Answer:
- 50 ft by 75 ft
- 3750 square feet
Step-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
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<em>Comment on the solution</em>
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
Answer:
You have to find the slope first. Which is y1-y1 divided by x1-x2
Then you find the y-intercept which you take the slope for m like for example if you find the slope, 2, then the equation should be y=2x+b. You take the coordinates on the problem and put them on the y or x on the equation. Then when you find the y-intercept you add it to the equation like for the example that I used above, you have to put the y-intercept on b. So if the y-intercept is 5 then the equation would be y=2x+5.
K= -3
3y = x+6 can be rewritten as y = 1/3x + 2
a perpendicular slope is the opposite reciprocal of the original slope
so instead of 1/3 it would be -3
therefore. k must equal -3 to be perpendicular to 3y = x+6
Volume = (Area of the base)x(Height)
66.85 = 15(H)
66.85/15 = H
H = 4.4567
The height is 4.4567mm.
Answer:
0.347
Step-by-step explanation:
n = 3
p = 1/6
r = 1
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
P = ₃C₁ (1/6)¹ (5/6)³⁻¹
P = 0.347
Or, using a calculator:
P = binompdf(n, p, r)
P = binompdf(3, 1/6, 1)
P = 0.347
