PLS SHOW FULL STEP .................

Transform each polar equation to an equation in rectangular coordinates and identify its shape.

Gemiola [76]

Answer:

(a) $x ^ 2 + y ^ 2 = 6 ^ 2$

(b) $(x-1) ^ 2 + y ^ 2 = 1$

Step-by-step explanation:

Remember that to convert from polar to rectangular coordinates you must use the relationship:

$x = rcos(\theta)$

$y = rsin(\theta)$

$x ^ 2 + y ^ 2 = r ^ 2$

In this case we have the following equations in polar coordinates.

(a) $r = 6$ .

Note that in this equation the radius is constant, it does not depend on $\theta$ .

As $r ^ 2 = x ^ 2 + y ^ 2$

Then we replace the value of the radius in the equation and we have to::

$x ^ 2 + y ^ 2 = 6 ^ 2$

Then $r = 6$ in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius $r = 6$ .

(b) $r = 2cos(\theta)$

The radius is not constant, the radius depends on $\theta$ .

To convert this equation to rectangular coordinates we write

$r = 2cos(\theta)$ Multiply both sides of the equality by r.

$r ^ 2 = 2 *rcos(\theta)$ remember that $x = rcos(\theta)$ , then:

$r ^ 2 = 2x$ remember that $x ^ 2 + y ^ 2 = r ^ 2$ , then:

$x ^ 2 + y ^ 2 = 2x$ Simplify the expression.

$x ^ 2 -2x + y ^ 2 = 0$ Complete the square.

$x ^ 2 -2x + 1 + y ^ 2 = 1$

$(x-1) ^ 2 + y ^ 2 = 1$ It is a circle centered on the point (1, 0) and with radio $r=1$

6 0

2 years ago

You are designing a toy box for a child’s bedroom. The toy box needs to be able to hold 1,500 cubic centimeters of toys. What mi

DochEvi [55]

Answer: 150x10

Step-by-step explanation:

4 0

3 years ago

Laboratory tests show that the lives of

SIZIF [17.4K]

<h3>Answer: 34%</h3>

This result is approximate.

=========================================================

Explanation:

mu = 750 = mean

sigma = 75 = standard deviation

The raw scores or x values are x = 750 and x = 825

Let's compute the z score for each x value

z = (x - mu)/sigma

z = (750 - 750)/75

z = 0

and

z = (x - mu)/sigma

z = (825 - 750)/75

z = 1

Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.

Use a z score table to determine that

P(z ≤ 0) = 0.5

P(z ≤ 1) = 0.84314 approximately

So,

P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)

P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)

P(0 ≤ z ≤ 1) = 0.84314 - 0.5

P(0 ≤ z ≤ 1) = 0.34314 approximately

The value 0.34314 then converts to 34.314% which rounds to 34%

Or you could use the empirical rule as shown below. The pink section on the right is marked 34% which is approximate. This pink section is between z = 0 and z = 1.

6 0

2 years ago

A categorical variable whose values are purely qualitative and unordered is called a _______ variable. Please type the correct a

MissTica

Answer: Nominal

Step-by-step explanation:

A categorical variable whose values are purely qualitative and unordered is called a Nominal variable. Nominal variables are qualitative variables that does not have a particular rank, order or value. An example of nominal variables are colour (red,blue etc), gender (male, female), skin and hair colour etc.

3 0

2 years ago

Lilly bottles 4 1/8 quarts of barbecue sauce. Then she bottles another 5 7/8 quarts of barbecue sauce. How many 1-cup servings o

Pani-rosa [81]

so there's 4 cups to a quart . so we just add 4 1/8 and 5 7/8 which gives us 10.

now that we have that we take ten and times it by 4 giving us 40. so there are 40 cups

5 0

3 years ago