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3 years ago

(-5, 4); slope-3 So what is the answer

1 answer:

4 0

Make a graph and start at the origin (0,0) count down 5 units and across to the right 4 units. Put a dot here. For every 1 unit the line moves to the right, it moves down 3.

You might be interested in

Solve this equation 2(x + 2)/3 = 6

Naddik [55]

Answer:

Step-by-step explanation:

2(x + 2)/3 = 6

multiply by : 3

2(x + 2) = 18

2x+4 = 18

2x = 18-4=14

x=14/2

x=7

3 0

3 years ago

Let y 00 + by0 + 2y = 0 be the equation of a damped vibrating spring with mass m = 1, damping coefficient b > 0, and spring c

stira [4]

Answer:

Step-by-step explanation:

Given that:

The equation of the damped vibrating spring is y" + by' +2y = 0

(a) To convert this 2nd order equation to a system of two first-order equations;

let y₁ = y

y'₁ = y' = y₂

So;

y'₂ = y"₁ = -2y₁ -by₂

Thus; the system of the two first-order equation is:

y₁' = y₂

y₂' = -2y₁ - by₂

(b)

The eigenvalue of the system in terms of b is:

$\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0$

$-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0$

$\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}$

$\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}$

(c)

Suppose $b > 2\sqrt{2}$ , then λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.

(d)

From λ² + λb + 2 = 0

If b = 3; we get

$\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\$

Now, the eigenvector relating to λ = -1 be:

$v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

$\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

Let v₂ = 1, v₁ = -1

$v = \left[\begin{array}{c}-1\\1\\\end{array}\right]$

Let Eigenvector relating to λ = -2 be:

$m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

$\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

Let m₂ = 1, m₁ = -1/2

$m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right]$

∴

$\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right]$

So as t → ∞

$\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }$

5 0

2 years ago

the westside bakery uses 440 pounds of sugar to make 1,000 cakes each cake contain the same amount of sugar how many pounds of s

rosijanka [135]

First of all, I like the name "westside" for a bakery. :)

OK, so, you can make a proportion for this problem.

440 lbs.= 1000 cakes.
? unknown = 1 cake.
440 divided by 1000 = 0.44 pounds

3 0

3 years ago

Three airlines serve a small town in Ohio. Airline A has 50% of all the scheduled flights, airline B has 30%, and Airline C has

lidiya [134]

Answer:

185

Step-by-step explanation:

cause if you add up 80+65+40 right?

7 0

3 years ago

The function f(x)=x^2 has been translated 9 units up and 4 units to the right to from the function g(x) which represents

leonid [27]

For translations like this use the formula:
f(x) = (x - h)² + k

where h is the lateral movement/shifts on the x-axis and k is the vertical movement/shifts on the y-axis.

Since g(x) is a movement to the right 4 units and up 9 units, your h is a positive 4 and k is a 9:

g(x) = (x - 4)² + 9

Here's a picture of your original graph f(x) and your translation g(x)

4 0

3 years ago