The system of equations 2x + 3y = 2 and y = (1/2)x + 3 have solutions at x = -2 and y = 2
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
From the system of equations 2x + 3y = 2 and y = (1/2)x + 3, the graph of the equation shows that the solution is at x = -2 and y = 2
Find out more on equation at: brainly.com/question/2972832
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7 oz bag:
110 ÷ 7 = 15.7143¢ per oz
9 oz bag:
146 ÷ 9 = 16.2222¢ per oz
So the answer is the 7 oz bag, hope this helps!
Answer:
y= x-4
Step-by-step explanation:
The corresponding homogeneous ODE has characteristic equation
with roots at
, thus admitting the characteristic solution

For the particular solution, assume one of the form



Substituting into the ODE gives



Then the general solution to this ODE is



Assume a solution of the form



Substituting into the ODE gives



so the solution is



Assume a solution of the form


Substituting into the ODE gives



so the solution is

Given Information:
Area of rectangle = 16 square feet
Required Information:
Least amount of material = ?
Answer:
x = 4 ft and y = 4 ft
Step-by-step explanation:
We know that a rectangle has area = xy and perimeter = 2x + 2y
We want to use least amount of material to design the sandbox which means we want to minimize the perimeter which can be done by taking the derivative of perimeter and then setting it equal to 0.
So we have
xy = 16
y = 16/x
p = 2x + 2y
put the value of y into the equation of perimeter
p = 2x + 2(16/x)
p = 2x + 32/x
Take derivative with respect to x
d/dt (2x + 32/x)
2 - 32/x²
set the derivative equal to zero to minimize the perimeter
2 - 32/x² = 0
32/x² = 2
x² = 32/2
x² = 16
x =
ft
put the value of x into equation xy = 16
(4)y = 16
y = 16/4
y = 4 ft
So the dimensions are x = 4 ft and y = 4 ft in order to use least amount of material.
Verification:
xy = 16
4*4 = 16
16 = 16 (satisfied)