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If $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal to
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If $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal toIf $\underline{a}=(2,1,-1)$ and $\underline{b}=(-1,2,1)$, then $2 \underline{a}-3 \underline{b}$ is equal to   A) $(1,-4,-5)$ B) $(7,-4,5)$ C ...
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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to
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The distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal toThe distance from the point $(1,1,1)$ to the plane $ 2 x-10 y+11 z-4=0 $ is equal to   A) $\dfrac{1}{3}$ B) 3 C) $\dfrac{1}{15}$ D) 5 E) no ...
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What is the product of $A$, $B$ and $C$?
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What is the product of $A$, $B$ and $C$?\begin{equation} \text { Given } A=\left\begin{array}{ll} 4 & 5 \end{array}\right, B=\left\begin{array}{llll} 1 & 1 & 2 & 1 \end{ar ...
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What is the distance $D$ between the point $P_{0}\left(x_{0}, y_{0}\right)$ and the line $a x+b y+c=0$ in $R^2$?
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Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to:
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Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to:Let $A$ be an $n \times n$ matrix with $I_{n}$ the identity matrix. The statement det $A \neq 0$ is equivalent to:   A. All the given options a ...
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The complex number $\frac{1-2 i}{1+2 i}$ is equal to
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The complex number $\frac{1-2 i}{1+2 i}$ is equal toThe complex number $\dfrac{1-2 i}{1+2 i}$ is equal to   A) $\dfrac{3}{5}+\dfrac{4}{5} i$ B) $-\dfrac{3}{5}+\dfrac{4}{5} i$ C) $\dfrac{3}{5}-\ ...
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If $\vec{a}=(2,1,-1)$ and $\vec{b}=(-1,2,1)$, then $2 \vec{a}-3 \vec{b}$ is equal to
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If $\vec{a}=(2,1,-1)$ and $\vec{b}=(-1,2,1)$, then $2 \vec{a}-3 \vec{b}$ is equal toIf $\vec{a}=(2,1,-1)$ and $\vec{b}=(-1,2,1)$, then $2 \vec{a}-3 \vec{b}$ is equal to   A) $(1,-4,-5)$ B) $(7,-4,5)$ C) $(7,-4,-5)$ D) $(7,4, ...
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asked in Mathematics Jan 13
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The distance from the point $(-1,1,1)$ to the plane
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The distance from the point $(-1,1,1)$ to the planeThe distance from the point $(-1,1,1)$ to the plane $$ 2 x-10 y+11 z-4=0 $$ is equal to   A) 3 B) $\frac{1}{3}$ C) 5 D) $\frac{1}{5}$ E) no ...
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asked in Mathematics Jan 13
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Prove Rolle's Theorem under the assumption that for the function $f$ on $[a, b]$ you have $f(x)>f(a)$ for some $x$ in the domain of $f$.
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What is the trick for factorizing a polynomial of the form \(ax^2+bx+c\) where \(a\neq1\)?
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Find the domain, the asymptotes (if any) of $f$ and classify each asymptote as vertical, horizontal or slant.
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Find the domain, the asymptotes (if any) of $f$ and classify each asymptote as vertical, horizontal or slant.Let $$ f(x)=\frac{x^{2}-3}{x+2} $$ You may use that $$ f^{\prime}(x)=\frac{x^{2}+4 x+3}{(x+2)^{2}} \quad \text { and } \quad f^{\prime \prime}(x)=\fra ...
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asked in Mathematics Jan 13
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Find the intercepts on the $x$ - and $y$-axes (if any) for the function $f(x)=\frac{x^{2}-3}{x+2}$ and discuss symmetry.
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Define a vector
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Define a vectorDefine a vector ...
by MathsGee Platinum
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asked in Mathematics Jan 13
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What is the trick for factorizing a polynomial of the form \(ax^2+bx+c\) where \(a\neq1\)?
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Prove the remainder theorem of polynomials
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Prove the remainder theorem of polynomialsProve the remainder theorem of polynomials ...
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For which values of \(x\) will \[ \sum_{k=1}^{\infty}(4 x-1)^{k} \] exist.
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Calculate \(S_{\infty}\) if \[ \sum_{p=1}^{\infty} 8(4)^{1-p} \]
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Calculate \(S_{\infty}\) if \[ \sum_{p=1}^{\infty} 8(4)^{1-p} \]Calculate \(S_{\infty}\) if \ \sum_{p=1}^{\infty} 8(4)^{1-p} \ ...
by Pieter SIlver Status
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asked in Mathematics Jan 11
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The unit circle is split into regions by the 4 lines that satisfy. How many of these regions have area \(\frac{\pi}{8}\) ?
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The unit circle is split into regions by the 4 lines that satisfy. How many of these regions have area \(\frac{\pi}{8}\) ?The unit circle is split into regions by the 4 lines that satisfy \ \begin{gathered} 6 x^{4}-7 x^{3} y-36 x^{2} y^{2}+ \\ 7 x y^{3}+6 y^{4}=0 \end{ga ...
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asked in Mathematics Jan 11
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Prove that \(A \cup \emptyset=A\)
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Prove that \(A \cup \emptyset=A\)Prove that \(A \cup \emptyset=A\) ...
by MathsGee Platinum
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Prove that \(A \subset A \cup B\) and \(B \subset A \cup B\)
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Prove that \(A \subset A \cup B\) and \(B \subset A \cup B\)Prove that \(A \subset A \cup B\) and \(B \subset A \cup B\) ...
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Prove that \(A \cup(B \cup C)=(A \cup B) \cup C\), (associative law)
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Prove that \(A \cup(B \cup C)=(A \cup B) \cup C\), (associative law)Prove that \(A \cup(B \cup C)=(A \cup B) \cup C\), (associative law) ...
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asked in Mathematics Jan 8
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Prove that \(A \cup B=B \cup A\), (commutative law)
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Prove that \(A \cup B=B \cup A\), (commutative law)Prove that \(A \cup B=B \cup A\), (commutative law) ...
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