We have
<span>y=cos x/(x</span>²+x+2) <span>on the closed interval [-1, 3]
</span><span>
we know that
</span>The average value of f(x) on the interval [a, b] is given by:
<span>F(avg) = 1/(b - a) ∫ f(x) dx (from x=a to b).
(b-a)=(3+1)------> 4
</span>= 1/4 ∫ cos(x)/(x² + x + 2) dx (from x=-1 to 3).
Note that [cos(x)/(x² + x + 2)] does not have an elementary anti-derivative.
By approximating techniques:
1/4 ∫ cos(x)/(x^2 + x + 2) dx (from x=-1 to 3) ≈ 0.182951
the answer is
<span>the average value of y = cos(x)/(x</span>²<span> + x + 2) on [-1, 3] is approximately 0.182951</span>
Standard position would be 2pi-11pi/6, or pi/6 in the fourth quadrant
The z-statistic can be calculated as the difference in the population mean and sample mean divided by the standard error. The standard error can be calculated as the standard deviation divided by square root of sample size. The standard error:
SE = 12/ sqrt(20) = 2.68
The z-statistic: (195 -208) 2.68 = -4.86
To find the difference in two lengths we need to subtract them
but here both length are given in mix fraction form
let us first try to write them in simple fraction form .
the first is : 2 7/8 we write it as : (8* 2 + 7 )/ 8 = 23/8
The second is : 1 1/2 we write it as : ( 2*1 + 1) /2 = 3/2
Let us now try finding difference : 23/8 - 3/2
as both have different number in the bottom we try to make a same number in denominator of both fractions .
2 can become by multiplying it to 4 .
let us multiply 3/2 by 4/4 it makes : ( 12 /8 )
now both fractions can be subtracted . (23/8 ) - ( 12/8 )
( 23 - 12 ) /8 = ( 11/8 )
that is the answer : 11/8 miles.
