Given that x=3sin​​θ-2 and y=3cos​​​θ+4.Show that (x+2)²+ (y-4)²=9​​​​​​

Answers

Answer 1

Answer:

First, plug-in x and y as 3sin​​θ-2 and 3cos​​​θ+4 into the equation, respectively:

[tex]((3\sin (\theta)-2)+2)^2 + ((3\cos (\theta)+4)-4)^2 = 9[/tex]

Then, +2 and -2 cancel out and +4 and -4 cancel out as well, leaving you with:

[tex](3\sin(\theta))^2+(3\cos(\theta))^2=9[/tex]

We can factor out 3^2 = 9 from both equations:

[tex]9(\sin(\theta)^2+cos(\theta)^2) = 9[/tex]

We know from a trigonometric identity that [tex]\sin(\theta)^2+cos(\theta)^2 = 1[/tex], meaning we can reduce the equation to:

[tex]9(1) = 9[/tex]

[tex]9=9[/tex]

And therefore, we have shown that (x+2)^2 + (y-4)^2 = 9, if x=3sin​​θ-2 and y=3cos​​​θ+4.

Hope this helped you.


Related Questions

Fill in the blank. Using the number line below, the plotted number is
when rounded to the nearest hundred.
150
200
250
300
350

Answers

I think it’s 400 hope it helps

Answer?
What is it?

7m-7-6m-16=1+4m

Answers

7m-7-6m-16=1+4m

7m - 6m - 7 - 16 = 1 + 4m

    m       -   23  = 1 + 4m

m - 23 + 23 = 1 + 23 + 4m

m = 4m + 24

m - 4m = 4m - 4m + 24

-3m = 24

m = 24: (-3)

m = - 8

hi again,

7m-7-6m-16=1+4m

7m-6m-4m=1+7+16

-3m=24

m=24/-3

m=-8

Hope this helps

Joogh bought reaps for $3 each and biscuits for $6 each. The total cost was 108. Write an equation in standard form showing the relationship reaps (x) and biscuits (y)

Answers

Answer:

3x + 6y = 108

Step-by-step explanation:

We are given the cost of x ($3) and y ($6) and the total cost (which will be on the right side of the = sign)We know that x + y = total. This means that we will add $3 and $6 to get the total.You would multiply $3 by x in case there is more than one reap purchased. This applies to biscuits as well.In conclusion, you would use this information to get...3x + 6y = 108 (or $3y + $6y = $108)

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

solve for the variable​

Answers

For this problem your going to want to do the equation backwards 100-4=96 then you want to divide 96 by -12 we already know that the variable is going to be a negative because two negatives equal a positive so if it’s easier for you to divide by taking off the negative sign you can go ahead and do so but 96/-12=-8 (please mark brainliest)

Use a calculator to find decimal estimates to two decimal places (hundredths) for the following irrational number: √19​

Answers

Answer:

The answer is 4.35, rounded two decimals to hundredths place.

some text here to make the answer slightly longer for some good reasons. yep.

HELP PLEASE! 40 POINTS AND WILL MARK BRAINLIEST.

Describe how to find the 12th term from the sequence below.
f(1)=4
f(n)=f(n-1)+5

Answers

The first term, f(1) = 4, to find the second term,

which is f(2-1) = f(1) = 4, so second term, f(2) = 4+5

hence 9, to find the terd term,

which is f(3-1) = f(2) = 9, so terd term, f(3) = 9+5

hence 14, so common difference is 5.

12 term is 59.


ASAP!!! FOR BRAINlIEST!!

Answers

Answer:

No

Step-by-step explanation:

the value x is used twice, meaning when graphed it is going to meet to points at the same time, which makes it not a functions.

- i hope this makes sense

Calculate the probability of rolling a 1 or 2 when using two dice (order does NOT
matter). Now calculate how often a 1 or 2 appeared in the scenario above against the
total number of appearances. Explain why these two numbers are the same or different.

Answers

The probability of rolling a 1 or a 2 is P = 4/9, this means that around 4/9 out of the N times we perform the experiment, we will see a 1 or a 2.

How to find the probability?

We assume that each number has the same probability of rolling up in both dices.

So, in each dice, the probability of rolling a 1 or a 2 is 2 out of 6, or:

p = 2/6 = 1/3

And if we get these on one of the dice, we don't want them in the other,

The probability of not rolling a 1 or a 2 is:

q = 4/6 = 2/3

The joint probability is the product of the two individual probabilities:

P = (1/3)*(2/3)

But, we also need to consider the case where we don't get an 1 or a 2 in the first dice roll, and we do get it on the second dice, then there are 2 permutations, so we need to add a factor 2.

P = 2*(1/3)*(2/3) = 4/9

Now we want to find how often a 1 or a 2 appear against the total number of appearances.

If the total number of appearances is N, then in 4/9 of these, the number 1 or 2 will appear, this is:

N*(4/9) times.

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

What is y=-1/4x+4 written in standard form?

Answers

Answer:

x + 4y = 16

Step-by-step explanation:

have a good day

Answer:

x + 4y = 16

Step-by-step explanation:

What is the solution of: 4-2x/7 - 3x+2/3

Answers

Answer:

  (-27x -2)/21

Step-by-step explanation:

Perhaps you want to combine the two fractions. This is done using a common denominator.

  [tex]\dfrac{4-2x}{7}-\dfrac{3x+2}{3}=\dfrac{3(4-2x)}{7\cdot3}-\dfrac{7(3x+2)}{7\cdot3}\\\\=\dfrac{3(4-2x)-7(3x+2)}{21}=\dfrac{12-6x-21x-14}{21}=\boxed{\dfrac{-27x-2}{21}}[/tex]

__

Additional comment

If you need to simplify this further, you can apply the distributive property.

  = -9/7x -2/21

pls answer , please brainlist

Answers

Option 4. Hope this helps :)

Answer: Option 4 - 1440

Step-by-step explanation:

2 Square Sides : Take 12 times 12 and times by two for both sides.

12 x 12 = 144     144 x 2 = 288

4 rectangular sides : The multiplication of 12 times 24

12 x 24 = 288    288 x 4 = 1152

Added All Together : 288 + 1152 = 1440

hich of these expressions is true?
a
2 < V10 <3
Ob
3 < V10 < 4
Pleaseeeee I have a midterm rn

Answers

Answer:

B

Step-by-step explanation:

[tex] \sqrt{10} = 3.162277...[/tex]

[tex]3 < \sqrt{10} < 4[/tex]

Please help me out :)

Determine the intercepts of the line

Answers

Answer:

x-intercept: (15/7 , 0)

y-intercept: (0, 5/2)

*just plug in y=0 to find the X-intercept and x=0 for the y-intercept

Find the length of the diagonal of the square 9m

Answers

The answer is : 6.36 m

If Chad drove 168 miles in 2 hours, how many hours will it take Chad to drive 840 miles traveling at the same rate?

Answers

Answer:

10 hours

Step-by-step explanation:

First we need to find the rate Chad is driving. The rate is equal to distance/time, so we do 168/2, which is 84 mph. Then we have to find the time, which is distance/rate, so that would be 840/84, which is 10 hours.

Answer:

10 hours

Step-by-step explanation:

If Chad drove 168 miles in 2 hours than he drove 84 miles in one hour. If he drove 840 miles than you divide 840 by 84 and you get 10 hours. To check your work you can do 84*10= 840 miles 84=representing the miles per hour and 10=representing the amount of hours he drove.

Starting at noon, the temperature dropped steadily at a rate of 0.8 degrees Celsius every hour. For each of these situations, write and solve an equation and describe what your variable represents. a. How many hours did it take for the temperature to decrease by 4.4 degrees Celsius?

Answers

Answer:

5.5 hours

Step-by-step explanation:

For every 1 hour, there is a 0.8 degrees Celsius drop in temperature.

Let "t" represent the total amount of temperature dropped.

Let "h" represent the number of hours

The given scenario can be represented with the equation below:

[tex] t = 0.8h [/tex]

To find the number of hours (h), it takes for the temperature to decrease by 4.4 degrees Celsius, plug in the value of t in the equation, and solve for h.

[tex] t = 0.8h [/tex]

[tex] 4.4 = 0.8h [/tex]

Divide both sides by 0.8

[tex] 5.5 = h [/tex]

It would take 5.5 hours for the temperature to decrease by 4.4 degrees Celsius.

Question Progress
Alan sees this offer.
Refurbished phone
45% OFF
Now only £88
How much was the phone before the discounted price?

Answers

Answer:

 x        45

___ = ____ (solve for x) = 39.6

88      100

88 + 39.6 = £127.60, was the original price.

The price before discount would be 127.6

3x^3 - 8y2 if x =2 and y =-3

Answers

I don’t kno I’m trynna find out

PLEASE HELP!!!!!!!!
also, show all work
Thank you:)

Answers

Problem 1

Answer:  104 cubic inches

----------------------

Explanation:

The prisms are similar so they have the same shape, but different sizes.

The linear scale factor from small to large is:

large/small = 10/4 = 2.5

Meaning that we multiply each dimension of the smaller prism by 2.5 to get the corresponding side length of the larger prism

4*2.5 = 10

This linear scale factor is then cubed to get the volume scale factor

(2.5)^3 = 15.625

Which tells us:

larger volume = 15.625*(smaller volume)

smaller volume = (larger volume)/15.625

smaller volume = (1625)/15.625

smaller volume = 104 cubic inches

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

Problem 2

Answer:  650 square inches

----------------------

Explanation:

We will go back to the linear scale factor of 2.5

This time, we square it to get (2.5)^2 = 6.25

This is the surface area scale factor.

larger surface area = 6.25*(smaller surface area)

larger surface area = 6.25*(104)

larger surface area = 650 square inches

What is the solution of the system shown in the graph?
Can anyone help out?? ​

Answers

Answer:

Where is the graph ?? It's missing.

Is it important to know the steps in solving your own problems? why or why not

Answers

Answer:

yes

Step-by-step explanation:

because when you include the steps, you can find out where you made a mistake (in case) and correct it easily.

What is 44.8 multipled by 44.8

Answers

Answer:

2007.04

Step-by-step explanation:

Cual es la ecuación de la recta que pasa por el punto (1, 2) y tiene una inclinación de 71.56505118

Answers

Answer:

La inclinación de una recta esta definida como el ángulo entre el eje x positivo y la recta.

Primero, podemos escribir genéricamente una recta como:

y = p*x + s

donde p es la pendiente de la recta, y s es la ordenada al origen.

Sabemos que para una recta que pasa por los puntos (a, b) y (c, d) podemos escribir la pendiente como:

p = (d - b)/(c - a)

Y también sabemos que si θ es el ángulo de inclinación, entonces:

p = tan(θ)

Entonces en este caso sabemos que:

p = tan(71.56505118°) = -0.828

Entonces esta recta es:

y = -0.828*x + s

y sabemos que pasa por el punto (1, 2), entonces podemos remplazar esos valores en la ecuación para encontrar el valor de s.

2 = -0.828*1 + s

s = 2 + 0.828 = 2.828

La ecuación es:

y = -0.828*x + 2.828

What is the difference between 7/10 and 14/15

Answers

Answer:

11

Step-by-step explanation:

What is an equation of the line that passes through the point (6,1) and is parallel to the line x+3y=15

Answers

Answer:

y=−1/3x+3

Step-by-step explanation:

(-7/10 + .15) divided by (-.125)

Answers

Answer:

4.4

Step-by-step explanation:

Hannah has a credit card with an APR of 11. 90% and a billing cycle of 30 days. The following table shows Hannah’s transactions in the month of April. Date Amount ($) Transaction 4/1 322. 95 Beginning balance 4/10 19. 87 Purchase 4/14 50. 00 Payment 4/19 71. 21 Purchase If Hannah’s credit card company calculates finance charges using the daily balance method, what will her April finance charge be? a. $2. 71 b. $3. 20 c. $3. 30 d. $3. 61.

Answers

The finance charge of April month of Hannah's credit card which is calculated by daily balance method is $3.30.

What is finance charge?

The finance charge is the amount of the money which borrowed, including the interest amount and other fees.

The following table shows Hannah’s transactions in the month of April.

       Date       Amount ($)   Transaction  

        4/1        322.95           Beginning balance

        4/10      19.87               Purchase    

        4/14      50.00              Payment  

        4/19      71. 21                Purchase

Average balance in the account,

[tex]A=(322.95\times10)+[(342.87)\times4]+(292.82\times5)+(364.03\times11)\\A=10069.41[/tex]

Hannah has a credit card with an APR of 11. 90% and a billing cycle of 30 days. The finance charges,

[tex]\rm FC=\dfrac{10069.41\times11.9}{365\times100}\\FC\approx3.30[/tex]

Hannah’s credit card company calculates finance charges using the daily balance method,

The finance charge of April month of Hannah's credit card which is calculated by daily balance method is $3.30.

Learn more about finance charges here;

https://brainly.com/question/4403314

Please help me this problem

Answers

Answer:

d) line l and m

Step-by-step explanation:

Line l and line m are parallel because <2 = <16 by the alternate exterior theorem.

Natalie is hiking up a mountain while simone is hiking down.

Answers

need more information

A regulation basketball has a diameter of about 9 in. What is the best approximation for the volume of this ball? 3050 in³ 382 in³ 215 in³ 84. 8 in³.

Answers

The best apporximation for the volume of this ball is 382 cubic inches.

What is the volume of the ball?

The volume of the ball is calculated by the formula V = 4 / 3πr³. This formula is the same in the whole world.

Given

A regulation basketball has a diameter of about 9 in.

The radius of the ball is;

[tex]\rm Radius = \dfrac{Diameter}{2}\\\\Radius=\dfrac{9}{2}\\\\Radius=4.5\ inches[/tex]

The volume of the ball is;

[tex]\rm Volume =\dfrac{4}{3}\pi r^3\\\\Volume=\dfrac{4}{3} \times 3.14 \times 4.5^3\\\\Volume =\dfrac{144.53}{3}\\\\Volume = 381.51\\\\Volume = 382 \ In^3 \ apporx[/tex]

Hence, the best apporximation for the volume of this ball is 382 cubic inches.

To know more about volume click the link given below.

https://brainly.com/question/10647788

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