if you are using bubble shoot fir sorting the given number is ascending order then find out the number of swapping needed 40,42,55,35,38
Answers
Answer:
\huge\text{$m=\dfrac{20}{7}\text{ or }m=4$}m=
7
20
or m=4
\huge\text{\underline{\underline{Explanation}}}
Explanation
\large\boxed{\text{Geometry}}
Geometry
We know that the tangent and the circle are apart by radius.
\text{$\cdots\longrightarrow d=r$}⋯⟶d=r
\large\boxed{\text{Standard form}}
Standard form
\text{$\cdots\longrightarrow(x^{2}-4x+4)+(y^{2}+6y+9)-4-9-3=0$}⋯⟶(x
2
−4x+4)+(y
2
+6y+9)−4−9−3=0
\text{$\cdots\longrightarrow(x-2)^{2}+(y+3)^{2}=4^{2}$}⋯⟶(x−2)
2
+(y+3)
2
=4
2
\large\boxed{\text{Properties of the circle}}
Properties of the circle
\text{$\bullet \text{The circle is centered at }(2,-3)$.}∙The circle is centered at (2,−3).
\text{$\bullet \text{The radius of the circle is }4$.}∙The radius of the circle is 4.
\large\boxed{\text{Distance formula}}
Distance formula
\cdots\longrightarrow d=\dfrac{|ax_{1}+by_{1}+c|}{\sqrt{a^{2}+b^{2}}}⋯⟶d=
a
2
+b
2
∣ax
1
+by
1
+c∣
\text{$\bullet\ a, b, c$ are the coefficients.}∙ a,b,c are the coefficients.
\text{$\bullet\ (x_{1}.y_{1})$ is the coordinate.}∙ (x
1
.y
1
) is the coordinate.
\large\boxed{\text{Solving for }m}
Solving for m
Now since we know \text{$a=3$}a=3 , \text{$b=-m$}b=−m , \text{$c=2$}c=2 , \text{$d=4$}d=4 and \text{$(2,-3)$}(2,−3) , we want the equation for mm .
\cdots\longrightarrow 4=\dfrac{|6+3m+2|}{\sqrt{9+m^{2}}}⋯⟶4=
9+m
2
∣6+3m+2∣
This is the wanted equation. Let's break this down.
\text{$\cdots\longrightarrow 16(9+m^{2})=(6+3m+2)^{2}$}⋯⟶16(9+m
2
)=(6+3m+2)
2
\text{$\cdots\longrightarrow 144+16m^{2}=9m^{2}+48m+64$}⋯⟶144+16m
2
=9m
2
+48m+64
\text{$\cdots\longrightarrow7m^{2}-48m+80=0$}⋯⟶7m
2
−48m+80=0
\text{$\cdots\longrightarrow(7m-20)(m-4)=0$}⋯⟶(7m−20)(m−4)=0
\text{$\cdots\longrightarrow m=\dfrac{20}{7}\text{ or }m=4$}⋯⟶m=
7
20
or m=4
\huge\text{\underline{\underline{Final answer}}}
Final answer
Hence, -
\text{$\cdots\longrightarrow\boxed{m=\dfrac{20}{7}\text{ or }m=4}$}⋯⟶
m=
7
20
or m=4
Answer:
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