Consider the limaçon with equation r = 3 + 4cos(θ). How does the quotient of a and b relate to the existence of an inner loop?

Consider The Limaon With Equation R = 3 + 4cos(). How Does The Quotient Of A And B Relate To The Existence

Answers

Answer 1

A polar graph that is a limacon has a formula similar to [tex]r=a+bcos\theta[/tex]

Option B is correct.

A  limacon has a formula similar to [tex]r=a+bcos\theta[/tex]

Case 1 .  If  a < b  or  [tex]\frac{b}{a}>1[/tex]

Then the curve is limacon with an inner loop.

Case 2.  If  a>b   or   [tex]\frac{b}{a}<1[/tex]

Then the limacon does not have an inner loop.

Here, given that,  [tex]r=3+4cos\theta[/tex]

It is observed that,  a < b  or [tex]\frac{b}{a}>1[/tex]

Therefore, the curve is limacon with an inner loop.

Hence, option B is correct.

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Related Questions

How many proportional relationships are shown

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Answer:

2 I think thats the answer

Step-by-step explanation:

help please ASAP!!!!!
you can zoom in to see better

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Answer:

true, false, and false

Step-by-step explanation:

I need help solving these!!!!​

Answers

Answer:

4. y = -1/2x + 5

5. y = -1/3x + 3

6. y = 1

Step-by-step explanation:

For #4:

Because these lines are parallel, we know that they will have the same slope.

To get b, or the y-intercept, I just started at the point (4,4) and used the slope to work backwards to the y-axis. This is really not the best way to do it (especially with big numbers) but it works in a pinch. Also, I forgot the better way :/

For #5:

These lines are perpendicular. That means that the slopes are reciprocals of the other and, when multiplied with each other, the answer will be -1.

The reciprocal of 3 is -1/3.

To get the y-intercept, I did the same as above.

For #6:

x = 2 is a vertical line. To make a line perpendicular to it, that is, to make a line that intersects with it at 90°, the answer line will have to be horizontal.

That means that our answer is y = ?

We know that the line passes through a very specific point (2,1), and the line provided in the question already gives us the x value of this point. All we have to do is set y equal to the y value.

So, y = 1.

I hope this helps!

5z + 3n -z2 ; n = 4.5 , z = 6 PLZ answer this

Answers

Answer:

5(6)+3(4.5)- 6(2)= 31.5

Step-by-step explanation:

Answer:

hmmmmm

Step-by-step explanation:

-413.4=-15.9n please help

Answers

Answer:

[tex]\boxed {n = 26}[/tex]

Step-by-step explanation:

Solve for [tex]n[/tex]:

[tex]-413.4 = -15.9n[/tex]

-Switch sides:

[tex]-15.9n = -413.4[/tex]

-Divide both sides by [tex]15.9[/tex] and expand by multiplying both numerator and denominator by [tex]10[/tex]:

[tex]\frac{-15.9n}{-15.9} = \frac{-413.4}{-15.9}[/tex]

[tex]n = \frac{-4134}{-159}[/tex]

-Divide [tex]-4134[/tex] and [tex]-159[/tex]:

[tex]n = \frac{-4134}{-159}[/tex]

[tex]\boxed {n = 26}[/tex]

Therefore, the value of [tex]n[/tex] is [tex]26[/tex].

-4(3/2x - 1/2) = -15

Answers

Answer:

2.8333333333333333333

Step-by-step explanation:

I have high iq

-4(3/2x - 1/2) = -15

Distribute -4

-6x + 2 = -15

Subtract 2 from both sides

-6x = -17

Divide 6 from both sides

x = 2.83333333333333333

What percent is:
45 of 36

Answers

Answer:

45 is 125% of 36, and 36 is 80% of 45.

Step-by-step explanation:

what is equivalent to x+x ?
a)xx
b)2x
c)x^2
d)2^x

Answers

I’m pretty sure the answer is 2x

Answer:

b

Step-by-step explanation:

I think it is B because x+x is two x's so it would be 2x. I hope this helped have a good day

What is the equation of this graphed line? Enter your answer in slope-intercept form in the box. please i really need help

Answers

Answer:

y = -9/8x+7

Step-by-step explanation:

First Find The Slope: 7--2/0-8=-9/8

Find Y Intercept=7

Than Write Equation: y=-9/8x+7

I WILL REWARD BRAINLIEST OKAY IM BEGGING YOU HELP ME

IN THAT PHOTO WHAT ARE THE X AND Y INTERCEPTS!?! WAIT DON'T LOOK AT THE PHOTO YET!!

PLEASE LOOK AT THIS EXAMPLE:

X intercept: ( ), ( )
Y intercept: ( ), ( )

NOW LOOK. AT THE PHOTO PLEASE!!​

Answers

Answer:

X-intercept: -10

Y-intercept: -45

(-10),(-45)

Step-by-step explanation:

Hop this helped, Have a Wonderful Day!!

In a particular​ game, the probability of winning $95 is 1/36 and the probability of losing $7 is 35/36. What is the expected value after playing this​ game? Round to the nearest cent.

Answers

Answer:

1.53

Step-by-step explanation:

1

36

(

85

)

+

(

35

36

)

(

4

)

=

E

V

 

85

36

140

36

=

E

V

55

36

=

E

V

E

V

$

1.53

The table shows the mean number of basketball goals made by four random samples of players from the school team during this year’s season. Sample # Sample Mean Number of Goals 1 7 2 4 3 5 4 8 Is a valid prediction for the mean of the population possible using these samples? No, there are not enough samples. Yes, the sample means are all less than 10. Yes, the variation of the sample means is small. No, the variation of the sample means is too great.

Answers

Answer:

Answer is C

Step-by-step explanation:

There is not enough samples.

Answer:

 Yes, the variation of the sample means is small.

Step-by-step explanation:

18. Which product is greater. (-4)-(-6) or
(-7).(-8)? Explain.

Answers

Answer:

So when u do (-4)-(-6) it equals 2.

But when u do (-7)*(-8) it equals 56

Therefore saying that (-7)*(-8)=56 is the greatest product.

Step-by-step explanation:

Will mark as brainless if you answer correctly

Answers

Answer:

ans=10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

10(4-7) /   -(4 - 1)

10(-3)  /    -(3)

-30    /    -3 =

10

If AABC and AXYZ are similar, which must be true?

Answers

Answer:

(D).

Step-by-step explanation:

ΔABC ~ ΔXYZ

(D).  [tex]\frac{AC}{XZ}[/tex] = [tex]\frac{BA}{YX}[/tex]

Read the following statement: Line segment MN is congruent to line segment OP.

Which of the following is an equivalent statement?


a
MN overbar is similar to OP overbar

b
MN overbar equals OP overbar

c
MN overbar is congruent to OP overbar

d
MN overbar is an element of OP overbar

Answers

Answer:c

Step-by-step explanation:

A local hamburger shop sold a combined total of 721 hamburgers and cheeseburgers on Thursday. There were 71 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?

Answers

Answer:771-71/2= 350 hamburgers and 350 +71 cheeseburgers

Step-by-step explanation:

plsss help 6th grade math

Answers

Answer:  D

Step-by-step explanation:

If you put -5 and +5 on a number line and count their distance from zero they are both the same distance.

7. Which of the following illustrates the commutative property of multiplication?
(1) 5(2x) =(5-2)x
(2) 4(2x+5) = 4 - 2x+4-5
(3) x2 +5=5+x2
(4) 2x -3x = 2-3-X-X
show work pleasee

Answers

x^2 + 5 = 5 + x^2 will give you the same answer. Also know as the commutative property. Answer is (3)

45×(−10)×45 STEP explanation ​

Answers

Answer:

-20,250

Step-by-step explanation:

PEMDAS

Multiply left to right

45 * -10 * 45

45* -10

-450 * 45 =

-20,250

Which is equivalent to 5+2(3x-4)=12x-11?
C. 9x=17
B. 6x=8
D. 9x=-39​

Answers

5+2(3x-4)=12x-11 is 5+6x -8 = 12x -11, 5-8+11= 12x-6x, “8= 6x” so option B is correct
The answer is letter b

best estimate for 563 / 15

Answers

Answer: 37 8/15 or 37.53

Step-by-step explanation:

use math_way its amazing for math problems, if i could give a rating it would definitely get 5 stars.

its a website and a app i believe it can be used for ios and android

aka apple and everything else

btw i had to add that (_) <that in the name because it wont let me say it normally


The sum of two numbers is 38. The smaller number is 22 less than the larger number. What are the numbers?

Answers

Answer:

30 and 8

Step-by-step explanation:

30 - 8 = 22

Ella swims four times a week at her clubs pool. She swims the same number of labs on Monday, Wednesday, and Friday, and 15 laps on Saturday. She swims a total of 51 labs each week. How many laughs does she swim on Monday?

Answers

52 laps is the correct answer. Explaining. Don’t have to I just took the test and got a 100

Remember that whole numbers that are next to each other, for example, 2 and 3, or 43, 44, and 45 are called consecutive numbers.

If n is the smallest of three consecutive integers, write an expression for the largest number.

Answers

Answer:

n +2

Step-by-step explanation:

If three numbers are consecutive, the 2nd number would be one more than the 1st number, and the 3rd number would be one more than the 2nd number.

Since the smallest number is n,

2nd consecutive number= n +1

3rd consecutive number

= n +1 +1

= n +2

Thus, the expression for the largest number is n +2.

Let's check!

If the smallest of the three consecutive number is 1, the 3rd consecutive number would be 3.

3rd consecutive number

= n +2

= 1 +2

= 3 (✓)

Thus, the expression is correct.

Select the correct answer.
Identify the end behavior and the zeros of function h.
h(x) = –13 – 9x2 + 41 +96
Based on these key features, which statement is true about the graph representing function h?
A. The graph is negative on the intervals (-00, -8) and (-4, 3).
B. The graph is positive on the intervals (-8, –4) and (3, 0).
C. The graph is positive on the intervals (-0, —8)and (-4, 3).
D. The graph is negative on the intervals (-3, 4) and (8,00).

Answers

Answer: C. The graph is positive on the intervals (-∞,-8) and (-4,3)

Step-by-step explanation: I guessed on my test and got it right. PLATO

David has available 40 yards of fencing and wishes to enclose a rectangular area.

Answers

Answer:

5 units will be your width and 15 will be your length so it would look like side#1=5 side #2=15 side number3 is 5 and side number 4 is 15 assuming that side 1 and 3 are parallel.

Step-by-step explanation:

yes

Solve for a when x is 12
X=
(1 + a)
(1 – a)

Answers

Answer:

so i checked on many apps cause im kinda stupid and didnt know and they all said a=11/13 but you could wait for sum1 else to answer

Step-by-step explanation:

10 Lakh More Than 93,23,654​

Answers

Answer:

10,323,654

Step-by-step explanation:

PQ is equal to RQ so b=?

Answers

Answer: 17

Step-by-step explanation:

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