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3 years ago

Convert the Cartesian equation x - 5 = 0 to a polar equation.

Mathematics

1 answer:

mylen [45]3 years ago

5 0

Answer:

r = 5sec(θ)

Step-by-step explanation:

The usual conversion is ...

y = r·sin(θ)

x = r·cos(θ)

The second of these can be used here.

r·cos(θ) -5 = 0

r·cos(θ) = 5

r = 5/cos(θ) = 5sec(θ)

A suitable polar equation is ...

r = 5sec(θ)

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Mars2501 [29]

Here we know that the initial velocity of the car is given by:

$V_i=(3.0\hat x+1.0\hat y)m/s$

And the final velocity of the car is given by:

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It took 3 seconds to attain the final velocity, so we have $t=3 s$

Therefore, the acceleration can be obtained by:

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$a=\frac{V_f-V_i}{t}$

Plugging the values of the initial, final velocity and the time, we get:

$a= \frac{(6\hat x-3\hat y)-(3 \hat x+1 \hat y)}{3} =\frac{6\hat x-3 \hat y -3 \hat x-1 \hat y}{3} =\frac{3 \hat x-4 \hat y}{3}$

So the acceleration of the car is given by:

$a=\frac{3 \hat x}{3} -\frac{4 \hat y}{3} =1 \hat x- \frac{4}{3} \hat y$

Now we need to find the direction of the average acceleration of the car:

$\theta=tan^{-1} \frac{y}{x}$

Here, x and y are the coefficients of the 'x' and 'y' components of the vector:

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<em />

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