Answer:
20 ft by 60 ft
Step-by-step explanation:
"What should the dimensions of the garden be to maximize this area?"
If y is the length of the garden, parallel to the stream, and x is the width of the garden, then the amount of fencing is:
120 = 3x + y
And the area is:
A = xy
Use substitution:
A = x (120 − 3x)
A = -3x² + 120x
This is a downward facing parabola. The maximum is at the vertex, which we can find using x = -b/(2a).
x = -120 / (2 · -3)
x = 20
When x = 20, y = 60. So the garden should be 20 ft by 60 ft.
Answer:
61/18
Step-by-step explanation:
Make the mixed fraction an improper fraction first. So instead of 1 1/3, it'll be 4/3.
Now in a rectangular prism, there's two of each congruent sides (three pairs in total).
You'll need to multiply (4/3)(3/4) by 2 because there's two of them.
This gives you (1)(2) which equals 2.
Next, take another set --> (4/3)(1/3)(2) again because there's two of them.
This gives you (4/9)(2) which equals 8/9.
Last, take the last set --> (3/4)(1/3)(2)
This gives you (1/4)(2) which equals 1/2.
Now that you have all the areas of the rectangles, add them all together.
2+8/9+1/2 which equals 61/18 inches squared.
Well 1/3 for savings means that you save 1/3*4500 or 1500 dollars.
You then have $3000 left. Of this if you spend 50% on food, you spend 0.5*3000 or 1500 dollars on food.
The rate of change of a linear equation (first degree) is equivalent to the slope of a line. Slope is described as the vertical movement (rise) of the line over its horizontal counterpart (run). In determining the rate of change or slope (m) given 1 data point (x',y'), point-slope form is applicable. Point-slope form is: (y-y') = m (x-x'). Substitute the given point (-5,-1) in the equation. By substitution, [y-(-1)] = m [x-(-5)]. Re-arranging the equation, the rate of change or slope is, m = (y+1)/(x+5).
Answer:
g(x)=f(x+3)+5
Step-by-step explanation:
