2(8x + 2) - 5 + 5x
2(8x) + 2(2) - 5 + 5x
16x + 4 - 5 + 5x
16x - 1 + 5x
16x + 5x - 1
21x - 1
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>
Answer:
Let x and y be the two positive integers the Christopher is thinking.
x is equal to 7
and y =20
Set up the ratios as proportional fractions:

We can simplify the first fraction to make the problem easier. Both the numerator and denominator of the first fraction can be divided by 3:


Both fractions now have the same denominator. Since both fractions have to equal each other, the numerators will also be the same. Therefore,
x = 4.