(a) Use a Riemann sum with m = n = 2 to estimate the value of the sin(x + y) dA R where R = [0, π] × [0, π]. Take the sample points to be lower left corners. (Round your answer to three decimal places.)

4.9361

Step-by-step explanation:

Rieman sum = ∫∫ΔA

ΔA = ΔxΔy

Δx =  = = pi/2 = Δy

ΔA =  pi/2 * pi/2 =

Evaluating at the four corners

=

= 2

∫∫ΔA = 2 *  = = 4.9361

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where,

here given table is,

price ($), x   :           18         23       25       29       30       33

pairs sold, y :         16         13         10       8         6       2

so, ,   ,   ,

and   ,

thus, slop of the given line is,

⇒  

⇒   ≈ 33