You have the following function:

Derivate implictly the previous expression, as follow:

Where you have used that:

Then, the implicit derivative of the given expression is:

Next, solve for y' as follow:

For this case, the first thing we must do is define a variable.
We have then:
x: unknown number
We now write the equation that models the problem:

From here, we clear the value of x.
We multiply both sides of the equation by 2:

We subtract 30 on both sides of the equation:

Answer:
The value of the unknown number is given by:

x+3<8
8-3 =5
X<5
any number less than 5 will work
Answer:

Step-by-step explanation:
Area of a circle with radius
: 
Circumference of a sector with radius
: 
Area of sector with angle
:
.
Arc length of sector with angle
: 
Using these equations, we get the following information:
Area of circle: 
Circumference of a circle: 
Area of sector: 
Arc length of sector: 
$11=2 hrs
2hrs=$11
+2(4hrs)=$22
+2(6hrs)=$33 hrs
so 6 hrs or 7 hours and some
minutes left