Solve this A tourist starts off from town A and travels for 50km on a bearing of N80°W to town B.At town B ,he continues for ano
1 answer:
Answer:
The point C is 12.68 km away from the point A on a bearing of S23.23°W.
Step-by-step explanation:
Given that AB is 50 km and BC is 40 km as shown in the figure.
From the figure, the length of x-component of AC = |AB sin 80° - BC cos 20°|
=|50 sin 80° - 40 cos 20°|=11.65 km
The length of y-component of AC = |AB cos 80° - BC sin 20°|
=|50 cos 80° - 40 sin 20°|= 5 km
tan= 5/11.65
=23.23°
AC= km
Hence, the point C is 12.68 km away from the point A on a bearing of S23.23°W.
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Answer:
Range = 115$
Standard Deviation = 43.76$
Variance = 1915.142$
Option A) The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are more important than the amount of variation in the area.
Step-by-step explanation:
We are given the data for prices in dollars for one night at different hotels in a certain region.
234, 160, 119, 131, 218, 207, 146, 141
Range:
Sorted data: 119, 131, 141, 146, 160, 207, 218, 234
Standard Deviation:
where are data points,
is the mean and n is the number of observations.
Sum of squares of differences = 4160.25 + 90.25 + 2550.25 + 1482.25 + 2352.25 + 1406.25 + 552.25 + 812.25 = 13406
Variance =
Measure of variance for someone searching for room:
Option A) The measures of variation are not very useful because when searching for a room, low prices, location, and good accommodations are more important than the amount of variation in the area.
Answer:
a)
The combined resistance of a circuit consisting of two resistors in parallel is given by:
where
R is the combined resistance
are the two resistors
We can re-write the expression as follows:
Or
In order to see if the function is increasing in r1, we calculate the derivative with respect to r1: if the derivative if > 0, then the function is increasing.
The derivative of R with respect to r1 is:
We notice that the derivative is a fraction of two squared terms: therefore, both factors are positive, so the derivative is always positive, and this means that R is an increasing function of r1.
b)
To solve this part, we use again the expression for R written in part a:
We start by noticing that there is a limit on the allowed values for r1: in fact, r1 must be strictly positive,
So the interval of allowed values for r1 is
From part a), we also said that the function is increasing versus r1 over the whole domain. This means that if we consider a certain interval
a ≤ r1 ≤ b
The maximum of the function (R) will occur at the maximum value of r1 in this interval: so, at