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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.
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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 ...
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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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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?
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Find the values of the constants \(a, b\) and \(c\) such that \[ \mathrm{f}(x)=a(x+b)^{2}+c \]
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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
(103,512 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 \(b\).
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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 \(k\).
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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.
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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
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The function $f$ defined by $y=f(x)=-x^{2}+6 x-5$ has
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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
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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
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The solution of the differential equation $\frac{d y}{d x}=\frac{x y}{x^{2}+y^{2}}$ is
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Show that $2^{x+1}+3.2^{x}=5.2^{x}$
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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
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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 51 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
(103,512 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 59 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 55 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 $0.5 x-12 x^{2}=0(a=-1.2, b=0.5, c=0)$
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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
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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 $g$.
1 answer 161 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 $x=-1$
1 answer 115 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
(103,512 points)
asked in Mathematics May 13, 2021
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