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3 years ago

Rewrite in polar form x^2 + y^2 - 6y - 8 = 0

Mathematics

2 answers:

fredd [130]3 years ago

6 0

the correct answer is B. r^2=6r sin 0+8

Arisa [49]3 years ago

3 0

Answer:

The correct answer option is $r^2-6rsin(\theta)=8$ .

Step-by-step explanation:

We are given the following equation and we are to rewrite it in polar form:

$x^2 + y^2 - 6y - 8 = 0$

$\left \{ {{x^2+y^2=r^2} \atop {y=rsin \theta}} \right.$

Here, we need to make a perfect square trinomial:

$[r^2-6rsin(\theta)+$ ___ $^2]=8$

$6rsin(\theta)$ ---> $2 .r.3.sin \theta$

Completing the square to get:

$r^2-6rsin(\theta)+[3sin(\theta)]^2-[3sin(\theta)]^2=8$

$[r-3sin(\theta)]^2=8+[3sin(\theta)]^2$ --> $[r-3sin(\theta)]^2=8+9sin^2(\theta)$

$r-3sin(\theta)=\sqrt{8+9sin^2(\theta)}$ --> $r=\sqrt{8+9sin^2(\theta)} +3sin(\theta)$

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Scarlett can make 7 cupcakes (the y value) with one cup of flour (the x value). How many cupcakes can she make with 9 cups of fl

HACTEHA [7]

Answer:

63=x*y

Step-by-step explanation:*

y = 7 x=1. so 9 will muiltiply 7 until there is 9 7s then you got the answer

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3 years ago

The data reflects the number of hours an employee spends working a checkout line (x), paired with the number of customers served

Whitepunk [10]

The slope of the line can be interpreted that with each additional hour, nearly 18 customers are served; option B

<h3>What is the slope of a line?</h3>

The slope of a line is the ratio of climb to that of run

Slope = change in y/change in x

The given graph is a graph of the number of hours an employee spends working a checkout line (x), against the number of customers served (y).

The slope of the graph can be written as follows:

Slope = change in the number of customers served/change in the number of hours an employee spends working

Therefore, the slope of the line can be interpreted that with each additional hour, nearly 18 customers are served.

In conclusion, slope of a line is ratio of change in y to change in x.

Learn more about slope at: brainly.com/question/16949303

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1 year ago

How would you describe a monomial? in less than 25 words.

bonufazy [111]

Answer:

number, variable, or a product of a number and one or more variables

3 0

2 years ago

Write an recursive formula for An, the nth term of the sequence 5, -2, -9,

oksian1 [2.3K]

Given:

The given sequence is:

$5,-2,-9,...$

To find:

The recursive formula for $a_n$ , the nth term of the sequence.

Solution:

We have,

$5,-2,-9,...$

Here, the first term is 5.

$-2-5=-7$

$-9-(-2)=-9+2$

$-9-(-2)=-7$

The common difference is -7.

The recursive formula for the nth term of the sequence is

$a_n=a_{n-1}+d$

Where, $d$ is the common difference.

Putting $d=-7$ in the above formula, we get

$a_n=a_{n-1}+(-7)$

$a_n=a_{n-1}-7$

Therefore, the recursive formula for the nth term of the sequence is $a_n=a_{n-1}-7$ .

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2 years ago

Find the standard deviation of the following data. Round your answer to one decimal place. x 0 1 2 3 4 5 P(X

lbvjy [14]

Answer:

$\sigma = 1.8$

Step-by-step explanation:

Given

$\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}$

Required

The standard deviation

First, calculate the expected value E(x)

$E(x) = \sum x * P(x)$

So, we have:

$E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2$

$E(x) = 2.7$

Next, calculate E(x^2)

$E(x^2) = \sum x^2 * P(x)$

So, we have:

$E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2$

$E(x^2) = 10.5$

The standard deviation is:

$\sigma = \sqrt{E(x^2) - (E(x))^2}$

$\sigma = \sqrt{10.5 - 2.7^2}$

$\sigma = \sqrt{10.5 - 7.29}$

$\sigma = \sqrt{3.21}$

$\sigma = 1.8$ --- approximated

5 0

3 years ago