Mathematics: What kind of symmetry is displayed by the graph of catenary y=e^x+e^-x/2

Step-by-step explanation:The formula of a distance between a point (x₀, y₀) and a line Ax + By + C = 0:We have the point D(5, 4) and the line 3x + 5y - 4 = 0.Substitute:...

What kind of symmetry is displayed by the graph

Ответ:

niti1409

04.01.2022

Mathematics

Option b

Step-by-step explanation:

To solve this problem we must test if the function is even.

If f(-x) = f(x) then the function is even and is symmetric with respect to the y-axis.

If f(-x) = -f(x) then the function is odd and has symmetry with respect to the origin.

We have the function:

$f(x) = \frac{e^x + e^{-x}}{2}$

We make:

$f(-x) = \frac{e^{-x} + e^{-(-x)}}{2}$

Rewriting the function we have

$f(-x) = \frac{e^{-x} + e^{x}}{2} = \frac{e^{x} + e^{-x}}{2}\\\\f(-x) = f(x)$

Finally, the function has symmetry with respect to the y axis.

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Ответ:

SmokeyRN

18.02.2020

Mathematics

$\large\boxed{d=\dfrac{31\sqrt{34}}{34}\approx5.32}$

Step-by-step explanation:

The formula of a distance between a point (x₀, y₀) and a line Ax + By + C = 0:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$

We have the point D(5, 4) and the line 3x + 5y - 4 = 0.

Substitute:

$x_0=5,\ y_0=4,\ A=3,\ B=5,\ C=-4$

$d=\dfrac{|(3)(5)+(5)(4)-4|}{\sqrt{3^2+5^2}}=\dfrac{|15+20-4|}{\sqrt{9+25}}=\dfrac{|31|}{\sqrt{34}}\cdot\dfrac{\sqrt{34}}{\sqrt{34}}=\dfrac{31\sqrt{34}}{34}$

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What kind of symmetry is displayed by the graph of catenary y=e^x+e^-x/2

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