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2 years ago

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How do you solve 2A= 4lw+2Lh+6wH for w

1 answer:

gizmo_the_mogwai [7]2 years ago

6 0

Answer:

$\displaystyle w=\frac{A-Lh}{2l+3H}$

Explanation:

Solving Equations by Isolation

We have this equation:

$2A= 4lw+2Lh+6wH$

Let's solve it for w step by step. First, we flip both sides

$4lw+2Lh+6wH =2A$

Subtracting 2Lh in both sides

$4lw+2Lh+6wH-2Lh =2A-2Lh$

Simplifying

$4lw+6wH =2A-2Lh$

Factoring w

$w(4l+6H) =2A-2Lh$

Dividing by (4l+6H)

$\displaystyle w=\frac{2A-2Lh}{4l+6H}$

Simplifying by 2:

$\displaystyle \boxed{w=\frac{A-Lh}{2l+3H}}$

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A 0.29 kg particle moves in an xy plane according to x(t) = - 19 + 1 t - 3 t3 and y(t) = 20 + 7 t - 9 t2, with x and y in meters

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Answer:

Part a)

$F = 7.76 N$

Part b)

$\theta = -137.7 degree$

Part c)

$\theta = -127.7 degree$

Explanation:

As we know that acceleration is rate of change in velocity of the object

So here we know that

$x = -19 + t - 3t^3$

$y = 20 + 7t - 9t^2$

Part a)

differentiate x and y two times with respect to time to find the acceleration

$a_x = \frac{d^2}{dt^2}(-19 + t - 3t^3)$

$a_x = \frac{d}{dt}(0 +1 - 9t^2)$

$a_x = -18t$

$a_y = \frac{d^2}{dt^2}(20 + 7t - 9t^2)$

$a_y = \frac{d}{dt}(0 +7 - 18t)$

$a_y = -18$

Now the acceleration of the object is given as

$\vec a = (-18t)\hat i + (-18)\hat j$

at t= 1.1 s we have

$\vec a = -19.8 \hat i - 18 \hat j$

now the net force of the object is given as

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$\vec F = (0.29 kg)(-19.8 \hat i - 18 \hat j)$

$\vec F = -5.74 \hat i - 5.22 \hat j$

now magnitude of the force will be

$F = \sqrt{5.74^2 + 5.22^2} = 7.76 N$

Part b)

Direction of the force is given as

$tan\theta = \frac{F_y}{F_x}$

$tan\theta = \frac{-5.22}{-5.74}$

$\theta = -137.7 degree$

Part c)

For velocity of the particle we have

$v_x = \frac{dx}[dt}$

$v_x = (0 +1 - 9t^2)$

$v_y = \frac{dy}{dt}$

$v_y = (0 +7 - 18t)$

now at t = 1.1 s

$\vec v = -9.89\hat i - 12.8 \hat j$

now the direction of the velocity is given as

$\theta = tan^{-1}(\frac{v_y}{v_x})$

$\theta = tan^{-1}(\frac{-12.8}{-9.89})$

$\theta = -127.7 degree$

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Answer:

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Explanation:

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Learn more about current:

brainly.com/question/4438943

brainly.com/question/10597501

brainly.com/question/12246020

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