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ivanzaharov [21]

2 years ago

13

The graph of r = -10 cos θ has which of the following characteristics?

1 answer:

Ronch [10]2 years ago

8 0

Step-by-step explanation:

If we convert

$r = - 10 \cos(x)$

to a Cartesian equation,

${r}^{2} = - 10 r \: \cos(x)$

${x}^{2} + {y}^{2} = - 10x$

${x}^{2} + 10x + {y}^{2} = 0$

${x}^{2} + 10x + 25 + {y}^{2} = 25$

$(x + 5) {}^{2} + {y}^{2} = 25$

So we have a circle with center (-5,0), with a diameter of 10.

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The average number of earthquakes that occur in Los Angeles over one month is 36. Assume the standard deviation is 3.6. if a ran

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Step-by-step explanation:

We assume that the number of earthquakes that occur in Los Angeles follows normal distribution.

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Step-by-step explanation:

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2 years ago

The point (6, 6) is on the graph y = f(x) . Find the corresponding coordinates of this point on the graph y = 4f[1/3x +9] -7

miss Akunina [59]

Answer:

Correct answer is:

<em>a. (-9,17)</em>

Step-by-step explanation:

We are given that a point (6, 6) lies on the graph of $y =f(x)$ .

Putting the values from the given point:

$6 =f(6)$

That means we are given that $f(6) =6$ ..... (1)

And we have to find the corresponding coordinates of this point on the graph of $y = 4f[\frac{1}3x +9] -7$

From equation (1), we know the value of $f(6)$ .

so, let us convert $f[\frac{1}3x +9]$ to a form such that it becomes equal to $f(6)$

$\Rightarrow \dfrac{1}{3}x +9 =6\\\Rightarrow \dfrac{1}{3}x=-3\\\Rightarrow x = -9$

So, let us put $x = -9$ in the given function:

$4f[\frac{1}3\times (-9) +9] -7\\\Rightarrow 4f[-3 +9] -7\\\Rightarrow 4f(6) -7$

Now, using equation <em>(1)</em>, putting $f(6)=6$

$\Rightarrow 4\times 6 -7\\\Rightarrow 24-7 \\\Rightarrow y = 17$

Therefore, the point the corresponding point is:

<em>a. (-9,17)</em>

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4 years ago