If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b − a) ≤ b f(x) dx a ≤ M(b − a). Use this property to estimate the value of the integral. π/9 5 tan(3x) dx π/12 (smaller value) (larger value)

the value of the integral is in the range:

0.006  ≤  int ≤  0.008

Step-by-step explanation:

First, we have the function

5*tan(3x), and the range in this case is: pi/12 ≤ x ≤ pi/9

Then, the first step is find the maximum and minimum of f(x) in this range.

We know that between 0 and pi/2, tan(x) is a growing function, then

then the limits are

5*tan(3*pi/9) = 5*tan(pi/3) = M=  0.091

5*tan(3*pi/12) = 5*tan(pi/4) =m = 0.069

Then the value of the integral is between:

0.069*(3.14/9 - 3.14/12) ≤  int ≤  0.091*(3.14/9 - 3.14/12)

0.006  ≤  int ≤  0.008

answer: a. 13/44

step-by-step explanation: judging by the information given to us, we are looking for experimental probability. we can see that 13 males have chosen chocolate ice cream. there are 44 ice creams in total (remember that the total is always the denominator). so our answer is 13/44.

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )