To graph the polar equation and find the common interior of r = 6 - 4 sin(θ) and r = -6 + 4 sin(θ), we can use a graphing utility such as Desmos or Wolfram Alpha. These tools allow us to visualize polar equations and explore their graphs.
When we enter the given polar equations into a graphing utility, it will plot the curves corresponding to each equation on the same graph. We can then observe the region where the curves overlap, indicating the common interior of the two equations.
The polar equation r = 6 - 4 sin(θ) represents a cardioid, a heart-shaped curve centered at the pole (origin) with a radius that varies based on the angle θ. The term 6 represents the distance from the origin to the furthest point on the cardioid, while the term -4 sin(θ) determines the variation in radius as the angle changes.
Similarly, the polar equation r = -6 + 4 sin(θ) also represents a cardioid but with a radius that is the mirror image of the first equation. The negative sign in front of the term indicates that the cardioid is reflected across the x-axis.
Using a graphing utility, we can plot both equations and observe the graph to determine the common interior. The graphing utility will provide a visual representation of the region where the two cardioids intersect or overlap.
In the graph, we can see the heart-shaped curves corresponding to each equation. The cardioids intersect in two regions, forming a figure-eight shape. This figure-eight region represents the common interior of the two polar equations.
The common interior of the two cardioids is the region where the radius values from both equations are positive. In this case, the figure-eight region is entirely within the positive region of the coordinate plane, indicating that the common interior consists of points with positive radius values.
To summarize, by graphing the polar equations r = 6 - 4 sin(θ) and r = -6 + 4 sin(θ) using a graphing utility, we can observe their overlapping regions, which form a figure-eight shape. This figure-eight represents the common interior of the two equations and consists of points with positive radius values.
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The Sugar Sweet Company is going to transport its sugar to market. It will cost $6500 to rent trucks, and it will cost an additional $250 for each ton of sugar
transported
Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this
equation to find the total cost to transport 14 tons of sugar.
Answer:
$10000 Total cost to transport 14 tons
Step-by-step explanation:
The total cost C(S) = $6500 + ($250/ton)S. This is a linear function with initial value $6500 and slope $250/ton.
C(14) = $6500 + ($250/ton)(14) = $10000 = Total cost to transport 14 tons
Answer:
hello! the answer is below!
Step-by-step explanation:
Let's write the equation.
6500 + 250s = c
Now put in our value for s.
6500 + 250 · 19 = 4750
The answers are
6500 + 250s = c
And
4750
Hope this helps! :)
Order the values of the differences from least to greatest. First, write the fractions as decimals. StartFraction 4 Over 5 EndFraction is and Negative 1 and one-half is . Next, plot the numbers on the number line. The greatest number is . Using the students' names, the correct order is .
Complete Question:
Ms. Perez's biology class grew sunflowers to learn about plants. During the first week, the average sunflower grew 3 inches. The table shows the difference from the average for three students.
Order the values of the differences from least to greatest.
Student: Raj. Difference (in.): 4/5
Student: Clara. Difference (in.): -1 1/2
Student: Jacob. Difference (in.): 0.9
Answer:
[tex]-1.5[/tex], [tex]0.8[/tex] and [tex]0.9[/tex]
The greatest is: 0.9
By student names: Clara, Raj and Jacob
Step-by-step explanation:
See comment for complete question
Given
Differences:
[tex]\frac{4}{5}[/tex], [tex]-1\frac{1}{2}[/tex], [tex]0.9[/tex]
Required
Order from least to greatest
We have: [tex]\frac{4}{5}[/tex], [tex]-1\frac{1}{2}[/tex], [tex]0.9[/tex]
First convert fractions to decimal
[tex]\frac{4}{5} = 0.8[/tex]
[tex]-1\frac{1}{2}= -1.5[/tex]
[tex]-\frac{3}{4} = -0.75[/tex]
So, the differences become:
[tex]0.8[/tex], [tex]-1.5[/tex], [tex]0.9[/tex]
Now arrange from least to greatest
[tex]-1.5[/tex], [tex]0.8[/tex] and [tex]0.9[/tex]
From the above representation,
The greatest is: 0.9
By student names, we have:
Clara, Raj and Jacob
This is done by simply replacing the numbers with the student name.
See attachment for number line
Answer:
4/5 is 0.8 , -1 1/2 is -1.5 , The greatest number is 1.3 , mia, raj, clara, jacob
Step-by-step explanation:
Other equipment totaled 33000. You earn a commission of 20% on every sale you make. If you put 35% of your earnings on this particular sale into a savings account what is the amount invested
9514 1404 393
Answer:
2310
Step-by-step explanation:
Assuming "this particular sale" totals 33000 in its entirety, the commission is ...
20% × 33000 = 6600
The amount of that going to the savings account is ...
35% × 6600 = 2310
The amount invested is 2310.
What is the area of this?
Answer:
Step-by-step explanation:
[tex]A=\frac{hb}{2}\\ \\ A=\frac{14(20)}{2}\\ \\ A=140ft^2[/tex]
Answer:
150 ft
Step-by-step explanation:
You use Pythagoras theorem to work out the base of the triangle.
<3
Simplify.
[tex]\frac{8\sqrt{6mn} + 6\sqrt{8mn} }{2\sqrt{2mn} }[/tex]
Help please! Thank youuuuuuuuu
Answer:
3 3/5 meters (B)
Step-by-step explanation:
Since this is perimeter, you must find the "outside".
The top side: 1/4 * 4 = 1
Left side: 1/5 * 4 = 4/5
Bottom: 1
Right side: 4/5
Add them up!
1 + 1 + 4/5 + 4/5
2 8/5
3 3/5
B!
✓3 correct to 5 decimal places
Answer:
1,73205
Step-by-step explanation:
First, count out the five decimal places, and then look at the sixth place:
[tex]\sqrt{3}[/tex] ≈ 1,73205 | 0807...
The sixth decimal is less than 5, so we round to the smaller side.
40 percent of what is 524
Answer:
1310
Step-by-step explanation:
Answer:
7.63
(Hope this helps! Btw, I am the first to answer.)
How far is the star away from
the earth in AU?
Answer:
6623 AU
Step-by-step explanation:
I assume the angle measure 0.000302 is in radians.
Draw a segment from the Sun to the Star.
Use the upper small triangle.
The angle at the Star measures 0.000151 radians.
The opposite leg measures 1 AU.
We need the hypotenuse which is the distance from the Star to Earth.
sin A = opp/hyp
sin 0.000151 rad = 1/x
x sin 0.000151 rad = 1
x = 1/(sin 0.000151 rad)
x = 6623
Answer: 6623 AU
The coordinates of one endpoint of a line segment are (4,-12). The length of the segment is 5 units. Determine four coordinates that could serve as the other endpoint of the given line segment.
Answer:
Step-by-step explanation:
Since we are given the starting position of the line segment and the length we can simply add or subtract the total length of the line segment to the x or y starting position. This would give us all the possible endpoints that are exactly 5 units away from the starting position in every direction. We can either add or subtract because this would give us the left, right, up, and down directions from the starting position. After making these changes we are left with the following four possible endpoints.
(-1 , -12)
(9 , -12)
(4, -17)
(4, -7)
Write an equation in slope intercept form. m=6, b=-8
Answer:
y=6x-8
Step-by-step explanation:
y=mx+b where m=slope and b=y-intercept.
Which of the following best describes the equation below?
y = -5x + 12
A.
nonlinear
B.
linear
C.
both linear and nonlinear
o
D.
neither linear nor nonlinear
Answer:
B. linear equation
Step-by-step explanation:
How can you tell that whether the equation is linear or nonlinear?
Using an Equation
Simplify the equation as closely as possible to the form of y = mx + b. Check to see if your equation has exponents. If it has exponents, it is nonlinear. If your equation has no exponents, it is linear.
y = -5x + 12 has no exponents that's why it is a linear equation.
Hope this helps:)
OMG, GUYSS please helppp this is due in like.. 10 mins.. will give brainliest, please also add an explanation... THANKYOU I LOVE YOU!!!!
House builders unload a large crate of bricks onto the bed of a truck. The bottom of the crate measures 1.0 m by 2.0 m, and the crate weighs 38 000 N. What pressure does the crate exert on the bed of the truck?
Answer:
19,000 pa.
Step-by-step explanation:
I hope this helps
HELP PELASE ASAPppppp
Answer:D
Step-by-step explanation:
(3a+2.5b)^2=9a^2+6.25b^2+*
Please help before Thursday
Step-by-step explanation:
We have (x + y)² = (x + y)(x + y) = x² + 2xy + y².
Let x be 3a and y be 2.5b.
Therefore (3a + 2.5b)²
= (3a)² + 2(3a)(2.5b) + (2.5b)²
= 9a² + 15ab + 6.25b².
Hence the '*' sign should be replaced with 15ab.
Answer:
Given that, ( 3a + 2.5b )² = 9a² + 6.25b² + *
We know that, ( x + y )² = x² + y² + 2xy
According to the above problem, we get
( 3a + 2.5b )² = (3a)² + (2.5b)² + (2×3a×2.5b)
( 3a + 2.5b )² = 9a² + 6.25b² + 15ab
Therefore,
The sign " * " should be 15ab.
15ab is the right answer.solve for x or find x
the answer is x= 4
AB and CD are the same length
8x-1 =31
8x=32
x=4
[
1
What is the distance between the points (-4, -8) and (10,-8)?
Need help
Answer:
2
Step-by-step explanation:
√(-8-8)^2 +(10+4)^2=
✓-32+28
✓4
=2
find the measure of the angle
PLEASE HELP!!!
I-ready!
Answer:
35,.......,..............
Having trouble solving this:
Answer:
1/250
Step-by-step explanation:
0.4% in fraction form is 0.004
or 4/1000
4/1000 reduced to it's simplest form is 1/250 (divide numerator and denominator by 4)
For a school fundraiser, Troy sold 28 bags of popcorn and 40 candy bars and made $282. Jake sold 17 bags of popcorn and 20 candy bars and made $160.50.
What was the cost of a bag popcorn?
A. $10.35
B. $6.00
C. $6.27
D. $6.50
Answer:
Cost of a bag popcorn = $6.5
Step-by-step explanation:
Given:
Number of popcorn bags sold by Troy = 28
Number of candy bar sold by Troy = 40
Number of popcorn bags sold by Jake = 17
Number of candy bar sold by Jake = 20
Amount Troy earn = $282
Amount Jake earn = $160.5
Find:
Cost of a bag popcorn
Computation:
Assume;
Cost of a bag popcorn = a
Cost of a candy bar = b
28a + 40b = 282..........eq1
17a + 20b = 160.5...............eq2
eq2 x 2
34a + 40b = 321.........eq3
eq3 - eq1
6a = 39
a = 6.5
Cost of a bag popcorn = $6.5
Please help due today in 10 minutes
Answer:
I can't help it's past due date. sorry
Step-by-step explanation:
I need the answer, ASAP.
Answer:
See below.
Step-by-step explanation:
It is similar because the order of operations is the same for fractions and for whole numbers.
It is different because when you add or subtract fractions, you need a common denominator. When you deal with whole numbers, there are no denominators.
Determine a quadratic equation in standard form that has each pair of roots.
X=5±√2/3
Step-by-step explanation:
you have to add 5 and 2 which is 7 and decide by 3 or estimate
Paul will pay for his new car in 36 monthly payments. If his car loan is for $20,538 then how much will Paul pay each month?
Answer:
570.50
Step-by-step explanation:
I think it's the correct answer maybe it is maybe it's not
Paul has acquired a car loan of amount $20,538 and is paying off the loan amount in 36 months.
This means that Paul will be paying $570.50 every month till the completion of 36 months.
The given parameters for the calculation of the monthly installment:
Loan amount= $20,538 Total months to repay the loan= 36 monthsCalculation of the monthly amount of Paul's loan:
[tex]\begin{aligned}\text{Monthly installment of loan}= \frac{\text{Total Amount of Loan Acquires}}{ \text{Total Time taken to Repay off the Loan}} \end{aligned}.[/tex]
[tex]\begin{aligned}\text{Monthly Installment of Loan}= \frac{\$20,538}{36}\end{aligned}[/tex]
[tex]\begin{aligned}\text{Monthly Installment of Loan}=\$570.50\end{aligned}[/tex]
Therefore, the monthly installment of paul will be $57.50.
To know more about the calculation of installment, refer to the link below:
https://brainly.com/question/84351
The ratio of dimes to quarters in a money bag is 12.2. If there are 8 quarters. How many dimes are there?
Answer:
98
Step-by-step explanation:
Given: The ratio of dimes to quarters in a money bag is 12.2
Also, there are 8 quarters.
To find: Number of dimes
Solution:
Number of dimes : Number of quarters = 12.2
Number of dimes : 8 = 12.2
Therefore,
Number of dimes = 12.2 × 8 = 97.6 ≈ 98
The perimeter of the triangular park shown on the right is 15x-2 what is the missing length
Answer:
missing length is 6x - 1
Step-by-step explanation:
To find missing length, add two known sides and subtract from perimeter
(15x - 2) - (4x + 4 + 5x - 5)
(15x - 2) - (9x - 1) = 6x - 1
What is 2/3 divided by 6/12? REDUCE ANSWER TO SIMPLEST FORM.
Answer:
1 1/3Step-by-step explanation:
To divide fractions, multiply by the reciprocal.
So we have:
2/3 x 12/6 = 24/18 = 4/3 = 1 1/3
What is the value of x?
Answer:
jhg hstu35kk4t6ek
3tnk63e6oktelrt
Step-by-step explanation:
4n5kdti3eo5
help find value of y please
Answer:
The third option
Step-by-step explanation:
60+y=180
y=120
Answer:
y = 120
Step-by-step explanation:
Which expression is equivalent to 5x² + 4x - 2?
a- (5x-1)(x+2)
b- (5x+1)(x-2)
c- (5x+1)(x+2)
d- none of these
Answer:
D because non of them work lol
Step-by-step explanation:
Hope this Helped