05/20/13
Find the area of the parallelogram?
Find the area of the parallelogram spanned by the vectors <1, 0, -1> and <-2, 2, 0>.
I have troubles with dot products.
05/20/13
Find the work done by the force?
A constant force F=<-1, 2, -5> acts on a particle as it moves from A(2, 4, 1) to B(-2, 1, 3). Find the work done by the force.
I have trouble for finding the dot products.
05/19/13
How many students only created a dessert?
Each student in a cooking class of 50 students is assigned to create a dessert, an appetizer, or both. The total number of students creating an appetizer is seven more than the number of students...
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05/19/13
What is the area of rectangle B?
Right triangle A has base b, height h, and area x. Rectangle B has length 2b and width 2h. What is the area of rectangle B in terms of x?
a) 2x
b) 4x
c) 6x
d) 7x
e) 8x
05/18/13
Find a potential function for the vector field?
Find a potential function for the vector field f(x, y)=2x/y i+(1-x^2)/y^2 j.
05/15/13
What was the ball's initial speed?
A spring gun at ground level fires a golf ball at an angle of 45 degrees. The ball lands 10 m away.
a) What was the ball's initial speed?
b) For the same initial speed, find the two firing angles...
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05/13/13
Find an equation of the plane?
Find an equation of the plane that passes through the point P(-1, 2, 1) and contains the line of intersection of the planes x+y-z=2 and 2x-y+3z=1.
05/11/13
What's the orbital period of the satellite?
A satellite circles planet X in an orbit having a radius of 10^8 m. If the radius of planet X is 10^7 m and the free fall acceleration on the surface of X is 20 m/s^2, what's the orbital period of...
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05/11/13
Find the arc length of the curve?
Find the arc length of the curve defined by r(t)=(t, sqrt(6)/2*t^2, t^3), -1<=t<=1.
r'(t)=<1, sqrt(6)t, 3t^2>
sqrt(1+6t^2+9t^4)
But how do I simplify this?
05/11/13
Find its position at t=1.
A particle starts at the origin with initial velocity i+j-k. Its acceleration is a(t)=ti+j+tk. Find its position at t=1.
05/11/13
Find the speed of the particle?
Find the speed of the particle with position function r(t)=e^3t i+e^-3t j+te^3t k when t=0.
05/11/13
Find dz/dy at (1, ln 2, ln 3) if z(x, y)?
Find dz/dy at (1, ln 2, ln 3) if z(x, y) is defined by the equation xe^y+ye^z+2lnx-2-3ln2=0.
05/06/13
What is the rate of change of temperature?
Suppose the temperature in degrees Celsius at a point (x, y) is described by a function T(x, y) satisfying Tx(2, 7)=4, Ty(2, 7)=2. The position of a crawling ant after t seconds is given by...
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05/06/13
Find the slope of the tangent line at theta=pi/2?
Find the slope of the tangent line at theta=pi/2 for the curve in the xy plane with the polar equation r=theta.
05/05/13
Find the perpendicular distance between the parallel planes?
Find the perpendicular distance between the parallel planes z+1=x+2y and 3x+6y-3z=4.
Find the area of the triangle?
Find the area of the triangle with vertices A(2, 1), B(5, 3), and C(6, 4).
05/04/13
Find the mass of the plate with density?
Find the mass of the plate with density p(x, y)=ky, where k is a positive constant and R is the region bounded by y=x^2 and x=y^2.
05/04/13
Evaluate the double integral?
Evaluate the double integral from 0 to 1 and x^2 to 1 of (x^3)(sin(y^3)) dy dx by reversing the order of integration.
I know how to solve the integral, I just don't know how to set up the new...
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05/02/13
Find the maximal value of f(x, y)?
Find the maximal value of f(x, y)=3y+4x on the circle x^2+y^2=1.
04/29/13
Find the z-intercept of the equation?
Let z=(e^x)(cos(xy)). Find the z-intercept of the equation of the tangent plane to the surface at (1, pi/2, 0).
04/29/13
Find a parametric representation of the surface?
Find a parametric representation of the surface z=3x+4y.
04/28/13
Let z=(x^2+y^2)^(3/2).
Let z=(x^2+y^2)^(3/2). What is (d^2*z)/(dx*dy) at (sqrt(2), sqrt(2))?
dz/dy=3y(x^2+y^2)^(1/2)
d/dx=3x(x^2+y^2)^(1/2)
What should I do next?
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