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Gnom [1K]
3 years ago
8

Saint Petersburg, Russia and Anchorage, Alaska, both have approximately the same latitude of 60 degrees. That means you can reac

h Saint Petersburg from Anchorage by flying directly east, or directly west. Assume the earth is a sphere of radius 6371 km. (a) By heading directly east, what is the distance from Anchorage (longitude 150 degrees W) to Saint Petersburg (longitude 30 degrees E)?
Mathematics
1 answer:
user100 [1]3 years ago
5 0

Answer:

Distance from Anchorage (longitude 150 degrees W) to Saint Petersburg (longitude 30 degrees E) = 10,002.47 KM

Step-by-step explanation:

As earth is a sphere of radius 6371 km.

Therefore at 60 degree latitude, the radius of circle can be calculated as shown below:

= 6371 * Cos 60

= 3185.5 KM

Saint Petersburg is nearly 180 degree about Anchorage by flying directly east.

So Distance from Anchorage (longitude 150 degrees W) to Saint Petersburg (longitude 30 degrees E) can be calculated as shown below:

= (180 * 2 * 3.1416 * 3185.5) / 360

= 10,002.47 KM

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OLga [1]

Answer:

x-intercept= (3⅓, 0)

y-intercept= (0, 4²⁄₇)

Please see the attached picture for the graph.

Step-by-step explanation:

-9x -7y= -30

Let's simplify the equation by dividing both sides by -1.

9x +7y= 30

x- intercept occurs at y= 0.

When y= 0,

9x +7(0)= 30

9x= 30

x= 30 ÷9

x = 3 \frac{1}{3}

Thus, x- intercept occurs at (3⅓, 0).

y-intercept occurs at x= 0.

When x= 0,

9(0) +7y= 30

7y= 30

y= 30 ÷7

y = 4 \frac{2}{7}

Thus, y- intercept occurs at (0, 4²⁄₇).

_____

To graph the equation, draw the x and y axis on a graph paper. Use an appropriate scale to divide the line into equal parts. Next, plot the points (3⅓, 0) and (0, 4²⁄₇). Then, join the two points with a straight line.

Notes:

  • x- intercept is the point at which the graph cuts through the x- axis. In this case, your x- axis is the horizontal line that runs from left to right of your graph paper. In order for a point to be on this horizontal line, look at the y- axis and notice that it sits at y= 0. The same reason applies for why the y- intercept occurs at x= 0. This has to do with the two axis cutting each other at the point (0,0), resulting in the x and y coordinates of 0 for the y and x intercepts respectively.

  • Simplifying the equation in the first step is not necessary, but it is a good practice and might reduce carelessness.

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The marginal price per pound (in dollars) at which a coffee store is willing to supply x pounds of Jamaican Blue Mountain coffee
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Answer:

Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.

Step-by-step explanation:

We are given the following information in the question:

The marginal price per pound (in dollars) is given by:

p'(x) = \displaystyle\frac{208}{(x+7)^2}

where x is the supply in pounds.

P(x) = \displaystyle\int p'(x)~dx =\displaystyle\int\displaystyle\frac{208}{(x+7)^2}~dx\\\\P(x) = \frac{-208}{(x+7)} + c\\\\\text{where c is the constant of integration.}

The coffee shop is willing to supply 9 pounds per week at a price of $7 per pound.

Thus, we are given that

P(9) = 7

Putting the values, we get,

P(x) = \displaystyle\frac{-208}{(x+7)} + c\\\\P(9) = 7\\\\\displaystyle\frac{-208}{(9+7)} + c = 7\\\\c = 7 + \frac{208}{16} = 20

P(x) = \displaystyle\frac{-208}{(x+7)} + 20

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