Answer:
- Using the y-axis to represent pounds, and the x-axis to represent kilograms, the graph is straight line going through the origin with a slope of 2.2 lbs/kg.
Explanation:
A constant conversion factor, such as 1 kg 2.2 lb, means that the two units are in direct proportion; thus the graph is a straight line that goes through the origin.
The conversion factor also gives the slope of the line.
Depending on which axis you choose for either unit the slope may be 2.2 pounds per kilogram, or 1/2.2 kilogram per pound.
When you use the y-axis for pounds and the x-axis for kilograms then the relationship is:
In that case, the slope is 2.2 pounds per kilogram.
Part A: the area of a rectangle is A= lw, so
A= lw
Height= 6x+3.= 9x
Width= 8
Which makes the expression to this area 9x x 8 ( 9x times 8 )
Part B: you do the same to get the expression here, so the expression would be
6x x 12 ( 6x times 12 )
The answer to this part is yes because both end up being 72x once you get the answer of each.
1. Find the equation of the line AB. For reference, the answer is y=(-2/3)x+2.
2. Derive a formula for the area of the shaded rectange. It is A=xy (where x is the length and y is the height).
3. Replace "y" in A=xy with the formula for y: y= (-2/3)x+2:
A=x[(-2/3)x+2] This is a formula for Area A in terms of x only.
4. Since we want to maximize the shaded area, we take the derivative with respect to x of A=x[(-2/3)x+2] , or, equivalently, A=(-2/3)x^2 + 2x.
This results in (dA/dx) = (-4/3)x + 2.
5. Set this result = to 0 and solve for the critical value:
(dA/dx) = (-4/3)x + 2=0, or (4/3)x=2 This results in x=(3/4)(2)=3/2
6. Verify that this critical value x=3/2 does indeed maximize the area function.
7. Determine the area of the shaded rectangle for x=3/2, using the previously-derived formula A=(-2/3)x^2 + 2x.
The result is the max. area of the shaded rectangle.
Answer:
y=5
Step-by-step explanation:
Answer:
3x^4+297
Step-by-step explanation:
First, simplify 6³ and 9².
6³ = 6•6•6 = 36•6 = 216
9² = 9•9 = 81
Add.
3x^4+216+81
3x^4+297
Note:
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