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3 years ago

What is 7k - 1.2=-19.8

Mathematics

1 answer:

mart [117]3 years ago

3 0

1) Add 1.2 to both sides

7k=21

2) Divide 7 on both sides.

k=3

Your answer is 3.

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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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3 years ago

3 ears of corn cost $1

lisov135 [29]

Yes 3 ears of corn cost $1

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3 years ago

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Philip saves $8 each month. How many months will it take him to save at least $60?

mars1129 [50]

7.5 months for him to save up to 60 ;)

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3 years ago

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Create an equivalent system of equations using the sum of the system and the first equation. x + 4y = 8 4x + y = 2

qaws [65]

Answer:

Equivalent systems of equations review

Step-by-step explanation:

We're given two systems of equations and asked if they're equivalent.

x + 4y = 8 (1)

4x + y = 2 (2)

Interestingly, if we sum the equations in System A, we get:

$x + 4y = 8 \\4x + y = 2 \\$

$5x+5y=10$

Replacing the first equation in System A with this new equation, we get a system that's equivalent to System A:

$5x+5y=10$

$4x + y = 2$

This is System B, which means that System A is equivalent to System B.

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3 years ago

Louise bought 114 pounds of roast beef at $2.00 per pound and 212 pounds of turkey at $1.50 per pound. What was her total cos

BlackZzzverrR [31]

To find the total cost of Roast Beef, multiply 114 lbs by $2 equaling $228. Next to find the total cost of the turkey, multiply 212 lbs by $1.5 equaling $318. The last step is to multiply the two sums giving you a total of $546

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4 years ago

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