The region bounded by y = e−x2, y = 0, x = 0, and x = b (b > 0) is revolved about the y-axis. (Round your answers to three decimal places.) (a) Find the volume of the solid generated when b = 2.

0.982 *  = 3.085 cubic units

Step-by-step explanation:

To find the volume of the solid generated by a region that is bounded by lines where x = 0 , x (b) = 2 we apply the formula given in the attachment below  

the required region boundaries are

y = e^-x2 , y = 0 ,  x = 0,  x = b ( b >0)

attached below is a detailed solution of the problem

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?