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3 years ago

8

Consider the circle with an equation in standard form: ( x – 4)² + ( y + 2)² = 36 . Explain in 2-3 sentences or explain the step

s used to find the radius and the center.

1 answer:

iragen [17]3 years ago

4 0

Answer:

The center of this circle is found at (4, -2) and the radius is 6.

Step-by-step explanation:

The equation for a circle in standard for is ( x – h)² + ( y - k)² = r². In this equation, (h, k) is the center of the circle and r is the radius.

From the given equation, ( x – 4)² + ( y + 2)² = 36, h is already subtracted from x, so h = 4, but the k is not subtracted, so (y + 2) = [y - (-2)], and we see that k is -2. Therefore, the center of the circle is (4, -2) and 36 = r². By taking the square root of 36, we find that r = 6.

The center of this circle is found at (4, -2) and the radius is 6.

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Is the function even or odd?

sweet [91]

Answer:

$f(\theta)=\cos(\theta)$ is an even function.

Step-by-step explanation:

Recall when it means when a function is even or odd. An even function has the following property:

$f(-x)=f(x)$

And an odd function has the following property:

$f(-x)=-f(x)$

So, let's test some values for cos(x).

Let's use π/3:

$f(\pi/3)=\cos(\pi/3)$

From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).

Now, let's find -π/3. This is the same as 5π/3. Thus:

$f(-\pi/3)=\cos(-\pi/3)$

And again from the unit circle, we can see that this is 1/2.

Therefore, despite the negative, the function outputs the same value.

Cosine is an even function.

Notes:

Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!

6 0

3 years ago

Samantha correctly solved the equation x2 -4x= 4 by completing the square. Which equation is part of her solution?

ycow [4]

Answer:

±

2

√

2

+

2

Step-by-step explanation:

7 0

3 years ago

Write 0.216 as a rational number in lowest terms

lozanna [386]

Answer:

$=\frac{27}{125}$

Step-by-step explanation:

$0.216$

$\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}$

$\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000$

$=\frac{0.216\cdot \:1000}{1000}$

$=\frac{216}{1000}$

$216,\:1000$

$\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}$

$2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3$

$2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5$

$\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}$

$=2\cdot \:2\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8$

$=8$

$=\frac{8\cdot \:27}{8\cdot \:125}$

$\mathrm{Cancel\:the\:common\:factor:}\:8$

$=\frac{27}{125}$

Hence, the correct answer is $=\frac{27}{125}$

6 0

2 years ago

What is -4 - (8) More text

son4ous [18]

Answer:

-12

Step-by-step explanation:

(-4) - 8

Keep Flip Change

Keep

(-4)

Flip

- to +

Change to opposite

8 to -8

Result

-4 + -8 = -12

5 0

2 years ago

Read 2 more answers

33. The number of batches of cookies that can be made in a bakery every hour is shown in the graph.

MAVERICK [17]

The equation of this line in slope intercept form is y= 3/7x

4 0

3 years ago