Write out the form of the partial fraction decomposition of the function appearing in the integral: ∫−4x−34x2+2x−8dx ∫−4x−34x2+2x−8dx determine the numerical values of the coefficients, aa and bb, where a≤ba≤b and −4x−34x2+2x−8 =adenominator+bdenominator.
a =
b=

Looks like the integrand is

The denominator is factorized as

Then we want to find constants such that

We can use the cover-up method to easily find and :

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm