid is then ...
A = (1/2)(16 m + 10 m)(5 m) = 65 m^2
The area of the white internal rectangle is ...
A = (2 m)(7 m) = 14 m^2
So, the shaded area is the difference:
65 m^2 -14 m^2 = 51 m^2 . . . . shaded area of the composite figure
_____
<em>Alternate approach</em>
Of course, you can also figure the area by adding the area of the triangular "roof" to the area of the larger rectangle, then subtracting the area of the smaller rectangle. Using the above formulas, that approach gives ...
(1/2)(5 m)(16 m - 10 m) + (5 m)(10 m) - (2 m)(7 m) = 15 m^2 + 50 m^2 -14 m^2
= 51 m^2
Answer:
x=8
Step-by-step explanation:
1. We assume, that the number 118 is 100% - because it's the output value of the task.
<span>2. We assume, that x is the value we are looking for. </span>
<span>3. If 118 is 100%, so we can write it down as 118=100%. </span>
<span>4. We know, that x is 47% of the output value, so we can write it down as x=47%. </span>
5. Now we have two simple equations:
1) 118=100%
2) x=47%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
118/x=100%/47%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 47% of 118
118/x=100/47
<span>(118/x)*x=(100/47)*x - </span>we multiply both sides of the equation by x
<span>118=2.12765957447*x - </span>we divide both sides of the equation by (2.12765957447) to get x
<span>118/2.12765957447=x </span>
<span>55.46=x </span>
x=55.46
<span>now we have: </span>
<span>47% of 118=55.46</span>
