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3 years ago

8

Solve the equation

1 answer:

zalisa [80]3 years ago

6 0

Simplify the fraction on the left
3(x -3) = 3(2x -3)
Divide by 3
x -3 = 2x -3
Subtract the left side
0 = (2x -3) -(x -3)
0 = x

The solution is x = 0.

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LA plane is trying to travel 250 miles at a bearing of 20° E of S, however, it ends 230 miles away from the

Semmy [17]

Answer:

The wind pushed the plane $65.01$ miles in the direction of $45.56 ^{\circ}$ East of North with respect to the destination point.

Step-by-step explanation:

Let origin, O, br the starting point and point D be the destination at 250 miles at a bearing of 20° E of S, but due to wind let D' be the actual position of the plane at 230 miles away from the starting point in the direction of 35° E of South as shown in the figure.

So, we have |OD|=250 miles and |OD'|=230 miles.

Vector $\overrightarrow{DD'}$ is the displacement vector of the plane pushed by the wind.

From figure, the magnitude of the required displacement vector is

$|DD'|=\sqrt{|AB|^2+|PQ|^2}\;\cdots(i)$

and the direction is $\alpha$ east of north as shown in the figure,

$\tan \alpha=\frac{|PQ|}{|AB|}\;\cdots(ii)$

From the figure,

$|AB|=|OA-OB|$

$\Rightarrow |AB|=|OD\cos 20 ^{\circ}-OD'\cos 35 ^{\circ}|$

$\Rightarrow |AB|=|250\cos 20 ^{\circ}-230\cos 35 ^{\circ}|$

$\Rightarrow |AB|=45.52$ miles

Again, $|PQ|=|OP-OQ|$

$\Rightarrow |PQ|=|OD\sin 20 ^{\circ}-OD'\sin 35 ^{\circ}|$

$\Rightarrow |PQ|=|250\sin 20 ^{\circ}-230\sin 35 ^{\circ}|$

$\Rightarrow |PQ|=46.42$ miles

Now, from equations (i) and (ii), we have

$|DD'|=\sqrt{|45.52|^2+|46.42|^2}=65.01$ miles, and

$\tan \alpha=\frac{|46.42|}{|45.52|}$

$\alpha=\tan^{-1}\left(\frac{|46.42|}{|45.52|}\right)=45.56 ^{\circ}$

Hence, the wind pushed the plane $65.01$ miles in the direction of $45.56 ^{\circ}$ E astof North with respect to the destination point.

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What is the effect on the figure k > 1 show your work please thankssss

skad [1K]

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Complete the recursive formula of the arithmetic sequence -3, -1, 1, 3,...

Strike441 [17]

Given:

The given arithmetic sequence is:

$-3,-1,1,3,...$

To find:

The recursive formula of the given arithmetic sequence.

Solution:

We have,

$-3,-1,1,3,...$

Here, the first term is -3. So, $b(1)=-3$ .

The common difference is:

$d=-1-(-3)$

$d=-1+3$

$d=2$

The recursive formula of an arithmetic sequence is:

$b(n)=b(n-1)+d$

Where, d is the common difference.

Putting $d=2$ , we get

$b(n)=b(n-1)+2$

Therefore, the recursive formula of the given arithmetic sequence is $b(n)=b(n-1)+2$ , where $b(1)=-3$ .

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MA_775_DIABLO [31]

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jolli1 [7]

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