Recent questions tagged prove

Find the common ratio of the geometric sequence $16,24,36,54, \ldots$ Then express each sequence in the form $a_{n}=a_{1} r^{n-1}$ and find the eighth term of the sequence.Find the common ratio of the geometric sequence $16,24,36,54, \ldots$ Then express each sequence in the form $a_{n}=a_{1} r^{n-1}$ and find the ei ...
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Find the common ratio of the geometric sequence $1,3,9,27, \ldots$ Then express each sequence in the form $a_{n}=a_{1} r^{n-1}$ and find the eighth term of the sequence.
Find the common ratio of the geometric sequence $1,3,9,27, \ldots$ Then express each sequence in the form $a_{n}=a_{1} r^{n-1}$ and find the eighth term of the sequence.Find the common ratio of the geometric sequence $1,3,9,27, \ldots$ Then express each sequence in the form $a_{n}=a_{1} r^{n-1}$ and find the eight ...
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What is aleph?
What is aleph?What is aleph? ...
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What is affirming the consequent?
What is affirming the consequent?What is affirming the consequent? ...
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If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A}^{T} \mathbf{v}$
If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A}^{T} \mathbf{v}$If A is an $n\times n$ matrix and u and v are $n\times 1$ matrices, then prove that $\boldsymbol{A u} \cdot \mathbf{v}=\mathbf{u} \cdot \boldsymbol{A} ... close 0 answers 44 views Let$\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$be a fixed vector in$R^{2}$. In each part, describe in words the set of all vectors$\mathbf{r}=(x, y)$that satisfy the stated condition.Let$\mathbf{r}_{0}=\left(x_{0}, y_{0}\right)$be a fixed vector in$R^{2}$. In each part, describe in words the set of all vectors$\mathbf{r}=(x, y) ...
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Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy
Show that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfyShow that two nonzero vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$ in $R^{3}$ are orthogonal if and only if their direction cosines satisfy $$\cos \ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \|\mathbf{v}\|=2 and \|\mathbf{w}\|=3, what are the largest and smallest values possible for \|\mathbf{v}-\mathbf{w}\| ? Give a geometric explanation of your results. 0 answers 12 views If \|\mathbf{v}\|=2 and \|\mathbf{w}\|=3, what are the largest and smallest values possible for \|\mathbf{v}-\mathbf{w}\| ? Give a geometric explanation of your results.If \|\mathbf{v}\|=2 and \|\mathbf{w}\|=3, what are the largest and smallest values possible for \|\mathbf{v}-\mathbf{w}\| ? Give a geometric exp ... close 0 answers 101 views Let \mathbf{u} be a vector in R^{100} whose i th component is i, and let \mathbf{v} be the vector in R^{100} whose i th component is 1 /(i+1). Find the dot product of \mathbf{u} and \mathbf{v}.Let \mathbf{u} be a vector in R^{100} whose i th component is i, and let \mathbf{v} be the vector in R^{100} whose i th component is 1 ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If \mathbf{v} is a vector in R^{n}, and if k is any scalar, then prove that \|k \mathbf{v}\|=|k|\|\mathbf{v}\| 1 answer 8 views If \mathbf{v} is a vector in R^{n}, and if k is any scalar, then prove that \|k \mathbf{v}\|=|k|\|\mathbf{v}\|If \mathbf{v} is a vector in R^{n}, and if k is any scalar, then prove that \|k \mathbf{v}\|=|k|\|\mathbf{v}\| ... close 1 answer 5 views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove the orthogonal projection theorem 1 answer 4 views Prove the orthogonal projection theoremProve the orthogonal projection theorem ... close 1 answer 5 views If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}=\|\mathbf{u}\|^{2}+\|\mathbf{v}\|^{2} $$If \mathbf{u} and \mathbf{v} are orthogonal vectors in R^{n} with the Euclidean inner product, then prove that$$ \|\mathbf{u}+\mathbf{v}\|^{2}= ...
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What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$
What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0},z_{0}\right)$ and the line $a x+b y+c z+d=0$ in $R^{3} ?$ ...
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Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is
Prove that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ isProve that, In $R^{3}$ the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}, z_{0}\right)$ and the plane $a x+b y+c z+d=0$ is  D=\frac{\left| ...
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Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.
Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$.Find the distance $D$ between the point $(1,-4,-3)$ and the plane $2 x-3 y+6 z=-1$. ...
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Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.
Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors.Show that $\mathbf{v}=(a, b)$ and $\mathbf{w}=(-b, a)$ are orthogonal vectors. ...
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Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.
Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain.Do the points $A(1,1,1), B(-2,0,3)$, and $C(-3,-1,1)$ form the vertices of a right triangle? Explain. ...
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Is it possible to have $\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$ Explain.
Is it possible to have $\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$ Explain.Is it possible to have $\operatorname{proj}_{\mathrm{a}} \mathbf{u}=\operatorname{proj}_{\mathbf{u}} \mathbf{a} ?$ Explain. ...
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A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?
A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do?A sailboat travels $100 \mathrm{~m}$ due north while the wind exerts a force of $500 \mathrm{~N}$ toward the northeast. How much work does the wind do ...
Express the vector $\mathbf{u}=(2,3,1,2)$ in the form $\mathbf{u}=\mathbf{w}_{1}+\mathbf{w}_{2}$, where $\mathbf{w}_{1}$ is a scalar multiple of $\mathbf{a}=(-1,0,2,1)$ and $\mathbf{w}_{2}$ is orthogonal to a. Express the vector $\mathbf{u}=(2,3,1,2)$ in the form $\mathbf{u}=\mathbf{w}_{1}+\mathbf{w}_{2}$, where $\mathbf{w}_{1}$ is a scalar multiple of $\m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$1 answer 4 views What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$What is the form of vector and parametric equations of lines in$R^{2}$and$R^{3}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Prove by induction that for every natural number$n$,$n^{3}+2 n$is divisible by 3 0 answers 3 views Prove by induction that for every natural number$n$,$n^{3}+2 n$is divisible by 3Prove by induction that for every natural number$n$,$n^{3}+2 n\$ is divisible by 3 ...