First term: a1 = 151
common difference: d = -14 (we decrease by 14 each time, eg, 151-14 = 137)
nth term of this arithmetic sequence is...
an = a1+d(n-1)
an = 151+(-14)(n-1)
an = 151-14n+14
an = -14n+165
This will be used in the formula below
Sn = n*(a1+an)/2
<span>Sn = n*(151+(-14n+165))/2
</span><span>S26 = 26*(151+(-14*26+165))/2 ... replace every n with 26
</span>S26 = -624
The final answer here is choice C) -624
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The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
SOLUTION:
GCF = 2
= 6y^3 + 10n^2
= 2 ( 3y^3 + 5n^2 )
Hope this helps! :)
Have a lovely day! <3
Answer by JKismyhusbandbae: Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically.
