# Recent questions tagged axis

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$D M$ is a diameter of circle $A . R T D \perp R C$, $R T=3 \mathrm{~cm}, R C=4 \mathrm{~cm}, M C=6 \mathrm{~cm}$ and $D M=2 x$.
$D M$ is a diameter of circle $A . R T D \perp R C$, $R T=3 \mathrm{~cm}, R C=4 \mathrm{~cm}, M C=6 \mathrm{~cm}$ and $D M=2 x$. $D M$ is a diameter of circle $A . R T D \perp R C$, $R T=3 \mathrm{~cm}, R C=4 \mathrm{~cm}, M C=6 \mathrm{~cm}$ and $D M=2 x$. &nbsp; ...
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Given $Q U=24 \mathrm{~cm}, Q C=16 \mathrm{~cm}, D A=6 \mathrm{~cm}$ and $C D=x$.
Given $Q U=24 \mathrm{~cm}, Q C=16 \mathrm{~cm}, D A=6 \mathrm{~cm}$ and $C D=x$. Given $Q U=24 \mathrm{~cm}, Q C=16 \mathrm{~cm}, D A=6 \mathrm{~cm}$ and $C D=x$. 1. Prove $\triangle Q U C \| \triangle A C D$ 2. C ...
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In $\triangle A C E, A B=B C, G E=15 \mathrm{~cm}$ and $A F=F E=E D$. Determine the length of $C E$.
In $\triangle A C E, A B=B C, G E=15 \mathrm{~cm}$ and $A F=F E=E D$. Determine the length of $C E$. In $\triangle A C E, A B=B C, G E=15 \mathrm{~cm}$ and $A F=F E=E D$. Determine the length of $C E$. &nbsp; ...
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Given circle $A B C D$ with $A B \| E F$.
Given circle $A B C D$ with $A B \| E F$. Given circle $A B C D$ with $A B \| E F$. a) Prove $C D E F$ is a cylindrical quad. b) If $\hat{D}_{2}=38^{\circ}$, calculate $\hat{E ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given circle centre \(M$ with a diameter of $20 \mathrm{~cm}$ and "chord $D F$ of $12 \mathrm{~cm}$. Determine the length of of chord $A C$.
Given circle centre $M$ with a diameter of $20 \mathrm{~cm}$ and "chord $D F$ of $12 \mathrm{~cm}$. Determine the length of of chord $A C$. Given circle centre $M$ with a diameter of $20 \mathrm{~cm}$ and &quot;chord $D F$ of $12 \mathrm{~cm}$. &nbsp; Determine the le ...
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Find the centroid of the area bounded by the parabola $y=x^{2}$ and the line $2 x+3$.
Find the centroid of the area bounded by the parabola $y=x^{2}$ and the line $2 x+3$.Find the centroid of the area bounded by the parabola $y=x^{2}$ and the line $2 x+3$. ...
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Find the centroid of the region bounded by the parabola $y=x^{2}$, the line $x=2$, and the $x$-axis.
Find the centroid of the region bounded by the parabola $y=x^{2}$, the line $x=2$, and the $x$-axis.Find the centroid of the region bounded by the parabola $y=x^{2}$, the line $x=2$, and the $x$-axis. ...
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A is a transformed object to image A'. Mention two types of transformation that took place.
A is a transformed object to image A'. Mention two types of transformation that took place. A is a transformed object to image A&#39;. Mention two types of transformation that took place. ...
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Find the maximum height above the $x$-axis of the cardioid $r=1+\cos \theta$.
Find the maximum height above the $x$-axis of the cardioid $r=1+\cos \theta$.Find the maximum height above the $x$-axis of the cardioid $r=1+\cos \theta$. ...
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Give an example of a function with one critical point which is also an inflection point.
Give an example of a function with one critical point which is also an inflection point.Give an example of a function with one critical point which is also an inflection point. ...
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For which vaues of $a$ and $b$ is $(1,6)$ a point of inflection of the curve $y=$ $x^{3}+a x^{2}+b x+1 ?$
For which vaues of $a$ and $b$ is $(1,6)$ a point of inflection of the curve $y=$ $x^{3}+a x^{2}+b x+1 ?$For which vaues of $a$ and $b$ is $(1,6)$ a point of inflection of the curve $y=$ $x^{3}+a x^{2}+b x+1 ?$ ...
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Find an orthogonal basis for $\mathcal{S}$ and use it to find the $3 \times 3$ matrix $P$ that projects vectors orthogonally into $\mathcal{S}$.
Find an orthogonal basis for $\mathcal{S}$ and use it to find the $3 \times 3$ matrix $P$ that projects vectors orthogonally into $\mathcal{S}$.Let $\mathcal{S} \subset \mathbb{R}^{3}$ be the subspace spanned by the two vectors $v_{1}=(1,-1,0)$ and $v_{2}=$ $(1,-1,1)$ and let $\mathca ... close 0 answers 47 views Linear maps \(F(X)=A X$, where $A$ is a matrix, have the property that $F(0)=A 0=0$, so they necessarily leave the origin fixed. It is simple to extend this to include a translation, Linear maps $F(X)=A X$, where $A$ is a matrix, have the property that $F(0)=A 0=0$, so they necessarily leave the origin fixed. It is simple t ...
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Find a linear map of the plane, $A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that does the following transformation of the letter $\mathbf{F}$ (here the smaller $\mathbf{F}$ is transformed to the larger one): a). Find a linear map of the plane, $A: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that does the following transformation of the letter $\mathbf{ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find a real \(2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$.
Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$.Find a real $2 \times 2$ matrix $A$ (other than $A=I$ ) such that $A^{5}=I$. ...
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Find a $3 \times 3$ matrix $A$ mapping $\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ that rotates the $x_{1} x_{3}$ plane by 60 degrees and leaves the $x_{2}$ axis fixed.Find a $3 \times 3$ matrix $A$ mapping $\mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ that rotates the $x_{1} x_{3}$ plane by 60 degrees and leav ...
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Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 degrees.
Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 degrees.Find a $3 \times 3$ matrix that acts on $\mathbb{R}^{3}$ as follows: it keeps the $x_{1}$ axis fixed but rotates the $x_{2} x_{3}$ plane by 60 ...
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Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.
Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed.Find a matrix that rotates the plane through $+60$ degrees, keeping the origin fixed. ...
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Find a $2 \times 2$ matrix that reflects across the horizontal axis followed by a rotation the plane by $+45$ degrees.
Find a $2 \times 2$ matrix that reflects across the horizontal axis followed by a rotation the plane by $+45$ degrees.Find a $2 \times 2$ matrix that reflects across the horizontal axis followed by a rotation the plane by $+45$ degrees. ...
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Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.
Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis.Find a $2 \times 2$ matrix that rotates the plane by $+45$ degrees followed by a reflection across the horizontal axis. ...
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Find the orthogonal projections of the vectors $\mathbf{e}_{1}=(1,0)$ and $\mathbf{e}_{2}=(0,1)$ on the line $L$ that makes an angle $\theta$ with the positive $x$-axis in $R^{2}$.Find the orthogonal projections of the vectors $\mathbf{e}_{1}=(1,0)$ and $\mathbf{e}_{2}=(0,1)$ on the line $L$ that makes an angle $\theta$ with the ...
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Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$.
Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$.Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$. ...
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Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.
Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.Consider the differential equation $\frac{d x}{d y}=\frac{y^{2}+y^{2} e^{\left(\frac{x}{y}\right)^{2}}+2 x^{2} e^{\left(\frac{x}{y}\right)^{2}}}{2 x y ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the intercepts on the$x$- and$y$-axes (if any) for the function$f(x)=\frac{x^{2}-3}{x+2}$and discuss symmetry. 0 answers 49 views Find the intercepts on the$x$- and$y$-axes (if any) for the function$f(x)=\frac{x^{2}-3}{x+2}$and discuss symmetry.Find the intercepts on the$x$- and$y$-axes (if any) for the function$f(x)=\frac{x^{2}-3}{x+2}$and discuss symmetry. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the area of the largest rectangle that can be inscribed between the curve$y=12-x^{2}$and the$x$-axis. 0 answers 118 views Find the area of the largest rectangle that can be inscribed between the curve$y=12-x^{2}$and the$x$-axis.Find the area of the largest rectangle that can be inscribed between the curve$y=12-x^{2}$and the$x$-axis. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What are the coordinates of the point $D$ if $A(-3,1)$, $B(4$, $0), C(0,-3)$ and $D$ are corners of a square? 1 answer 207 views What are the coordinates of the point $D$ if $A(-3,1)$, $B(4$, $0), C(0,-3)$ and $D$ are corners of a square?What are the coordinates of the point $D$ if $A(-3,1)$, $B(4$, $0), C(0,-3)$ and $D$ are corners of a square? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is a good problem solving framework in mathematics? 1 answer 61 views What is a good problem solving framework in mathematics?What is a good problem solving framework in mathematics? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the values of the constants $a, b$ and $c$ such that $\mathrm{f}(x)=a(x+b)^{2}+c$ 1 answer 65 views Find the values of the constants $a, b$ and $c$ such that $\mathrm{f}(x)=a(x+b)^{2}+c$\ \mathrm{f}(x)=2 x^{2}+8 x+1 \ Find the values of the constants $a, b$ and $c$ such that \ \mathrm{f}(x)=a(x+b)^{2}+c \ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given that the minimum point of $\mathrm{C}$ has coordinates $(4,-3)$ find the values of $a$ and $b$. 1 answer 83 views Given that the minimum point of $\mathrm{C}$ has coordinates $(4,-3)$ find the values of $a$ and $b$.The curve $\mathrm{C}$ has the equation \ x^{2}+a x+b=0 \ Where $a$ and $b$ are constants Given that the minimum point of $\mathrm{C}$ has ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The equation of the graph of $\mathrm{g}$ is given by $g(x)=2^{x+1}-1$ Determine the $X$ and $Y$ Intercepts and draw the sketch of the graph 0 answers 96 views The equation of the graph of $\mathrm{g}$ is given by $g(x)=2^{x+1}-1$ Determine the $X$ and $Y$ Intercepts and draw the sketch of the graphThe equation of the graph of $\mathrm{g}$ is given by $g(x)=2^{x+1}-1$. Determine the $X$ and $Y$ Intercepts and draw the sketch of the graph. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Given that $(5,2),(-4, k)$ and $(2,1)$ lie on a straight line, find the value of $k$. 1 answer 124 views Given that $(5,2),(-4, k)$ and $(2,1)$ lie on a straight line, find the value of $k$.Given that $(5,2),(-4, k)$ and $(2,1)$ lie on a straight line, find the value of $k$. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If $f(x)=-4^{x}$, write down $g(x)$ the inverse of $f(x)$ and draw $f$ and $g$ on the same set of axis. 1 answer 220 views If $f(x)=-4^{x}$, write down $g(x)$ the inverse of $f(x)$ and draw $f$ and $g$ on the same set of axis.If $f(x)=-4^{x}$, write down $g(x)$ the inverse of $f(x)$ and draw $f$ and $g$ on the same set of axis. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If the graph of$y=-x^{2}+6 x-5$is reflected in the$x$-axis and the resulting graph is then reflected in the$y$-axis, the new equation is 0 answers 223 views If the graph of$y=-x^{2}+6 x-5$is reflected in the$x$-axis and the resulting graph is then reflected in the$y$-axis, the new equation isIf the graph of$y=-x^{2}+6 x-5$is reflected in the$x$-axis and the resulting graph is then reflected in the$y$-axis, the new equation is (A)$y ...
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The function $f$ defined by $y=f(x)=-x^{2}+6 x-5$ has
The function $f$ defined by $y=f(x)=-x^{2}+6 x-5$ hasThe function $f$ defined by $y=f(x)=-x^{2}+6 x-5$ has (A) A minimum $y$ value and a negative $y$ -intercept. (B) A maximum $y$ value and a positive $... close 1 answer 158 views A regression analysis between apples (y) and oranges (x) resulted in the following least-squares line:$\mathrm{y}=100+2 \mathrm{x}$. What is the implication if oranges are increased by$1 ?$A regression analysis between apples (y) and oranges (x) resulted in the following least-squares line:$\mathrm{y}=100+2 \mathrm{x}$. What is the impl ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If$1+3+5+\cdots+97+99$is subtracted from$2+4+6+\cdots+98+100$, the answer is 0 answers 107 views If$1+3+5+\cdots+97+99$is subtracted from$2+4+6+\cdots+98+100$, the answer isIf$1+3+5+\cdots+97+99$is subtracted from$2+4+6+\cdots+98+100$, the answer is ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The solution of the differential equation$\frac{d y}{d x}=\frac{x y}{x^{2}+y^{2}}$is 1 answer 90 views The solution of the differential equation$\frac{d y}{d x}=\frac{x y}{x^{2}+y^{2}}$isThe solution of the differential equation$\frac{d y}{d x}=\frac{x y}{x^{2}+y^{2}}$is ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that$2^{x+1}+3.2^{x}=5.2^{x}$1 answer 134 views Show that$2^{x+1}+3.2^{x}=5.2^{x}$Show that$2^{x+1}+3.2^{x}=5.2^{x}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If$\omega=\frac{z}{z-\frac{1}{3} i}$and$|\omega|=1$, then$\mathrm{z}$lies on 1 answer 90 views If$\omega=\frac{z}{z-\frac{1}{3} i}$and$|\omega|=1$, then$\mathrm{z}$lies on If$\omega=\frac{z}{z-\frac{1}{3} i}$and$|\omega|=1$, then$\mathrm{z}$lies on 1) an ellipse 2) a circle 3) a straight line 4) a parabola ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If$\left|z^{2}-1\right|=|z|^{2}+1$, then$z$lies on 1 answer 97 views If$\left|z^{2}-1\right|=|z|^{2}+1$, then$z$lies onIf$\left|z^{2}-1\right|=|z|^{2}+1$, then$z$lies on 1) the real axis 2) an ellipse 3) a circle 4) the imaginary axis. ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 The graph of the function$y=f(x)$is symmetrical about the line$x=2$, then 1 answer 124 views The graph of the function$y=f(x)$is symmetrical about the line$x=2$, thenThe graph of the function$y=f(x)$is symmetrical about the line$x=2$, then 1)$f(x+2)=f(x-2)$2)$f(2+x)=f(2-x)$3)$f(x)=f(-x)$4)$f(x)=-f(-x)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Solve$0.5 x-12 x^{2}=0(a=-1.2, b=0.5, c=0)$1 answer 128 views Solve$0.5 x-12 x^{2}=0(a=-1.2, b=0.5, c=0)$Solve$0.5 x-12 x^{2}=0(a=-1.2, b=0.5, c=0)$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Suppose that the point$(1,4)$is on the graph of$y=f(x) .$Find a point on the graph when$y$is translated left 3 units and reflected across the$x$-axis. 0 answers 269 views Suppose that the point$(1,4)$is on the graph of$y=f(x) .$Find a point on the graph when$y$is translated left 3 units and reflected across the$x$-axis.Suppose that the point$(1,4)$is on the graph of$y=f(x) .$Find a point on the graph when$y$is translated left 3 units and reflected across the$x ...
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The graph of $g(x)=-2^{x}+8 \quad$ is sketched below. $A$ and $B$ are the $y$ - and $x$ -intercepts respectively of $g$.
The graph of $g(x)=-2^{x}+8 \quad$ is sketched below. $A$ and $B$ are the $y$ - and $x$ -intercepts respectively of $g$. The graph of $g(x)=-2^{x}+8 \quad$ is sketched below. $A$ and $B$ are the $y$ - and $x$ -intercepts respectively of $g$. Write down the r ...
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The diagram below shows the hyperbola $g$ defined by $g(x)=\frac{2}{x+p}+q$ with the asymptotes $y=1$ and $x=-1$
The diagram below shows the hyperbola $g$ defined by $g(x)=\frac{2}{x+p}+q$ with the asymptotes $y=1$ and $x=-1$ The diagram below shows the hyperbola $g$ defined by $g(x)=\frac{2}{x+p}+q$&nbsp;with the asymptotes $y=1$ and $x=-1$. The graph of $g$ intersects t ...
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A $475 \mathrm{~nm}$ wavelength laser produces a diffraction pattern using a diffraction grating of slit spacing D. What is the range of values D can have that will produce exactly 15 bright spots on a screen $10.0$ meters away.A $475 \mathrm{~nm}$ wavelength laser produces a diffraction pattern using a diffraction grating of slit spacing D. What is the range of values D can ...
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How would you go about solving the differential equation $\frac{d^{2} x}{d t^{2}}=-x$ with $x(0)=1$ and $x^{\prime}(0)=1$ with each of the methods listed in the previous problem.How would you go about solving the differential equation $\frac{d^{2} x}{d t^{2}}=-x$ with $x(0)=1$ and $x^{\prime}(0)=1$ with each of the methods lis ...
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Grade 12 - Paper 1 - The graph of $g(x)=a x^{3}+b x^{2}+c x$, a cubic function having a $y$ -intercept of 0, is drawn below. The $x$ -coordinates of the turning points of $g$ are $-1$ and 2 . The graph of $g(x)=a x^{3}+b x^{2}+c x$, a cubic function having a $y$ -intercept of 0, is drawn below. The $x$ -coordinates of the turning points o ...
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Grade 12 - Paper 1 - Determine $f^{\prime}(x)$ from first principles if $f(x)=2 x^{2}-1$.
Grade 12 - Paper 1 - Determine $f^{\prime}(x)$ from first principles if $f(x)=2 x^{2}-1$.Grade 12 - Paper 1 - Determine $f^{\prime}(x)$ from first principles if $f(x)=2 x^{2}-1$. ...
Grade 12 - Paper 1 - The graph of $f(x)=3^{-x}$ is sketched below. $A$ is the $y$ -intercept of $f$. $\mathrm{B}$ is the point of intersection of $f$ and the line $y=9$.
Grade 12 - Paper 1 - The graph of $f(x)=3^{-x}$ is sketched below. $A$ is the $y$ -intercept of $f$. $\mathrm{B}$ is the point of intersection of $f$ and the line $y=9$. The graph of $f(x)=3^{-x}$ is sketched below. $A$ is the $y$ -intercept of $f$. $\mathrm{B}$ is the point of intersection of $f$ and the line $y=9$. ...