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Recent questions in Parametric equations, polar coordinates, and vector-valued functions
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-11
Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-09
Use the table of values of
\(f(x, y)\)
to estimate the values of
\(fx(3, 2)\)
,
\(fx(3, 2.2)\)
, and
\(fxy(3, 2)\)
.
\(\begin{array}{|c|c|}\hline y & 1.8 & 2.0 & 2.2 \\ \hline x & & & \\ \hline 2.5 & 12.5 & 10.2 & 9.3 \\ \hline 3.0 & 18.1 & 17.5 & 15.9 \\ \hline 3.5 & 20.0 & 22.4 & 26.1 \\ \hline \end{array}\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-09
Determine whether the given vectors are orthogonal, parallel,or neither:
\(u=(-3,\ 9,\ 6)\)
\(v=(4,\ -12,\ -8)\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-09
Change from rectangular to cylindrical coordinates. (Let
\(r\geq0\)
and
\(0\leq\theta\leq2\pi\)
.)
a)
\((-2, 2, 2)\)
b)
\((-9,9\sqrt{3,6})\)
c) Use cylindrical coordinates.
Evaluate
\(\int\int\int_{E}xdV\)
where E is enclosed by the planes
\(z=0\)
and
\(z=x+y+10\)
and by the cylinders
\(x^{2}+y^{2}=16\)
and
\(x^{2}+y^{2}=36\)
d) Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
\(z=\sqrt{x^{2}+y^{2}}\)
and the sphere
\(x^{2}+y^{2}+z^{2}=8\)
.
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-08
1) Find the area of the part of the plane
4x + 3y + z = 12
that lies in the first octant.
2) Use polar coordinates to find the volume of the given solid.
Bounded by the paraboloid
\(z = 5 + 2x^2 + 2y^2\)
and the plane z = 11 in the first octant
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-07
Express as a trigonometric function of one angle.
a)
\(\cos2\sin(-9)-\cos9\sin2\)
Find the exact value of the expression.
b)
\(\sin\left(\arcsin\frac{\sqrt{3}}{2}+\arccos0\right)\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-06
Find the length of the curve.
\(r(t)=\langle6t,\ t^{2},\ \frac{1}{9}t^{3}\rangle,\ 0\leq t\leq1\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-04
Find an equation of the plane.
The plane through the points (4, 1, 4), (5, -8, 6), and (-4, -5, 1)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-06-04
Find an equation of the plane tangent to the following surface at the given point.
\(7xy+yz+4xz-48=0;\ (2,2,2)\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-25
Find the points on the ellipse
\(4x^2 + y^2 = 4\)
that are farthest away from the point (-1, 0).
(x, y) = ( ) (smaller y-value)
(x, y) = ( )(larger y-value)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-19
Find the volume of the solid generated by revolving the standed region about the x-axis.
Te volume of the solid is ? cubic units.
The equation:
\(4x+3y=24\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-13
Find a basis for the eigenspace corresponding to the eigenvalue of A given below.
\(A=\begin{bmatrix}4 & 0&2&0 \\4 & 2&10&0\\3&-4&17&0\\2&-2&8&3 \end{bmatrix} , \lambda=3\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-13
Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-12
Evaluate the following integral in cylindrical coordinates triple integral
\(\int_{x=-1}^{1}\int_{y=0}^{\sqrt{1-x^{2}}}\int_{z=0}^{2}\left(\frac{1}{1+x^{2}+y^{2}}\right)dzdxdy\)
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-12
Find a unit vector that is orthogonal to both
\(i+j\)
and
\(i+k\)
.
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-08
Find the points on the cone
\(z^2 =x^2+y^2\)
that are closest tothe point (2, 2,0).
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-04
Find an area of shaded region
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-05-03
Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y:
\(f(x,y)=\begin{cases}xe^{-x(1+y)} & x\geq0\ and\ \geq0\\ 0 & otherwise \end{cases}\)
a) What is the probability that the lifetime X of the first component exceeds 3?
b) What are the marginal pdf's of X and Y? Are the two lifetimes independent? Explain.
c) What is the probability that the lifetime of at least one component exceeds 3?
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-03-18
to what property does (-6 + 3 ) + 1 = -6 + (3 + 1) belong to
Parametric equations, polar coordinates, and vector-valued functions
ANSWERED
asked 2021-03-18
Write a short paragraph explaining this statement. Use the following example and your answers Does the particle travel clockwise or anticlockwise around the circle? Find parametric equations if the particles moves in the opposite direction around the circle. The position of a particle is given by the parametric equations
\(x = sin t, y = cos t\)
where 1 represents time. We know that the shape of the path of the particle is a circle.
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