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2 years ago

According to the graph, what is the value of the constant in the equation below?

Mathematics

2 answers:

MA_775_DIABLO [31]2 years ago

5 0

Answer:

Step-by-step explanation:

12345 [234]2 years ago

3 0

<h3>Answer: A) 20</h3>

Explanation:

The equation $\text{Height} = {\text{Constant} \over \text{Width}}$ rearranges to $\text{Constant} = \text{Height}*\text{Width}$

To find the constant, we simply multiply the x and y coordinates of any of the point shown:

constant = x*y = 4*5 = 20
constant = x*y = 5*4 = 20
constant = x*y = 10*2 = 20
constant = x*y = 20*1 = 20

The general equation is y = 20/x, which rearranges to xy = 20.

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3 years ago

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

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

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

So we have

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

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

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

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3 years ago

How can the number 1 be written as a fraction a number line

JulijaS [17]

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3 years ago

A line passes through the points (-2, 9) and (1, 3).

siniylev [52]

Answer:

slope = -2

y-intercept = 5

Step-by-step explanation:

1) Find slope:

$\frac{3-9}{1-(-2)}$ = $\frac{-6}{3}$ = -2

-2 = slope

2) Find y intercept trough point slope and slope-intercept forms

y - y1 = m (x - x1)

y - 9 = -2 (x + 2)

y - 9 = -2x -4

+ 9 + 9

y = -2x + 5

y = mx + b with b being the y-intercept

5 = y-intercept

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2 years ago

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nevsk [136]

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3 years ago