If you bike 8 miles south and then 6 miles east, what is the distance you are from your starting point? 10 miles 100 miles 14 mi
1 answer:
Answer:
10 miles
Step-by-step explanation:
Given: Bike goes 8 miles south and then 6 miles east
To find: distance between the final point and the starting point
Solution:
<u>Pythagoras Theorem</u>
In a right angled triangle, square of hypotenuse is equal to the sum of squares of the two sides.
In ΔOAB,
Put
Take square root on both sides.
So, distance between the final point and the starting point is 10 miles
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Answer:
The Taylor series is .
The radius of convergence is .
Step-by-step explanation:
<em>The Taylor expansion.</em>
Recall that as we want the Taylor series centered at its expression is given in powers of
. With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of
.
Then,
Now, in order to make a more compact notation write . Thus, the above expression becomes
Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,
Now, substitute in the previous equality. Thus,
<em>Radius of convergence.</em>
We find the radius of convergence with the Cauchy-Hadamard formula:
Where stands for the coefficients of the Taylor series and
for the radius of convergence.
In this case the coefficients of the Taylor series are
and in consequence . Then,
Applying the properties of roots
Hence,
Recall that
So, as we get that
.
Answer:
Step-by-step explanation: