Question

The curvature of the curve y = f (x) is zero at every point on the curve. Which one of the following

could be f (x)?​

Answer 1

Step-by-step explanation:

Step-by-step explanation:

\begin{gathered}\implies \sf{\dfrac{10x+3y}{5x+2y} = \dfrac{9}{5} }\\\\\\\implies \sf{\dfrac{10x\frac{y}{y} +3y}{5x\frac{y}{y}+2y}=\dfrac{9}{5} }\\\\\\\implies \sf{\dfrac{y\big(10\frac{x}{y}+3\big)}{y\big(5\frac{x}{y}+2\big)}=\dfrac{9}{5} }\end{gathered}

⟹

5x+2y

10x+3y

=

5

9

⟹

5x

y

y

+2y

10x

y

y

+3y

=

5

9

⟹

y(5

y

x

+2)

y(10

y

x

+3)

=

5

9

Let \dfrac{x}{y}=k

y

x

=k ,

\begin{gathered}\implies\sf{\dfrac{10k+3}{5k+2}=\dfrac{9}{5}} \\\\\implies\sf{5(10k+3)=9(5k+2) }\\\\\implies\sf{k=\dfrac{3}{5}}\end{gathered}

⟹

5k+2

10k+3

=

5

9

⟹5(10k+3)=9(5k+2)

⟹k=

5

3

Hence,

\begin{gathered}\implies \sf{\dfrac{2x+y}{x+2y} }\\\\\\\implies \sf{\dfrac{2x\frac{y}{y} +y}{x\frac{y}{y}+2y} }\\\\\\\implies \sf{\dfrac{y\big(2\frac{x}{y}+1\big)}{y\big(\frac{x}{y}+2\big)} }\end{gathered}

⟹

x+2y

2x+y

⟹

x

y

y

+2y

2x

y

y

+y

⟹

y(

y

x

+2)

y(2

y

x

+1)

\begin{gathered}\implies\sf{\dfrac{2k+1}{k+2} =\dfrac{2\big(\frac{3}{5}\big)+1}{\frac{3}{5}+2} }\\\\\implies\sf{ \dfrac{11}{13} }\end{gathered}

⟹

k+2

2k+1

=

5

3

+2

2(

5

3

)+1

⟹

13

11

Question 2:

Let the x should be added,

⇒ (2 + x)/(5 + x) = 6/11

⇒ 11(2 + x) = 6(5 + x)

⇒ 22 + 11x = 30 + 6x

⇒ 11x - 6x = 30 - 22

⇒ 5x = 8

⇒ x = 8/5

8/5 should be subtracted

Answer 2

Answer:

mrnrmtkrmen

Step-by-step explanation:

नजर में ट् रो रहा था और एक अँ धे श क् ष क र ति क र ka kya ho gya tha ki baat kr rha tha