# Recent questions tagged tangent

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Given $A C$ is a tangent of the blue circle and $B$ is a 90 degrees, what is the area of $\triangle A B C$ ?
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Given $A C$ is a tangent of the blue circle and $B$ is a 90 degrees, what is the area of $\triangle A B C$ ? Given $A C$ is a tangent of the blue circle and $B$ is a 90 degrees, what is the area of $\triangle A B C$ ? ...
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Determine $5+12+19+\cdots+54$
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Determine $5+12+19+\cdots+54$Determine $5+12+19+\cdots+54$ ...
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What is the equation of the normal to the curve $y=(3 x+10)^2$ at the point $(-3,1)$ ?
0 answers 228 views
What is the equation of the normal to the curve $y=(3 x+10)^2$ at the point $(-3,1)$ ?What is the equation of the normal to the curve $y=(3 x+10)^2$ at the point $(-3,1)$ ? ...
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0 answers 217 views
Consider the perimetrically defined curve $x(t)=t-\sin 2 t, y=4-3 \cos t$, $0 \leq t \leq 10$. Find the values for the parameter $t$ where the tangent line of the curve is vertical.Consider the perimetrically defined curve $x(t)=t-\sin 2 t, y=4-3 \cos t$, $0 \leq t \leq 10$. Find the values for the parameter $t$ where the t ...
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Let $x^{2}+2 x \arctan y=y \cos x$. Find $y^{\prime}$ at $\left(\dfrac{\pi}{2},-1\right)$.
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Let $x^{2}+2 x \arctan y=y \cos x$. Find $y^{\prime}$ at $\left(\dfrac{\pi}{2},-1\right)$.Let $x^{2}+2 x \arctan y=y \cos x$. Find $y^{\prime}$ at $\left(\dfrac{\pi}{2},-1\right)$. ...
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Evaluate $\int \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$
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Evaluate $\int \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$Evaluate $\int \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ ...
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Determine whether the integral $\int_{0}^{1} \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ is convergent or divergent.
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Determine whether the integral $\int_{0}^{1} \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ is convergent or divergent.Determine whether the integral $\int_{0}^{1} \dfrac{1}{\left(1+x^{2}\right) \arctan x} d x$ is convergent or divergent. ...
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Find $\frac{d}{d x}\left(x \int_{2}^{x^{2}} \frac{1}{9+t^{2}} d t\right)$
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Find $\frac{d}{d x}\left(x \int_{2}^{x^{2}} \frac{1}{9+t^{2}} d t\right)$Find $\frac{d}{d x}\left(x \int_{2}^{x^{2}} \frac{1}{9+t^{2}} d t\right)$ ...
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Determine whether the integral $\int_{3}^{3+e} \ln (x-3) d x$ is convergent or divergent. If convergent, give the value the integral converges to.
0 answers 44 views
Determine whether the integral $\int_{3}^{3+e} \ln (x-3) d x$ is convergent or divergent. If convergent, give the value the integral converges to. Determine whether the integral $\int_{3}^{3+e} \ln (x-3) d x$ is convergent or divergent. If convergent, give the value the integral converges to. ...
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Determine whether the improper integral $$\int_{1}^{\infty} \frac{\ln x}{(x+1)^{2}} d x$$ converges or diverges. If it converges, find its value.
0 answers 36 views
Determine whether the improper integral $$\int_{1}^{\infty} \frac{\ln x}{(x+1)^{2}} d x$$ converges or diverges. If it converges, find its value.Determine whether the improper integral $$\int_{1}^{\infty} \frac{\ln x}{(x+1)^{2}} d x$$ converges or diverges. If it converges, find its value. ...
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0 answers 50 views
Determine, giving reasons, whether the sequence $$\left\{a_{n}\right\}=\left\{\frac{5-n+3 n^{2}}{7 n^{2}-19}\right\}$$ is convergent or divergent. If it is convergent, state to what value it converges.Determine, giving reasons, whether the sequence $$\left\{a_{n}\right\}=\left\{\frac{5-n+3 n^{2}}{7 n^{2}-19}\right\}$$ is convergent or divergent. I ...
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The unit circle is split into regions by the 4 lines that satisfy. How many of these regions have area $\frac{\pi}{8}$ ?
1 answer 50 views
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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Show that $\{(\cos t, \sin t): t \in \mathbb{R}\}=\left\{(x, y): x^{2}+y^{2}=1\right\}$.
1 answer 51 views
Show that $\{(\cos t, \sin t): t \in \mathbb{R}\}=\left\{(x, y): x^{2}+y^{2}=1\right\}$.Show that $\{(\cos t, \sin t): t \in \mathbb{R}\}=\left\{(x, y): x^{2}+y^{2}=1\right\}$. ...
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Let $u_{1}=(k, 2,3), u_{2}=(2,3,1), \quad t_{3}=(3,3,2), \quad \mu_{4}=(2,3,1)$ be vectors in $\mathbf{R}^{3}$. Which of the vectors, if any, are equal?
1 answer 143 views
Let $u_{1}=(k, 2,3), u_{2}=(2,3,1), \quad t_{3}=(3,3,2), \quad \mu_{4}=(2,3,1)$ be vectors in $\mathbf{R}^{3}$. Which of the vectors, if any, are equal?Let $u_{1}=(k, 2,3), u_{2}=(2,3,1), \quad t_{3}=(3,3,2), \quad \mu_{4}=(2,3,1)$ be vectors in $\mathbf{R}^{3}$. Which of the vectors, if any, are equa ...
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The equation of a curve is $y=x^{3}-x^{2}-2 x-3$. Find the equation of the tangent to this curve at the point $(3,9)$.
1 answer 241 views
The equation of a curve is $y=x^{3}-x^{2}-2 x-3$. Find the equation of the tangent to this curve at the point $(3,9)$.The equation of a curve is $y=x^{3}-x^{2}-2 x-3$. Find the equation of the tangent to this curve at the point $(3,9)$. ...
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1 answer 2.5K views
A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at $\mathrm{A}$ enclosing an angle of $60^{\circ}$. The area enclosed by these tangents and the arc of the circle isA pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at $\mathrm{A}$ enclosing an angle of $60^{\circ} ... close 0 answers 232 views In the diagram,$\mathrm{PQR}$is an isosceles triangle such that$\mathrm{PQ}=\mathrm{PR}=7 \mathrm{~cm}$and$\mathrm{PRQ}=35^{\circ}$Using as much of the information given below as is necessary, calculate In the diagram,$\mathrm{PQR}$is an isosceles triangle such that$\mathrm{PQ}=\mathrm{PR}=7 \mathrm{~cm}$and$\mathrm{PRQ}=35^{\circ}$Using ... close 1 answer 1.3K views close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What is the general equation of a tangent line in calculus? 1 answer 413 views What is the general equation of a tangent line in calculus?What is the general equation of a tangent line in calculus? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let$\underline{u}=(12,-2)$and$\underline{v}=(3,0 \quad 1)$be vectors$m \mathbb{R}^{3}$0 answers 93 views Let$\underline{u}=(12,-2)$and$\underline{v}=(3,0 \quad 1)$be vectors$m \mathbb{R}^{3}$(a) Let$\underline{u}=(12,-2)$and$\underline{v}=(3,0 \quad 1)$be vectors$m \mathbb{R}^{3}$(i) Calculate$\underline{u} \times \underline{v}$(ii ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Can you express the following in terms of a, b and c? 1 answer 65 views Can you express the following in terms of a, b and c? Can you express the following in terms of a, b and c? a.&nbsp;&nbsp;&nbsp;&nbsp;cos&nbsp;θ b.&nbsp; &nbsp; tan&nbsp;θ c.&nbsp; &nbsp; s ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show me how I can evaluate the following without using a calculator. 1 answer 123 views Show me how I can evaluate the following without using a calculator.Show me how I can evaluate the following without using a calculator. (sin 30° - tan 45°) / (sin 90° - cos 60°) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine the equation of the tangent to the curve 1 answer 138 views Determine the equation of the tangent to the curve Determine the equation of the tangent to the curve ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Explain what is tangent? 1 answer 108 views Explain what is tangent?Explain what is tangent? ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle at A and AE=EC. 1 answer 950 views In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle at A and AE=EC. In the diagram below, BOC is a diameter of the circle. AP is a tangent to the circle at A and AE=EC. &nbsp; Prove that: BA$\parall ...
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O is the centre of circle TNSPR. $P\hat{O}S = 60^{\circ}$ and PS=NT
1 answer 276 views
O is the centre of circle TNSPR. $P\hat{O}S = 60^{\circ}$ and PS=NT O is the centre of circle TNSPR. $P\hat{O}S = 60^{\circ}$ and PS=NT Calculate the size of $P\hat{R}S$ and $N\hat{S}T$ &nbsp; &nbsp; ...
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In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects $A\hat{B}C$. Let $\hat{B_{1}} =x$
1 answer 806 views
In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects $A\hat{B}C$. Let $\hat{B_{1}} =x$ In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects $A\hat{B}C$. Let $\hat{B_{1}} =x$ Prove ...
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Prove that $AP=BP$
1 answer 118 views
Prove that $AP=BP$Consider a circle, with centre $O$. Choose a point $P$ outside the circle. Draw two tangents to the circle from point $P$, that meet the circle at $A$ ...
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What is a tangent in geometry?
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What is a tangent in geometry?What is a tangent in geometry? ...
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The gradient of the tangent to the curve of $f(x) = -2x^{2}$ at a point $(a;b)$ on the curve is 6. Determine the value of a
1 answer 441 views
The gradient of the tangent to the curve of $f(x) = -2x^{2}$ at a point $(a;b)$ on the curve is 6. Determine the value of aThe gradient of the tangent to the curve of $f(x) = -2x^{2}$ at a point $(a;b)$ on the curve is 6. Determine the value of a ...
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