jon has y stickers. he uses 20 stickers and divides the remainder equally between his two sisters. find the number of stickers e
2 answers:
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The mass of the wire is found to be 40π√2 units.
<h3>How to find the mass?</h3>To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass =
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
Further simplifying;
Now, use integration to find the mass of the wire;
Therefore, the mass of the wire is estimated as 40π√2 units.
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5
a. First five terms: 9,13,17,21,25
b. Sum of first 25 terms = 1425
c. The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.
Further explanation:
Given
Formula of sequence
<u>1. First 5 terms:</u>
For first 5 terms, we have to put n=1,2,...5,
So,
<u>2. Sum of first 25 terms:</u>
For that we have to find 25th term first
The formula for sum is:
<u>3. Type of sequence</u>
The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.
i.e.
Keywords: Arithmetic sequence, Sum of arithmetic sequence
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