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3 years ago

13

What is the circumference of the circle defined by x^2+6x +y^2-12y-4=0.

1 answer:

KengaRu [80]3 years ago

5 0

Answer:

44.0

Step-by-step explanation:

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Θ is in Quadrant III and cos^2 0= 1/4

pychu [463]

I think you mean to say $\cos^2\theta=\dfrac14$ . If $\theta$ is in the third quadrant, then $\sin\theta$ and $\cos\theta$ . Recall that

$\sin^2\theta+\cos^2\theta=1\implies\sin\theta=\pm\sqrt{1-\cos^2\theta}$

We expect $\sin\theta$ to be negative, so we take the negative root. We end up with

$\sin\theta=-\sqrt{1-\dfrac14}=-\dfrac{\sqrt3}2$

We also know to expect $\cos\theta$ , so

$\cos\theta=\pm\sqrt{\dfrac14}\implies\cos\theta=-\dfrac12$

By definition, we have

$\cot\theta=\dfrac{\cos\theta}{\sin\theta}$

and so

$\cot\theta=\dfrac{-\frac12}{-\frac{\sqrt3}2}=\dfrac1{\sqrt3}$

7 0

3 years ago

Evaluate the logarithm.

eimsori [14]

Answer:

$x \approx 0.954$

Step-by-step explanation:

The logarithm is evaluated as follows:

$x = 2\cdot \log 3$

$x = \log 3^{2}$

$x = \log 9$

The value of the logarithm can be estimated by means numeric methods, which can be easily used on calculators (i.e. Macaulay Series)

$x \approx 0.954$

8 0

3 years ago

What is the standard form of this expression? (4y-9)(2y-3)

Setler [38]

Answer:

-22y+27

Step-by-step explanation:

(4y-9)(2y-3)

<u>Distribute:</u>

8y-12y-18y+27

<u>Combine like terms:</u>

8y-12y-18y=-22y

-22y+27

3 0

3 years ago

What is the area of the polygon below in square units?<br> 4 cm<br> 12 cm<br> 18 cm

stepan [7]

There is no polygon there

8 0

2 years ago

(5a^2+6a+2)-(7a^2-7a-5)

krok68 [10]

For this case we must simplify the following expression: $(5a^ 2 + 6a + 2) - (7a^ 2-7a-5) =$

We eliminate the parentheses taking into account that:

$- * + = -\\- * - = +$

So:

$5a ^ 2 + 6a + 2-7a ^ 2 + 7a + 5 =$

We add similar terms taking into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

$5a ^ 2-7a^2 + 6a + 7a +2 +5 =\\-2a ^ 2 + 13a + 7$

Answer:

$-2a ^ 2 + 13a + 7$

8 0

3 years ago