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Recent questions tagged axis

\(D M\) 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 \(D M=2 x\).

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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 \(D M=2 x\).
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Given \(Q U=24 \mathrm{~cm}, Q C=16 \mathrm{~cm}, D A=6 \mathrm{~cm}\) and \(C D=x\).

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Given \(Q U=24 \mathrm{~cm}, Q C=16 \mathrm{~cm}, D A=6 \mathrm{~cm}\) and \(C D=x\).
1 answer 53 views
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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 \(C D=x\). 1. Prove \(\triangle Q U C \| \triangle A C D\) 2. C ...
by Pieter Gold Status
(31,957 points)
asked in Mathematics Apr 17
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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 \(C E\).

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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 \(C E\).
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Given circle \(A B C D\) with \(A B \| E F\).

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Given circle \(A B C D\) with \(A B \| E F\).
1 answer 57 views
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Given circle \(A B C D\) with \(A B \| E F\). Given circle \(A B C D\) with \(A B \| E F\). a) Prove \(C D E F\) is a cylindrical quad. b) If \(\hat{D}_{2}=38^{\circ}\), calculate \(\hat{E ...
by MathsGee Platinum
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asked in Mathematics Apr 17
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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 \(A C\).

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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 \(A C\).

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Find the centroid of the area bounded by the parabola \(y=x^{2}\) and the line \(2 x+3\).
1 answer 266 views
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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.
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A is a transformed object to image A'. Mention two types of transformation that took place.

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A is a transformed object to image A'. Mention two types of transformation that took place.
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Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\).
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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 \(r=1+\cos \theta\). ...
by Pieter Gold Status
(31,957 points)
asked in Mathematics Feb 4
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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 \(y=\) \(x^{3}+a x^{2}+b x+1 ?\)
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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 \(\mathcal{S}\).
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, 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):

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Find a real \(2 \times 2\) matrix \(A\) (other than \(A=I\) ) such that \(A^{5}=I\).
0 answers 46 views
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Find a matrix that rotates the plane through \(+60\) degrees, keeping the origin fixed.
0 answers 66 views
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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.
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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.
0 answers 126 views
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Find the equation of the plane that contains the $z$-axis and the point $(3,1,2)$.
0 answers 188 views
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Using the substitution $x=v y$ or otherwise, find the general solution of the differential equation.
0 answers 99 views
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 ...
by MathsGee Platinum
(119,140 points)
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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Find the area of the largest rectangle that can be inscribed between the curve $y=12-x^{2}$ and the $x$-axis.
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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?

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What is a good problem solving framework in mathematics?
1 answer 61 views
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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 \ ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Nov 9, 2021
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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 ...
by MathsGee Platinum
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asked in Mathematics Nov 9, 2021
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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

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Given that \((5,2),(-4, k)\) and \((2,1)\) lie on a straight line, find the value of \(k\).
1 answer 124 views
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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
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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
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The function $f$ defined by $y=f(x)=-x^{2}+6 x-5$ has
0 answers 78 views
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 $ ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Aug 7, 2021
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If $1+3+5+\cdots+97+99$ is subtracted from $2+4+6+\cdots+98+100$, the answer is
0 answers 107 views
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The solution of the differential equation $\frac{d y}{d x}=\frac{x y}{x^{2}+y^{2}}$ is
1 answer 90 views
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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 $2^{x+1}+3.2^{x}=5.2^{x}$ ...
by Student SIlver Status
(10,904 points)
asked in Mathematics Jun 14, 2021
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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 ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Jun 9, 2021
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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. ...
by MathsGee Platinum
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asked in Mathematics Jun 9, 2021
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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) $f(x)=-f(-x)$ ...
by MathsGee Platinum
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asked in Mathematics Jun 9, 2021
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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 $0.5 x-12 x^{2}=0(a=-1.2, b=0.5, c=0)$ ...
by Maths Genie Bronze Status
(5,562 points)
asked in Mathematics Jun 1, 2021
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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 $g$.

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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 $g$.
1 answer 281 views
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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 $g$. Write down the r ...
by MathsGee Platinum
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asked in Mathematics May 18, 2021
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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 $x=-1$

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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 $x=-1$
1 answer 294 views
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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 graph of $g$ intersects t ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics May 13, 2021
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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 .

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Grade 12 - Paper 1 - Determine $f^{\prime}(x)$ from first principles if $f(x)=2 x^{2}-1$.
1 answer 155 views
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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 $y=9$.

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