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3 years ago

What are the Cartesian coordinates of a point with polar coordinates (17, 60 degrees)?

Mathematics

1 answer:

nirvana33 [79]3 years ago

8 0

Answer:

C. (8.5, 14.72)

Step-by-step explanation:

You can translate the coordinates using ...

(x, y) = (r·cos(θ), r·sin(θ))

Filling in the given polar coordinates, (r, θ) = (17, 60°), we have ...

(x, y) = (17·cos(60°), 17·sin(60°)

(x, y) = (8.5, 14.72)

If you sketch the vector, you realize that the short side of the triangle (the x-coordinate) is half the length of the hypotenuse (17). This is because you recognize the side-length relationships in a 30°-60°-90° triangle. Only one answer choice shows that value.

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borishaifa [10]

Option A

The solution is $(0, \frac{-1}{4})$

Solution:

Given system of equations are:

3x + 6y = 1 ------ eqn 1

x - 4y = 1 ------ eqn 2

We have to find solution to system of equations

We can use substitution method

From eqn 2,

x = 1 + 4y -------- eqn 3

Substitute eqn 3 in eqn 1

3(1 + 4y) + 6y = 1

3 + 12y + 6y = 1

18y = 1 - 3

18y = -2

Divide both sides by 18

$y = \frac{-2}{18}\\\\y = \frac{-1}{4}$

Substitute the above value of y in eqn 3

$x = 1 + 4 \times \frac{-1}{4}\\\\x = 1-1\\\\x = 0$

Thus solution is $(0, \frac{-1}{4})$

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3 years ago

When you subtract one negative integer from another will your answer be greater than or less than the integer you started with

MatroZZZ [7]

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5 0

3 years ago

An ant can travel at a constant speed of 980 inches every 5 minutes. How far does the ant travel in 1 minute? The ant travels 19

ycow [4]

Answer:

The ant travels 1,372 inches in 7 minutes.

Step-by-step explanation:

Since 1 minute = 196 inches

1 × 7 = 7

196 × 7 = 1,372

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