X1 = 4 so sqrt(4) = 2
x2 = 9 so sqrt(9) = 3
3-2 = 1
9-4 = 5
rate of change = 1/5
Answer:
See explanation
Step-by-step explanation:
Let x in be the base side length and y in be the height of the box. Since the base is a square, we have

The volume of the box is

The surface area of the box is

The graph of the function SA(S) is shown in attached diagram.
Find the derivative of this function:

Equate this derivative to 0:

So, the dimensions that produce a minimum surface area for this aluminum box are:

Answer:
x = 47
Step-by-step explanation:
KY + YV = KV
KY + 22 = x
KY = x - 22
By angle bisector property:

<span><em>12 pennies, 3 nickles, and 2 dimes</em>
p = number of pennies
n = number of nickles
d = number of dimes
p(1) + n(5) + d(10) = 47
that is, the number of pennies x 1 cent + number nickles x 5 cents
+ number of dimes x ten cents equals 47 cents
p = 4n
p + n + d = 17
Substituting 4n for p in the above
4n + n + d = 17
5n + d = 17
Subtract 5n from each side
d = 17 - 5n
We will now substitute 4n for p and ( 17-5n ) for d in
the equation
p(1) + n(5) + d(10) = 47
4n(1) +n(5) + (17-5n)(10) = 47
9n + 170 - 50n = 47
-41n + 170 = 47
Subtract 170 from each side
-41n = 47 - 170
-41n = -123
Divide each side by -41
n = 3
Since p = 4n
p = 4(3)
p = 12
Since p + n + d = 17
12 + 3 + d = 17
15 + d = 17
d = 2
So we have 12 pennies, 3 nickles and 2 dimes
12 + 3(5) + 2(10) ?= 47
12 + 15 + 20 ?= 47</span>