Evan Cruzen
November 1, 2016
5.2 Exponential and Logarithmic
Models
Exercises 8, 10, 18, page 303
Exercises 4, 6, 16 page 318
Page 303
8)
Midpoint formula: ((x1 + x2 )/2),((y1 + y2 )/2)
((-3+5)/2),((3+7)/2)
(1,5)
Radius formula: r = (x2 - x1 )2 +(y2 - y1 )2 )^(1/2)
r = (5 + 3)2 + (-7 - 13)2 )^(1/2)
{Reduce[r == 4 * Sqrt[29], {r}], N[Reduce[r == 4 * Sqrt[29], {r}], 6]}
r ⩵ 4
29 , r ⩵ 21.5407
The standard equation for a circle is (x - h)2 + (y - k)2 = r 2 .
The equation for this circle is (x - 1)2 + (y - 5)2 = 464.
10)
A graph of the equation given is shown below.
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ContourPlot- 2 + x ^ 2 + 3 + y ^ 2 == 9, {x, - 3.3, 7.3}, {y, - 8.3, 2.3}
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0
-2
-4
-6
-8
-2
0
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6
18)
The slope of the line that represents traveling from the first city to the second city is y=(56/53)x-56.
Since we know that the formula for the circle that represents the radio transmitter’s receivable distance
is x^2 + y^2 = 44^2, we can use a graphing calculator to find the two points that the line and circle
intersect. (graphed using desmos.com)
Now that we know these two points, we can solve for the distance between them using the formula
Distance = ((x2 - x1)^2 + (y2 - y1)^2)^(1/2) (obtained from goo.gl/IaJ95x)
Distance = 42.63 miles
During the trip, you will be able to listen to the transmitter for approximately 42.63 miles.
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4)
30 * pi/180 = 0.524 radians
6)
((11pi)/6) * (180/pi) = 330 degrees
16)
Formula" A
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