Find the tangential and normal components of the acceleration vector
$r(t)=(3t-{t}^{3})i+3{t}^{2}j$

FobelloE
2020-11-02
Answered

Find the tangential and normal components of the acceleration vector
$r(t)=(3t-{t}^{3})i+3{t}^{2}j$

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asked 2021-02-11

Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in $M}_{2\times 4$ with the property that FA = 0 (the zero matrix in ${M}_{3\times 4})$ . Determine if H is a subspace of $M}_{2\times 4$

asked 2021-05-29

Find a vector equation and parametric equations for the line segment that joins P to Q.

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

P(0, - 1, 1), Q(1/2, 1/3, 1/4)

asked 2021-05-29

Which of the following expressions are meaningful? Which are meaningless? Explain.

a)$(a\cdot b)\cdot c$

$(a\cdot b)\cdot c$ has ? because it is the dot product of ?.

b)$(a\cdot b)c$

$(a\cdot b)c$ has ? because it is a scalar multiple of ?.

c)$|a|(b\cdot c)$

$|a|(b\cdot c)$ has ? because it is the product of ?.

d)$a\cdot (b+c)$

$a\cdot (b+c)$ has ? because it is the dot product of ?.

e)$a\cdot b+c$

$a\cdot b+c$ has ? because it is the sum of ?.

f)$|a|\cdot (b+c)$

$|a|\cdot (b+c)$ has ? because it is the dot product of ?.

a)

b)

c)

d)

e)

f)

asked 2021-05-17

Find the scalar and vector projections of b onto a.

$a=(4,7,-4),b=(3,-1,1)$

asked 2022-08-21

Given a vector $u=(x,y,z)\in {\mathbb{R}}^{3}$ and a $3\times 3$ real matrix M, I woud like to know if there exists some formulas to express in other manner the two quantities: $\mathrm{\nabla}\mathrm{\nabla}\cdot (Mu)$ and $\mathrm{\nabla}\times (Mu)$ in terms of M and u.

Also, I want to know for which type of matrix M we have

$\mathrm{\nabla}\mathrm{\nabla}\cdot (Mu)=M\mathrm{\nabla}\mathrm{\nabla}\cdot u$

and

$\mathrm{\nabla}\times (Mu)=M\mathrm{\nabla}\times u.$

Also, I want to know for which type of matrix M we have

$\mathrm{\nabla}\mathrm{\nabla}\cdot (Mu)=M\mathrm{\nabla}\mathrm{\nabla}\cdot u$

and

$\mathrm{\nabla}\times (Mu)=M\mathrm{\nabla}\times u.$

asked 2022-08-19

${f}_{\mathbf{X}}({x}_{1},\dots ,{x}_{k})=\frac{\mathrm{exp}(-\frac{1}{2}(\mathbf{x}-\mathit{\mu}{)}^{\mathrm{T}}{\mathbf{\Sigma}}^{-1}(\mathbf{x}-\mathit{\mu}))}{\sqrt{(2\pi {)}^{k}|\mathbf{\Sigma}|}}$

I believe ${x}_{1},...{x}_{k}\in {\mathbb{R}}^{d}$

How is range of ${f}_{\mathbf{X}}$ a scalar?

I believe ${x}_{1},...{x}_{k}\in {\mathbb{R}}^{d}$

How is range of ${f}_{\mathbf{X}}$ a scalar?

asked 2022-07-15

Are four non zero vectors are always linearly dependant

If three vectors are on the z-x plane and the fourth vector is not in this plane, the vectors would be linearly independent, no?

If three vectors are on the z-x plane and the fourth vector is not in this plane, the vectors would be linearly independent, no?