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4 years ago

One point or two-point perspective

Mathematics

1 answer:

serious [3.7K]4 years ago

7 0

Two point perspective because of two points on the horizon.

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

4 years ago

How do you do 0.5y = 17

aleksley [76]

34 you do 17×2 and get what you multiplily that by 0 .5

3 0

3 years ago

The midpoint of AB is M (5,5). If the coordinates of A are (7, 8), what are the

zalisa [80]

Answer:

(3,2) just use a slope triangle (over 2 up 3) and do it in reverse

6 0

2 years ago

If f(x) = 4x - 3, then f '(x) is<br>

lord [1]

Answer:

f'(x) = 4

Step-by-step explanation:

Derivative of 3 (constant number) is 0
Derivative of 4x is 4
f'(x) = 4 - 0 = 4

8 0

3 years ago

How do I identify the lines of symmetry in a conic section?

astra-53 [7]

Lines of symmetry in a conic section : x = 0; y =0

8 0

3 years ago