calc check: hooke's law
A force of 27N is required to maintain a spring stretched from its natural length of 12cm to a length of 15cm. How much work is done in stretching the spring from 15 to 25cm? and this is what i did.. please check to see if i did it correctly.. thanks :) f=27N 12cm to 15cm f(x)...
calculus
Given the differential equation: dy/dx = y(1+x), y(0)=1, Use Euler's method with step size .1 to approximate y(.3). y' = y(1+x), y'(0) = 1(1+0)=1 ->the solution has slope 1 at the point (0,1); x0=0, y0=1, h=0.1, F(x,y)=y(1+x) y1=y0+h*F(x0,y0) y1=1 + 0.1(1(1+0)) ...
Calculus - Hydrostatic Pressure
Please check my work: Find the hydrostatic pressure on one end of a water trough full of water, the end of which is a trapezoid with given dimensions: top of trapezoid = 20 feet, sides of trapezoid both = 8 feet, bottom of trapezoid = 12 feet. Depth of water = 8 feet Density o...
Calculus - Seperable Equations
Solve the separable differential equation (dy/dx)=y(1+x) for y and find the exact value for y(.3). dy/dx = y(1+x) dy/y = (1+x)dx Integral (dy/y) = Integral (1+x)dx ln (y) = x + (1/2)x^2 + C y = e^(x + (1/2)x^2 + C) y(0.3) = e^(0.345 + C) I am stuck here. How do I solve for C t...
Calculus
Given the differential equation: dy/dx = y(1+x), y(0)=1, Use Euler's method with step size .1 to approximate y(.3). y' = y(1+x), y'(0) = 1(1+0)=1 ->the solution has slope 1 at the point (0,1); x0=0, y0=1, h=0.1, F(x,y)=y(1+x) y1=y0+h*F(x0,y0) y1=1 + 0.1(1(1+0)) ...
Calculus - Orthogonal Trajectories
Find the orthogonal trajectories of the family of curves: y = k*(e^-x) --------------- so k = y/(e^-x) differentiating we get: 1 = -k(e^-x)*(dx/dy) 1/(dx/dy) = -k(e^-x) dy/dx = -k(e^-x)...substituting for k: dy/dx = -(y/(e^-x))*(e^-x) dy/dx = -y Integral(1/=y)dy = Integral dx ...
Calculus - Center of Mass
Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2. X = 1/Area*Integral from a to b: x*f(x)dx Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx How do I find the area for this? Once I know that, is this the correct set up? X = 1/Area*In...
Calculus
Solve the differential equation. Let C represent an arbitrary constant. (Note: In this case, your answer willto have a negative sign in front of the arbitrary C.) (dz)/(dt) + e^(t+z) = 0 --------------- (dz/dt) + (e^t)(e^z) = 0 (dz/dt) = -(e^t)(e^z) dz = -(e^t)(e^z)dt (dz/e^z)...
Calculus
The tank shown is full of water. Given that water weighs 62.5 lb/ft3, find the work required to pump the water out of the tank. The tank shown is a hemisphere with r = 5 ft. The water is to be pumped out at the top. First I solved for ri, ri / (5 - xi) = 5 / 5 ri = 5 - xi Vi =...
Calculus
The tank shown is full of water. Given that water weighs 62.5 lb/ft3, find the work required to pump the water out of the tank. The tank shown is a hemisphere with r = 5 ft. The water is to be pumped out at the top. First I solved for ri, ri / (5 - xi) = 5 / 5 ri = 5 - xi Vi =...
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