Convert the following equation to cartesian coordinates. describe the resulting curve.
r = 9/7cos theta + 2sin theta
1. Write the Cartesian equation.
2. Describe the curve.

Answers

Answer 1

Answer:

The rules for change of coordinates are:

r = √(x^2 + y^2)

θ = tan(y/x)

and:

x = r*cos(θ)

y = r*sin(θ)

1) Now we have the equation:

r = (9/7)*cos(θ) + 2*sin(θ)

Let's multiply both sides by r:

r^2 = r*(  (9/7)*cos(θ) + 2*sin(θ) )

r^2 = (9/7)*r*cos(θ) + 2*r*sin(θ)

Now we can replace:

r*cos(θ) by x and r*sin(θ) by y

r^2 = (9/7)*x + 2*y

And we know that:

r = √(x^2 + y^2)

then:

r^2 = x^2 + y^2

So we can replace that in our equation:

x^2 + y^2 = (9/7)*x + 2*y

This is the equation in cartesian coordinates.

2) Now we want to describe the curve.

We can rewrite this as:

[x^2  - (9/7)*x] + [ y^2 - 2*y] = 0

Now we can complete squares:

So we need to add and subtract:

(4.5/7)^2 and 1^2

[x^2  - 2*(4.5/7)*x + (4.5/7)^2 -  (4.5/7)^2] + [ y^2 - 2*y + 1 - 1]  = 0

(x - (4.5/7) )^2 + (y - 1)^2   - 1 - (4.5/7) = 0

(x - (4.5/7) )^2 + (y - 1)^2  = 1 + 4.5/7

So this is the equation of a circle, centered at:

( 4.5/7, 1) and with a radius √(1 + 4.5/7)


Related Questions

The temperature in a commercial freezer over four days are -2.36 F, 1.68F, -1.81F, and 0.67F what is the mean temperature of the freezer over the four days

Answers

Answer: -0.455F

Step-by-step explanation:

The mean temperature of the freezer over the four days will be gotten by adding the total temperature and then dividing by 4. This will be:

= (-2.36 + 1.68F + -1.81F + 0.67F) / 4

= -1.82F/4

= -0.455F

The mean temperature is -0.455F

what is the midpoint of the segment shown below? (-2,4) (6,-4)

Answers

solution :

let's assume the Coordinates be x and y

By using Section formula,

[tex] \boxed{ x = (\dfrac{x_2 + x_1}{2} )}[/tex]

[tex]x = \dfrac{ - 2 + 6}{2} [/tex]

[tex]x = \dfrac{4}{2} [/tex]

[tex]x = 2[/tex]

____________________

[tex] \boxed {y = (\dfrac{y_2 + y_1}{2} )}[/tex]

[tex] \dfrac{ - 4 + 4}{2} [/tex]

[tex] \dfrac{0}{4} [/tex]

[tex]0[/tex]

____________________

[tex]\mathrm{Therefore \:\:the\:\: Coordinates\:\: of \:\:the\;\; mid-point\;\: of \;\;the\:\: given\:\: segment\:\; is}[/tex]

[tex] \huge \boxed{(2,0)}[/tex]

_____________________________

[tex]\mathrm{ \#TeeNForeveR} \: ☃[/tex]

WILL



GIVE

BRAINLIST



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Answers

Answer:

67.6

Step-by-step explanation:

first, to find the mean you add up all the numbers and you would get 338. Next, you divide by how many numbers there are (5) so 338 divided by 5 equals 67.6

Hey Besties! Pls help! 50 pts!
Which is the graph of f(x) = one-fourth(4)x?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It curves up to the left and goes through points (2, 1) and (0, 4).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1. It curves up to the left and goes through points (1, 1) and (0, 4).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and goes through points (3, 2) and (4, 4).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and goes through points (1, 1) and (2, 4).

Answers

The graph of the function [tex]f(x) = \frac 14(4)^x[/tex] is (d) on a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and goes through points (1, 1) and (2, 4).

What are functions?

Functions are used to represent equation, graphs and tables

The equation of the function is given as:

[tex]f(x) = \frac 14(4)^x[/tex]

The above function is an exponential function that has an initial value of 1/4 and a rate of 4

When x = 2,

f(2) = 4

When x = 1,

f(1) = 1

Hence, the graph of the function [tex]f(x) = \frac 14(4)^x[/tex] is (d)

Read more about exponential functions at:

https://brainly.com/question/11464095

Answer:

graph one

Step-by-step explanation:

did it on ed .

\-x+sqrt1−x
2
\-=sqrt2(2x
2
−1)

Answers

Answer:

3sqrt2

Step-by-step explanation:

b jhf vj fjvfd vmnd fmv ndkfv mndfvdf nkvvdf lkv nf khlfd hjvdf

A is a set containing five different numbers. B is a set containing
four different numbers, all of which are members of A. Which of
the following statements CANNOT be true?

Answers

Answer:

"the median of a is equal to the median of b" cannot be true.

Step-by-step explanation:

The statement "the range of A is less than the range of B. cannot be true.

What is mean?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

The given statements are:

The mean of A is equal to the mean of B,The median of A is equal to the median of B,The range of A is equal to the range of B,The range of A is less than the range of B.

The range of A < the range of B --> the range of a subset cannot be more than the range of a whole set.

Thus, the statement "the range of A is less than the range of B. cannot be true.

Learn more about the mean here:

https://brainly.com/question/22871228

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50 points!!!!! need answer ASAP

Answers

Answer:

the first option

Step-by-step explanation:

i believe

Can two different angles have the same reference angle?

Answers

It is the angle between the terminal side and the x axis. As the point moves into each quadrant, note how the reference angle is always the smallest angle between the terminal side and the x axis.

Pls help me, if you get it right I will give you Brainlist!​

Answers

Answer:

B. 31.4

Step-by-step explanation:

● you use the equation to find the circumstance of a circle so 2(pi)r.

● plug in the numbers into the equation 2(3.14)(5)

● evaluate. 2(15.70) = 31.4

A line for tickets to a Broadway show had a mean waiting time of 20 minutes with a standard deviation of 5 minutes.


What percentage of the people in line waited for more than 28 minutes?

Answers

Answer:

5.48% of the people in line waited for more than 28 minutes

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean waiting time of 20 minutes with a standard deviation of 5 minutes.

This means that [tex]\mu = 20, \sigma = 5[/tex]

What percentage of the people in line waited for more than 28 minutes?

The proportion is 1 subtracted by the p-value of Z when X = 28. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{28 - 20}{5}[/tex]

[tex]Z = 1.6[/tex]

[tex]Z = 1.6[/tex] has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

As a percentage:

0.0548*100% = 5.48%

5.48% of the people in line waited for more than 28 minutes

Add a sale this week a suit is being sold for $476 this is a 15% discount from the original price what is the original price

Answers

If the $476 is a 15% discount then $476 is 85% of the OG price. The original price is $560.

560 * .15 = 84.
560 - 84 = 476.

Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 7xex, a = 0

Answers

Answer:

The four first terms are:

[tex]7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}[/tex]

Step-by-step explanation:

The function is:

[tex]f(x)=7xe^{x}[/tex]

The Taylor series around a is given by:

[tex]F(x)=\sum^{\infty}_{n=0} \frac{f^{n}(a)(x-a)^{n}}{n!}[/tex]

The first 4 terms will be:

[tex]F(x)=f(0)+\frac{f^{'}(0)(x)}{1}+\frac{f^{''}(0)(x)^{2}}{2}+\frac{f^{'''}(0)(x)^{3}}{6}[/tex]  

Let's find first the derivatives:

[tex]f'(x)=7(xe^{x}+e^{x})[/tex]

[tex]f'(0)=7(0e^{0}+e^{0})=7[/tex]

[tex]f''(x)=7xe^{x}+7e^{x}+7e^{x}=7xe^{x}+14e^{x}[/tex]  

[tex]f''(0)=14[/tex]  

[tex]f'''(0)=21[/tex]

[tex]f''''(0)=28[/tex]    

[tex]F(x)=0+\frac{7(x)}{1}+\frac{14(x)^{2}}{2}+\frac{21(x)^{3}}{6}+\frac{28(x)^{4}}{24}[/tex]

Therefore, the four first terms are:

[tex]7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}[/tex]

I hope it helps you!

 

   

So the Taylor series for the function informed will be:

[tex]7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}[/tex]

The function is:

[tex]f(x)= 7e^xx[/tex]

The Taylor series around a is given by:

[tex]f(x)= \sum \frac{f^n (a) (x-a)^n }{n!}[/tex]

The first four terms will be:

[tex]F(x)=f(0)+\frac{f'(0)(x)}{1}+\frac{f''(0)(x)^2}{2} + \frac{f'''(0)(x)^3}{6}[/tex]

Let's find first the derivaties:

[tex]f'(x)= 7(e^xx+e^x)\\f'(0)= 7\\f''(x)= 7e^xx+14e^xx\\f''(0)=14\\f'''(0)= 21\\f''''(0)= 28[/tex]

[tex]F(x)= 0+\frac{7x}{1}+\frac{14x^2}{2}+\frac{21x^3}{6}+\frac{28x^4}{24}[/tex]

Therefore, the four first terms are:

[tex]7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}[/tex]

See more about Taylor series at : brainly.com/question/6953942

Solve for X: -10+3X<4

Answers

Answer:

x<14/3

Step-by-step explanation:

-10+3x<4

3x<4+10

3x<14

x<14/3

If this helps please mark as brainliest

help plz
which is right

Answers

Answer:

B

Step-by-step explanation:

Answer:

I think the anwser is

B.2cot x sec x

HOPE IT HELPED

What are the slopes of the lines.

Answers

The slope m of a line is one of the elements in the equation of a line when written in the "slope and intercept" form: y = mx+b. The m in the equation is the slope of the line described here.

One of a equation of a line

A box can be filled completely using 16 layers of 7 units cubes. What is the volume of
the box?

Answers

The volume of the box is 112

Volume can be described as the amount/quantity of space that an object occupies.

The box is completely filled with 16 layers and 7 unit cubes. Hence the volume can be calculated as follows

= 16 × 7

= 112

Hence the volume of the box is 112


Please see the link below for more information
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a store sells 3 hats for a total of $47.25. the cost if each hat is the same. what is the cost, in dollars, of one hat in the store

Answers

Answer: $15.75

Step-by-step explanation: 47.25/3=15.75

Answer:

15.75

Step-by-step explanation:

if there’s 3 hats for 47.25, just divide.

47.25 / 3 = 15.75

you can double check my tripling this answer to see if you get 47.25

15 x 3 = 47.25

47.25 = 47.25

-45, -16,-9 ,7,33 least to greatest

Answers

Answer:

-45 -16 -9 7 33

Abigail is going to cover the label on a Pringle's can and decorate it for
Mother's Day. The can has a diameter of 4.5 inches and a height of 14
inches. What is the minimum amount of paper that she needs for the
project?

Answers

Answer:

[tex]Area = 229.6125in^2[/tex]

Step-by-step explanation:

Given

[tex]h = 14in[/tex] --- height

[tex]d =4.5in[/tex] --- diameter

Required

The minimum amount of paper needed

This implies that we calculate the surface area of the can (cylinder)

This is calculated as:

[tex]Area = 2\pi r(r + h)[/tex]

Where

[tex]r = \frac{1}{2}d[/tex]

So, we have:

[tex]r = \frac{1}{2} *4.5[/tex]

[tex]r = 2.25[/tex]

This gives:

[tex]Area = 2 * 3.14 * 2.25(2.25 + 14)[/tex]

[tex]Area = 2 * 3.14 * 2.25*16.25[/tex]

[tex]Area = 229.6125in^2[/tex]

what is the length of segment bd

Answers

Answer:

10 if not mistaking, sorry if im wrong

Step-by-step explanation:

Answer:

BD = 16

Step-by-step explanation:

AB and AC are both radii

AB  = AC =  6 + 4 = 10

BE = 8 because it's the leg of a right triangle with 6² + 8² = 10²

BD = 2 * BE = 2 * 8 = 16

Um gato come 5 ratos por dia. Quantos ratos 5 gatos comem em 5dias?​

Answers

Answer:

1 gato come 5 ratos em 1 dia X 5 = 5 gatos come 25 ratos por dia

5 gatos come 25 ratos por dia X 5 = 25 gatos come 125 ratos por dia

four of the angle of a Pentagon are 70°,90°,100° and 145°. What is the side of a fifth angle?​

Answers

Answer: 135°

Step-by-step explanation:

The sum of the angles in a pentagon is equal to 540°, and the sum of the first four angles is 405°.

70 + 90 + 100 + 145 = 405

540 - 405 = 135

find the volume. the base is regular.
PLEASE HELP ASAP

Answers

Answer:

V≈14590.8

Step-by-step explanation:

plz mark brainliest

Help me on this . It’s important

Answers

Answer:

The answer is 16.

Step-by-step explanation:

6 x 3 = 18

18 - 2 =16

6n- 2= ?
6(3) - 2 —> substitute the “n” with 3
=18-2 —> 6 times 3 equals 18 and =16 subtract 2

Provide your steps!!
•••••••••••••••••••••••••

Answers

Answer:

946 ft²

Step-by-step explanation:

28 x 7 = 196

30 x 25 = 750

750 + 196 = 946 ft²

7 to 2 = __to 6 help plz​

Answers

Answer:

19 would be the naswer

Step-by-step explanation:

find the answer of
31050×2³​

Answers

The answer for 31050*(2^3)= 248400 :)

If mSW = (12x-5)°, mTV= (2x+7)°,and m angle TUV = (6x-19)°, find mSW

Answers

Given:

Consider the below figure attached with this question.

m(arc(SW)) = (12x-5)°, m(arc(TV))= (2x+7)°,and measure of angle TUV = (6x-19)°.

To find:

The m(arc SW).

Solution:

Intersecting secant theorem: If two secants intersect outside the circle, then the angle on the intersection is half of the difference of the larger subtended arc and smaller subtended arc.

Using Intersecting secant theorem, we get

[tex]m\angle TUV=\dfrac{1}{2}(m(arc(SW))-m(arc(TV)))[/tex]

[tex]6x-19=\dfrac{1}{2}((12x-5)-(2x+7))[/tex]

[tex]6x-19=\dfrac{1}{2}(12x-5-2x-7)[/tex]

[tex]6x-19=\dfrac{1}{2}(10x-12)[/tex]

Multiply both sides by 2.

[tex]2(6x-19)=10x-12[/tex]

[tex]12x-38=10x-12[/tex]

[tex]12x-10x=38-12[/tex]

[tex]2x=26[/tex]

Divide both sides by 2.

[tex]x=13[/tex]

Now, the measure of arc SW is:

[tex]m(arc(SW))=(12x-5)^\circ[/tex]

[tex]m(arc(SW))=(12(13)-5)^\circ[/tex]

[tex]m(arc(SW))=(156-5)^\circ[/tex]

[tex]m(arc(SW))=151^\circ[/tex]

Therefore, the measure of arc SW is 151 degrees.

Can somebody help me with my mathia

Answers

Answer:

Sure i can try helping u with ur mathia lol

Step-by-step explanation:

guys please help its my final either i pass or not

Answers

Answer:

Step-by-step explanation:

1 yes 2 no 3 no 4 yes 5 no

Answer:

1. yes

2. yes

3. no

4. yes

5. no

Step-by-step explanation:

go to mathwa* and type in the same equation and click to see if function or not.

gl on the final

this guy above me is wrong for #2

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