Answer:
7.85 km
Step-by-step explanation:
Let x represent the distance from the refinery to point P. Then the distance under the river from point P to the storage tanks is ...
√(2² +(9 -x)²) = √(x² -18x +85)
In units of $200,000, the cost of the pipeline will be ...
c = x + 2√(x² -18x +85)
The derivative with respect to x is ...
dc/dx = 1 +(2x -18)/√(x² -18x +85)
When we set this to zero, we can get the equation ...
√(x² -18x +85) +(2x -18) = 0
And this can be rewritten as ...
3x^2 -54x +239 = 0
which has solution
x = 9 -(2/3)√3 ≈ 7.8453
Point P should be located about 7.85 km from the refinery.
_____
It is interesting to note that the angle the pipe makes with the riverbank is given by arccos(1/2), where the 1/2 is the ratio of overland to under-river costs. That angle is 60°, so the distance along the riverbank from the storage facility to point P is 2cot(60°) = (2/3)√3 ≈ 1.1547 km. You will recognize this as the value subtracted from 9 km in the solution above.
This "angle solution" is the generic solution to this sort of problem where the route costs are different and part of the route is along the edge of the higher-cost path.
Answer and Step-by-step explanation:
Charlotte reads 4 books each week
b = number of books she reads each week
w = number of weeks that she reads
The number of books depends on the number of weeks, so
independent variable: w
dependent variable: b
b = 4w
╔═══╦═════════╦════╗
║ w ║ b = 4w ║ b ║
╠═══╬═════════╬════╣
║ 0 ║ b = 4*0 ║ 0 ║
╠═══╬═════════╬════╣
║ 1 ║ b = 4*1 ║ 4 ║
╠═══╬═════════╬════╣
║ 2 ║ b = 4*2 ║ 8 ║
╠═══╬═════════╬════╣
║ 3 ║ b = 4*3 ║ 12 ║
╠═══╬═════════╬════╣
║ 4 ║ b = 4*4 ║ 16 ║
╠═══╬═════════╬════╣
║ 5 ║ b = 4*5 ║ 20 ║
╚═══╩═════════╩════╝
Answer:(
6
−
2
)
+
(
3
+
1
)
6
−
2
+
3
+1
Step-by-step explanation:
Add the numbers
Combine like terms
Answer:
You can solve this with common sense, but I'll do it for you and read my explanation before you demand an answer.
Step-by-step explanation:
When you look at a right angle, one forms 90°
A square has 4 sides, each should measure 90°.
That is how we know that point C measures 90°.
Now let's solve for x.
100+(x+10)+90°=90°
Solve the equation:
100+x+10+90=90
Step 1 : Solve for both sides.
100+x+10+90=90
(x)+(100+10+90)=90 ADD LIKE TERMS!
x+200=90
Step 2: Subtract 200 from both sides so you can make them equal.
x+200−200=90−200
x=−110
So, we get that <em>x=-110</em>. So <em>the blank side</em> should measure <em>90 degrees</em>.
Answer:
The answer is 1
Step-by-step explanation:
-50+50=1
