Which costs more per gallon? 5 gallons for $12.50 or 11 gallons for $26.40
1 answer:
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We first obtain the equation of the lines bounding R.
For the line with points (0, 0) and (8, 1), the equation is given by:
For the line with points (0, 0) and (1, 8), the equation is given by:
For the line with points (8, 1) and (1, 8), the equation is given by:
The Jacobian determinant is given by
The integrand x - 3y is transformed as 8u + v - 3(u + 8v) = 8u + v - 3u - 24v = 5u - 23v
Therefore, the integration is given by:
![63 \int\limits^1_0 \int\limits^{1}_0 {(5u-23v)} \, dudv =63 \int\limits^1_0\left[\frac{5}{2}u^2-23uv\right]^{1}_0 \\ \\ =63\int\limits^1_0(\frac{5}{2}-23v)dv=63\left[\frac{5}{2}v-\frac{23}{2}v^2\right]^1_0=63\left(\frac{5}{2}-\frac{23}{2}\right) \\ \\ =63(-9)=|-576|=576](https://tex.z-dn.net/?f=63%20%5Cint%5Climits%5E1_0%20%5Cint%5Climits%5E%7B1%7D_0%20%7B%285u-23v%29%7D%20%5C%2C%20dudv%20%3D63%20%5Cint%5Climits%5E1_0%5Cleft%5B%5Cfrac%7B5%7D%7B2%7Du%5E2-23uv%5Cright%5D%5E%7B1%7D_0%20%5C%5C%20%20%5C%5C%20%3D63%5Cint%5Climits%5E1_0%28%5Cfrac%7B5%7D%7B2%7D-23v%29dv%3D63%5Cleft%5B%5Cfrac%7B5%7D%7B2%7Dv-%5Cfrac%7B23%7D%7B2%7Dv%5E2%5Cright%5D%5E1_0%3D63%5Cleft%28%5Cfrac%7B5%7D%7B2%7D-%5Cfrac%7B23%7D%7B2%7D%5Cright%29%20%5C%5C%20%20%5C%5C%20%3D63%28-9%29%3D%7C-576%7C%3D576)
For the line with points (0, 0) and (8, 1), the equation is given by:
For the line with points (0, 0) and (1, 8), the equation is given by:
For the line with points (8, 1) and (1, 8), the equation is given by:
The Jacobian determinant is given by
The integrand x - 3y is transformed as 8u + v - 3(u + 8v) = 8u + v - 3u - 24v = 5u - 23v
Therefore, the integration is given by:
Answer:
x=2
Step-by-step explanation:
-3x+7=1
subtract 7 from both sides: -3x+7-7=1-7
simplify: -3x=-6
divide both sides by -3:
simplify: x=2
Remark
This will have 2 solutions. I will enclose a graph to show how it is done.
4|2x - 2| + 10 = 34 Subtract 10
Solution
4|2x - 2| = 34 - 10
4|2x - 2| = 24 Divide by 4
|2x - 2| = 24/4
|2x - 2| = 6
Solution 1
2x - 2 = 6 Add 2
2x = 6 + 2
2x = 8 Divide by 2
x = 8/2
x = 4
Solution 2
Make the 6 into - 6 and solve again
|2x - 2| = - 6
2x - 2= -6 Add 2 to both sides.
2x = - 6 + 2
2x = - 4 Divide by 2
x = - 4/2
x = - 2
Answer
There are 2 solutions
(-2,0) and (4,0) See the graph below.
This will have 2 solutions. I will enclose a graph to show how it is done.
4|2x - 2| + 10 = 34 Subtract 10
Solution
4|2x - 2| = 34 - 10
4|2x - 2| = 24 Divide by 4
|2x - 2| = 24/4
|2x - 2| = 6
Solution 1
2x - 2 = 6 Add 2
2x = 6 + 2
2x = 8 Divide by 2
x = 8/2
x = 4
Solution 2
Make the 6 into - 6 and solve again
|2x - 2| = - 6
2x - 2= -6 Add 2 to both sides.
2x = - 6 + 2
2x = - 4 Divide by 2
x = - 4/2
x = - 2
Answer
There are 2 solutions
(-2,0) and (4,0) See the graph below.