Answer:
0.314 gallon is required to cover a circular region with a radius of 40 feet
Step-by-step explanation:
Given
a gallon of paint will cover about 400 square feet in a single coat
To Find:
Number of gallons required to cover a circular region with a radius of 40 feet = ?
Solution:
Step 1: Finding Area of the circular region
The area of the circular region, A = 
where r is the radius
Now substituting r = 40 , we get
A = 
Step 2: Finding the number of gallons of paint required
To cover 400 sq feet = 1 gallon
so to cover 1 square feet = 
gallon
Now to cover 125.6 ft we need
=> 0.314 gallon
First solve for x in the first equation. So you'll have to substitute,
5(3x-7)=20
15x-35=20
Then add 35 to both sides.
15x=55
Divide 55 by 15.
So x = 3.66...
Then plug in 3.7 for x in 6x-8
6(3.7)-8
Its approximately 14.2
Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:
By expanding the previous equation:
The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:
Since there is no accumulation within the tank, expression is simplified to this:
By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where 
.
The solution of this equation is:
The salt concentration after 8 minutes is:
The instantaneous amount of salt in the tank is:
Answer:
x = 9; y = 1
Step-by-step explanation:
