5. the inverse laplace transform of? +-? is given by (a) 15.0e-31 cos(7t + 30.0? )u(t) (b) 30.0e-t cos(3t+30.0ult) (c) 15.0e-71 cos(3t + 45.0? )u(t) (d) 2.36e-1t cos(58+274u(t) (e) none of the above . in the partial fraction expansion .itwier + ? ? the value of " + coefficient c? is given by (a) 0.54 v (b) 1.68 v (c) 2.00 v (d) 2.50 v (e) 5.00 v 7. the behavioe of a certain circuit is described by the transfer function h(s)- where v, is the laplace-domain inpat of the circuit, vo, is the laplace-domain out pat of the circuit, and is the corresponding time-domain output of the cireuit. if the isput to the circuit is gives by vt then what valme does vo(t) approach as t goes to infimity? (a) 0.75 v (b) 03v (c) 1.5 v (d) oo v (e) 0 v s. consider the laplace- domaltn signa and creouding time domai ft) " c" the value of ro-) is given by (a) 0.5 (b) 4.0 (d) oo (e) 0.0 9. evaluate the integral (e-)+t-2)+(-4)t (a) 17 (b)-1 (c) 2 (d) 3 (e) noae of the above

x=half

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the answer is b