3x−2y=12;−3x+8y=−6
Step: Solve3x−2y=12for x:
3x−2y=12
3x−2y+2y=12+2y(Add 2y to both sides)
3x=2y+12
3x
3
=
2y+12
3
(Divide both sides by 3)
x=
2
3
y+4
Step: Substitute
2
3
y+4forxin−3x+8y=−6:
−3x+8y=−6
−3(
2
3
y+4)+8y=−6
6y−12=−6(Simplify both sides of the equation)
6y−12+12=−6+12(Add 12 to both sides)
6y=6
6y
6
=
6
6
(Divide both sides by 6)
y=1
Step: Substitute1foryinx=
2
3
y+4:
x=
2
3
y+4
x=
2
3
(1)+4
x=
14
3
(Simplify both sides of the equation)
Answer:
x=
14
3
and y=1
Answer:
1. Car Mart sell 11 cars per day.
You can use the table by looking at day 2 and day 3. You can see underneath it, it shows how many cars is left after that particular day. So from day 2, you have 43 cars left and day 3, you got 32 cars left. From 43 car to 32 car is losing 11 car. So each day the Car Mart sell 11 car.
2. First we know that after 3 days, Winston have 32 cars left and after 5 day, it has 12 cars left.
Step-by-step explanation:
Just use the coefficients for each variable and put it in a matrix. Is the second question set equal to something? Because then you would put it in place as the question mark. (Did the pic come through?)
So the 3x3 matrix is made up of the coefficients and then to augment the matrix, you add another column at the end with the solutions. Good luck!
Answer:
d
Step-by-step explanation:
Answer:
- Base Length of 68cm
- Height of 34 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume 

Surface Area of the box = Base Area + Area of 4 sides

Step 2: Find the derivative of A(x)

Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-628864%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-628864%3D0%5C%5C2x%5E3%3D628864%5C%5Cx%5E3%3D314432%5C%5Cx%3D%5Csqrt%5B3%5D%7B314432%7D%5C%5C%20x%3D68)
Step 4: Verify that x=68 is a minimum value
We use the second derivative test

Since the second derivative is positive at x=68, then it is a minimum point.
Recall:

Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 68cm
- Height of 34 cm.