Search 70,009 tutors

# 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.

# 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.

# 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...

# 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

Evaluate (d^100/(dx^95 dy^2 dx^3))(ye^x(x)+cos(x)).

# 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.

# 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...

# 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.

# 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...

# 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?

# 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.

# 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.

# Find the normal vector to the plane?

Find the normal vector to the plane 3x+2y+6z=6.

# 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.

# 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 x(t)=sqrt(1+t),...

# 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.

# 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).

# 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.

# 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...

# 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.

# Find (d^2*z)/(dx^2)+(d^2*z)/(dy^2).

z=(e^x)(cos(y)). Find (d^2*z)/(dx^2)+(d^2*z)/(dy^2).

# 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).

# Find a parametric representation of the surface?

Find a parametric representation of the surface z=3x+4y.

# 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?

# Find the limit?

Find lim as (x, y)--->(0, 0) for (8x^2*y^2)/(x^4+y^4). lim as (0, y)--->(0, 0) =0/y^4=0 lim as (x, 0)--->(0, 0) =0/x^4=0 The limit is 0, right? But doesn't exist is the answer for...

# Let aT be the tangential component of the acceleration?

Let aT be the tangential component of the acceleration vector of r(t)=. What is (aT)^2 at t=pi/2? r'(t)=<1-cos(t), sin(t), 0> r''(t)= r'(pi/2)=<1,...

# Let a=<2, 3, 1> and b=<-2, 5, -3>?

Let a=<2, 3, 1> and b=<-2, 5, -3>. Find the absolute value of a+b.

# Find the curvature of the curve of intersection?

Find the curvature of the curve of intersection of the cylinder x^2+y^2=16 and the plane x+z=5 at (4, 0, 1).

# Find the Cartesian equation for the curve?

Find the Cartesian equation for the curve described by the polar equation r=1/(1-sin(theta)).

# What is the y-component of r(pi/2)?

If r'(t)= and r(0)=<1, 1, 2>. What is the y-component of r(pi/2)? r(t)=<-cos(t), -sin(t), t^2> r(pi/2)=-1 So -1 is the answer?

# Let k(x) be the curvature of y=ln(x) at x.

Let k(x) be the curvature of y=ln(x) at x. Find the limit as x approaches to the positive infinity of k(x).

# Find the domain of r(t)?

Find the domain of r(t)=. Answer: (-1, 1)U(1, positive infinity) But how do you figure this out?

# Find the curvature of the curve?

Find the curvature of the curve r(t)=(t+1)i+2(t^2-1)j+(t-2)k. r'(t)=i+4tj+k sqrt(1^2+(4t)^2+1^2)=sqrt(2+16t^2) r''(t)=4j r'(t)xr''(t)=? Please show your work step by step from...

# What's f(x, -x^2, x^2)?

If f(x, y, z)=(z^2+x^2-y)/(2x^2+y), what's f(x, -x^2, x^2)? Answer: x^2+2 I have no idea to do this.

# What's the arc length for the curve?

What's the arc length for the curve defined by r(t)=3sin(t)i+3cos(t)j+4tk for 0<=t<=10? (Answer: 50) r'(t)=<3cost, -3sint, 4>

# Determine the minimum surface area?

Determine the minimum surface area of a closed rectangular box with volume 8 ft^3.

# Find the shortest distance between the planes?

Find the shortest distance between the planes 2x+3y-z=2 and 2x+3y-z=4.

# If f(x, y, z)=sin(3x-yz)?

If f(x, y, z)=sin(3x-yz), where x=e^(t-1), y=t^3, z=t-2, what's df/dt(1)? df/dt=(df/dx)(dx/dt)+(df/dy)(dy/dt)+(df/dz)(dz/dt) (3cos(3x-yz))(e^(t-1))+(cos(3x-z))(3t^2) +(cos(3x-y))(1) What...

# If f(x, y, z)=sin(3x-yz), where x=e^(t-1),?

If f(x, y, z)=sin(3x-yz), where x=e^(t-1), y=t^3, z=t-2, what's df/dt(1)?

# What's the length of the curve?

What's the length of the curve r(t)=<2 cos t, 2 sin t, sqrt(5)> from 0<=t<=2pi?

# True or False? The integral from 0 to 2pi?

True or False? The integral from 0 to 2pi, from 0 to 4, from r to 4 dz dr dtheta represents the volume enclosed by the cone z=sqrt(x^2+y^2) and the plane z=4.

# Use Stokes' Theorem to evaluate the surface integral?

Use Stokes' Theorem to evaluate the surface integral where F= and where S is the portion of z=1-x^2-y^2 above the xy-plane with n upward. Answer: -pi x^2+y^2=1...

# Use Stokes' Theorem to evaluate the line integral?

Use Stokes' Theorem to evaluate the line integral where F=<(x^2)(e^x)-y, sqrt(y^2+1), z^3> and where C is the boundary of the portion of z=4-x^2-y^2 above the xy-plane. The curl is <0, 0, 1> but...

# Show that the limit does not exist?

Show that lim (x, y)-->(0, 0) (3x^2(y))/(x^4+y^2) does not exist.

# Find the directional derivative of f(x, y)?

Find the directional derivative of f(x, y)=x^2*y+4y^2 at (2, 1) for u=<1/2, sqrt(3)/2>. Answer: 2+6sqrt(3) <2xy, 8y> at (2, 1)=<4, 8> <4, 8>*<1/2, sqrt(3)/2>=2+4sqrt(3) This doesn't...

# Find the directional derivative?

Find the directional derivative of f(x, y)=x^2*y+4y^2 at (2, 1) for u=<1/2, sqrt(3)/2>. Answer: 2+6sqrt(3) The gradient is <2xy, 8y> at (2, 1)=<4, 8> And <4, 8>*<1/2, sqrt(3)/2>=2+4sqrt(3) This...

# Find the gradient of f(x, y)?

Find the gradient of f(x, y)=2e^4x/y-2x at (2, -1). Answer: <-8e^-8-2, -16e^-8> Step by step, I really don't know this completely.