The internal dimension of a cylindrical container has a base area of 20 cm^2 and a height of 10 cm. What is the internal volume
1 answer:
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Answer:
The estimate of In(1.4) is the first five non-zero terms.
Step-by-step explanation:
From the given information:
We are to find the estimate of In(1 . 4) within 0.001 by applying the function of the Maclaurin series for f(x) = In (1 + x)
So, by the application of Maclurin Series which can be expressed as:
Let examine f(x) = In(1+x), then find its derivatives;
f(x) = In(1+x)
f'(0)
f ' ' (x)
f ' ' (x)
f ' ' '(x)
f ' ' '(x)
f ' ' ' '(x)
f ' ' ' '(x)
f ' ' ' ' ' (x)
f ' ' ' ' ' (x)
Now, the next process is to substitute the above values back into equation (1)
To estimate the value of In(1.4), let's replace x with 0.4
Therefore, from the above calculations, we will realize that the value of as well as
which are less than 0.001
Hence, the estimate of In(1.4) to the term is is said to be enough to justify our claim.
∴
The estimate of In(1.4) is the first five non-zero terms.
Answer:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).
Step-by-step explanation:
The final position of the surveyor is represented by the following vectorial sum:
(1)
And this formula is expanded by definition of vectors in rectangular and polar form:
(1b)
Where:
- Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.
- Length of each vector, in kilometers.
- Bearing of each vector in standard position, in sexagesimal degrees.
If we know that ,
,
and
, then the resulting coordinates of the final position of the surveyor is:
According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:
And the distance from the camp is calculated by the Pythagorean Theorem:
The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).