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3 years ago

Ethan's solution and reasoning for solving an equation are shown below: 4/2 x - 10 =30

Mathematics

2 answers:

Mekhanik [1.2K]3 years ago

8 0

Answer:

Step-by-step explanation:

jek_recluse [69]3 years ago

5 0

Answer:

x = 20

Step-by-step explanation:

4/2x - 10 =30

Divide 4/2.

2x - 10 =30

Add 10 to both sides.

2x = 30 + 10

2x = 40

Divide 2 into both sides.

2x/2 = 40/2

x = 20

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Solution :

Let $v_0$ be the unit vector in the direction parallel to the plane and let $F_1$ be the component of F in the direction of $v_0$ and $F_2$ be the component normal to $v_0$ .

Since, $|v_0| = 1,$

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From figure,

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We know that the direction of $F_1$ is opposite of the direction of $v_0$ , so we have

$F_1 = -5\sqrt3 v_0$

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The unit vector in the direction normal to the plane, $v_1$ has components :

$(v_1)_x= \cos 30^\circ = \frac{\sqrt3}{2}$

$(v_1)_y= -\sin 30^\circ =- \frac{1}{2}$

Therefore, $v_1=\left< \frac{\sqrt3}{2}, -\frac{1}{2} \right>$

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$|F_2 | = |F| \sin 30^\circ = 10 \times \frac{1}{2} = 5$

∴ $F_2 = 5v_1 = 5 \left< \frac{\sqrt3}{2}, - \frac{1}{2} \right>$

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Therefore,

$F_1+F_2 = \left< -\frac{5\sqrt3}{2}, -\frac{15}{2} \right> + \left< \frac{5 \sqrt3}{2}, -\frac{5}{2} \right>$

$= = F$

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