Let
so that the Lagrangian is
You have
Solving for
, you find four potential critical points, each giving values of
listed below:
Before you choose any of these, keep in mind that
is not a plane, so you need to also check for any possible critical points within the disk
.
The gradient is zero when
and
. At this point, you have
.
So, there are two maxima, both 50, and one minimum, -4.
Answer:
8 feet.
Step-by-step explanation:
If we know the shadow (30 ft) of a tower (15 ft), we can use use the ratio
where 'x' is the height of the telephone pole. Cross multiply, and we get the equation . The rest of the problem is pretty straightforward, we divide both sides by 30 to find x. In the end, you will find that the height of the telephone pole is 8 feet.
Hope this helped!
Answer:
a = (p - b)/2
Step-by-step explanation:
Isolate the variable, a. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and =
Parenthesis
Exponents (& roots)
Multiplication
Division
Addition
Subtraction
~
First, subtract b from both sides:
p (-b) = 2a + b (-b)
p - b = 2a
2a = p - b
Next, divide 2 from both sides:
(2a)/2 = (p - b)/2
a = (p - b)/2
a = (p - b)/2 is your answer.
~
Answer:
36 gallons
Step-by-step explanation:
y = 4/5x
Let x = 45 minutes
y = 4/5 (45)
y = 36 gallons