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Calculus
the volume of a growing spherical cell is v=4/3πr^3, where the radius r is measured in micrometers 1 μm=10^-6m. find the rate of change with respect to r when r=5 μm.
Calculus
r
and r2
r
are unit vectors in the x-y plane making angles a and b with the positive
x-axis. By considering r1 . r2
r r
, derive
cos (a − b) = cos a cos b + sin a sin b
and r2
r
are unit vectors in the x-y plane making angles a and b with the positive
x-axis. By considering r1 . r2
r r
, derive
cos (a − b) = cos a cos b + sin a sin b
Calculus
Determine a unit vector perpendicular to the plane of A = ˆi − 2ˆj + kˆ
r
and B = 2ˆi + 3ˆj − kˆ
r
.
r
and B = 2ˆi + 3ˆj − kˆ
r
.
Calculus
Determine the unit vector normal to the surface (x − 2)2 + (y + 1)2 + z2 = 9 at the point
(2, 1, 4).
(2, 1, 4).
Calculus
paper clips are made from about 0.9 cm of wire what is the greatest number of paper clips that can be made from 10m of wire?
Calculus
You are designing a rectangular poster to contain 256 in^2 of printing with a 3-in. margin at the top and bottom and a 2-in. margin at each side. What overall dimensions will minimize the amount of paper used? (Round to the nearest whole inch if necessary)
Calculus
if C(50)=4600 and Cprime(50)=28 estimate C(55)
Calculus
The force on a particle is described by 9x^3-2 at a point x along the -axis. Find the work done in moving the particle from the origin to x=2.
Calculus
A trough is 10 meters long, 3 meters wide, and 3 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 3 meters, and base, on top, of length 3 meters). The trough is full of water (density 1000 kg/m^3 ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use g=9.8 m/s^2 as the acceleration due to gravity.)
Calculus
A carpet which is 8 meters long is completely rolled up. When x meters have been unrolled, the force required to unroll it further is
f(x)= 600/((x+2)^2)
How much work is done unrolling the entire carpet? Your answer must include the correct units.
f(x)= 600/((x+2)^2)
How much work is done unrolling the entire carpet? Your answer must include the correct units.
