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.
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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.
Which answers have a negative sign and which answers have no negative signs. Put them in the right box that has a negative or no negative sign.
In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
We know that out of the 1996 people, 294 had high blood pressure. We can use that to create a fraction.
294/1996 = 147/998 = 0.14729...
The probability of the next person having blood pressure is about 15%.
Answer:
t=−3 or t=−12
Step-by-step explanation:
Step 1: Subtract -36 from both sides.
t2+15t−(−36)=−36−(−36)
t2+15t+36=0
Step 2: Factor left side of equation.
(t+3)(t+12)=0
Step 3: Set factors equal to 0.
t+3=0 or t+12=0
t=−3 or t=−12
