Answer:
Step-by-step explanation:
Let r be the radius of the semicircle, then 2r is the width of the rectangle. Let y be the length of the rectangle. The perimeter of the window consists of two lengths, one width and length of semicircle, then
Express y:
The area of the window is
Substitute y into the area expression:
Find the derivative A':
Equate A' to 0:
When 
then 
and the function A is increasing, when 
then 
and the function A is decreasing. This means that at point the function A takes it maximal value (the area is maximal).
Answer:
$48.30
Step-by-step explanation:
If the dinner was $42.00 and they wanted to give a 15% tip, then to find that start by multiplying 42 by 0.15
42.00 x 0.15 = 6.3
now add $6.30 to $42.00
42 + 6.3 = 48.3
Answer:
7 - 2.25
= 7 - 2
= 5 - 0.25
= 4.75
9 - 1.9
= 9 - 1
= 8 - 0.9
= 7.1
I hope this helps and that you have a great day!
<em />
<em>Ravenna</em>
What do you mean answer key??
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
