#7 & 8 please
09. Problem 7 Find the area of the region that lies inside the curve R 3 cos & and outside the curve R = 1 +cos. Problem 8 Find the limit of the sequence a, n sin (1/n). if it exists.
Answers
the area of the region that lies inside the curve r = 3 cosθ and outside the curve r = 1 + cosθ is 3π.
Problem 7: To find the area of the region that lies inside the curve r = 3 cosθ and outside the curve r = 1 + cosθ, we need to find the points of intersection between the two curves.
r = 3 cosθ => r^2 = 3r cosθ => x^2 + y^2 = 3x
r = 1 + cosθ => r - cosθ = 1 => √(x^2 + y^2) - x = 1
Squaring both equations and simplifying, we get:
x^2 + y^2 = 3x (1)
x^2 + y^2 - 2x = 1 (2)
Subtracting equation (2) from equation (1), we get:
x = 2
Substituting x = 2 into equation (1), we get:
y^2 = 2y => y = 0, 2
So the two curves intersect at the points (2, 0) and (2, 2).
To find the area of the region between the two curves, we can integrate the difference between the two curves with respect to θ from 0 to 2π:
Area = ∫[0,2π] (1/2)(3cosθ)^2 dθ - ∫[0,2π] (1/2)(1+cosθ)^2 dθ
= (9/2)π - (3/2)π
= 3π
Therefore, the area of the region that lies inside the curve r = 3 cosθ and outside the curve r = 1 + cosθ is 3π.
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Related Questions
What is the value of x? Round to the nearest tenth
Need help fast!!
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according to a survey of 1,166 adult college students, the mean number of alcoholic beverages consumed per week is 11, with a standard deviation of 5 beverages. what test statistic is calcuated for this scenario?
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The scenario for test statistic is estimated z-score to make inferences about the population mean which is unknown.
x is the sample mean = 11
μ is the population mean = unknown
σ is the population standard deviation = 5
And n is the sample size= 1,166
Assuming a normal distribution for the number of alcoholic beverages consumed per week,
Use a z-test to calculate the test statistic.
The formula for the z-score is,
z = (x - μ) / (σ / √(n))
Since the population mean is unknown,
Not possible to calculate the exact z-score,
Calculate an estimated z-score using the sample mean,
z = (x - μ) / (σ / sqrt(n))
z = (11 - μ) / (5 / sqrt(1166))
z ≈ (11 - μ) / 0.146
Therefore, need to know the population mean μ for the z-score in the calculated test statistic.
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Does anybody know the answer to this ?
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Answer:
A
Step-by-step explanation:
Olivia is going to an amusement park. The price of admission into the park is $40, and once she is inside the park, she will have to pay $4 for every ride she rides on. How much money would Olivia have to pay in total if she goes on 13 rides? How much would she have to pay if she goes on r rides?
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***Olivia would pay 92$ in total if she goes on 13 rides
If she goes on r rides she would have to pay t=40+4r***
what is 100,572×135,689
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Answer:
13,646,514,108
I hope this helps!
50 points !!!!!!!! please hep !!!!
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Solve for θ :
r = 1/32 v₀² sin(2θ)
32r / v₀² = sin(2θ)
arcsin(32r / v₀²) = 2θ
⇒ θ = 1/2 arcsin(32r / v₀²)
Note that in projectile motion, we're only concerned with launch angles in the range 0 ≤ θ ≤ π/2, so there are no issues with taking inverse sines.
How should I do this?
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Step-by-step explanation:
\( \sf \: \dfrac{m}{4} (6m - 8) + \dfrac{m}{2} (10m - 2)\)
\( \tiny {\sf \dfrac{m}{4} \times 6m - \dfrac{m}{4 } \times 8 + \dfrac{m}{2} \times 10m - \dfrac{m}{2} \times 2}\)
\( \sf \: \dfrac{3 {m}^{2} }{2} - 2m + 5 {m}^{2} - m\)
\( \sf \: \dfrac{3 {m}^{2} + 10 {m}^{2} }{2} - 2m - m\)
\( \sf \: \dfrac{13 {m}^{2} }{2} - 3m\)
This is the required answer
if 2/5 of a man's money is 4500. what is the total money
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Answer:
Total money= 11250
In attachment
Pls help me its due in 20 minutes
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Answer:
1. B
2. G
3. A
4. G
Step-by-step explanation:
Hope this helps. Not 100% sure about the final one but if nobody answers by the time its due go ahead and use what you got.
Pleaseeeeee helpppppp!
I will mark brainliest, but pls only if you know the answer
Its Geometry A
Answers
Answer:
see explanation
Step-by-step explanation:
A base angle
B leg
C vertex angle
D leg
E base angle
F base
in any isosceles triangle there are 2 congruent legs and 2 congruent base angles.
the base angles are opposite the congruent legs
the remaining side, the base is the 3rd side of the triangle
the vertex angle is formed by the 2 congruent legs
2 apples cost 2 dabloons.
How much does 1 apple cost
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Find the constants m and b in the linear function f(x)=mx+b so that f(7)=9 and the straight line represented by f has slope −3.
m=
b=
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To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.
The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.
The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.
Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.
Solving for b, we find b = 30.
Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.
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help!! will give brainl.ly <3
Answers
Answer:
7.5
Step-by-step explanation:
Since the triangles are congruent, corresponding sides will have the same lengths. So since line AC is 7.5, line HT must also be 7.5
13 points answer this asappppp
Find the value of the function below for the given x-value
F{x} = -5x-1 when x=-3
A.15
B 14
C-16
D-14
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please help (probability question)!
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Answer:
There are 64 possible outcomes.
Step-by-step explanation:
Each flip has 2 options, heads or tails.
head tail
One flip has 2 outcomes. When you flip again, you can get this set of 4 outcomes:
head-head tail-head
head-tail tail-tail
Then when you flip a third coin, each of those cases has 2 cases itself. As you can see, each flip that is added, the total number of outcomes doubles. For 6 flips, you do 2x2x2x2x2x2 or \(2^{6}\).
How many solutions does this equation have?
a + 3 + 2a = -1+ 3a + 4
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Answer:
Infinite
Step-by-step explanation:
Hope that this helps!
Answer:
Step-by-step explanation:
2 or 3 im not v sure tho
which colonial power colonized Ghana?
Answers
Answer:
The british
Step-by-step explanation:
Answer:
The Britsh
Step-by-step explanation:
Formal colonialism first came to the region we today call Ghana in 1874, and British rule spread through the region into the early twentieth century. The British called the territory the “Gold Coast Colony."
Please quick I need help! Worth 100 POINTS
a) Describe how the line of best fit and the correlation coefficient can be used to determine the correlation between the two variables on your graph.
b) Describe the type of correlation between the two variables on your graph. How do you know?
c) Does the correlation between the variables imply causation? Explain.
d) How do you calculate the residuals for a scatterplot?
e) Calculate the residuals for your scatterplot in step 2d.
f) Create a residual plot for your data.
g) Does your residual plot show that the linear model from the regression calculator is a good model? Explain your reasoning.
Answers
Answer:
Step-by-step explanation:
Given the data showing the relationship between GPA and hours of study :
From the regression model given :
Regression equation is:
y = 0.141x + 1.096
Also, the regression Coefficient, R = 0.957
Step-by-step explanation:
a) Describe how the line of best fit and the correlation coefficient can be used to determine the correlation between the two variables on your graph.
From the regression equation, we can infer if the relationship or correlation between the two variables is positive or negative from the value of the slope, a positive slope Value means a positive relationship while a negative slope value means a negative relationship.
The Correlation Coefficient, R also gives the strength of relationship, with values close to - 1 or 1 depicting a strong relationship while positive and negative R values also depictava positive or negative relationship.
Here there is a strong positive relationship between GPA and Hours.
Correlation does not imply causation. Correlation only shows the type of relationship between variables and it does not mean that high GPA values are causes by long hours of study and vice versa
b)
A) The line of best fit gives a general outlook on the data while the correlation is the exact points showcased to calculate or show for a data set or table.
B) Between the two variables it is a positive correlation because they both increase in the same direction. Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction.
C) Not really considering the fact they are both headed in the same direction. It would if say one was increasing and the other was going in the opposite direction.
D) So, to find the residual I would subtract the predicted value from the measured value
E)
Ex: (Your first row)
9.2 - 2.23 = 6.97
c)
No, we can never tell that correlation is equal to causation. It is a common misconception when looking at data tables.
For instance, if we have a table that shows a correlation of scores on two tests in a row. We may see that there is a correlation between the two numbers. Students who did well on the first test may have done well on the second as well, and those who have not done well on the first may have done poorly on the second.
However, doing bad on the first test does not cause someone to do bad on the second one. Likely the cause is their studying habits, intelligence or aptitude in the area.
So in this example, there is correlation between the sets of data, but it does not prove causation.
d)
A residual is the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). It is the vertical distance from the actual plotted point to the point on the regression line.
e)
Answer:
the residual is 0
Step-by-step explanation:
The residual is zero because you don't have a trend line. Once you have a trend line the residual is the distance between the y-values(data or dots) and the trend line
f)
The estimated GPA of a student who studies for 15 hours a week is 3.21.
Given:
The table with the GPA of students along with the studying hours of students.
To find:
The residual plot for the given data.
GPA of a student who studies for 15 hours a week.
Solution:
The residual plot of the given data is an image attached.
The equation from the plot:
Where:
x = Hours of studies
y = GPA of student
If the student studies for 15 hours his or her GPA can be estimated as:
The estimated GPA of a student who studies for 15 hours a week is 3.21.
just look at the picture i’m confused, whoever gets it right gets a thanks and brainliest whatever that is lol
Answers
Answer:
The three points lie on a straight line
A line through the points passes through the origin
The graph shows a proportional relationship
Step-by-step explanation:
Given statements:
a) The three points do not lie on a straight line.
b) The three points lie on a straight line.
c) A line through the points passes through the origin.
d) A line through the points does not pass through the origin.
e) The graph shows a proportional relationship.
f) The graph does not show a proportional relationship.
For the first and second statements, we can see that the points are able to be connected with a straight, diagonal line (see attached graph). This makes statement a false, and statement b true.
a = false
b = true
For the third and fourth statements, we can see that on the attached (revised) graph on my answer, that the line can continue and pass through the origin, or (0,0). This means that statement c is true, and statement d is false.
c = true
d = false
For the fifth and sixth statements, we know that a relationship is proportional if it is a straight line and passes through the origin when graphed. We have already concluded above that both of these are true, so this means that the graph does represent a proportional relationship. This means that statement e is true, and statement f is false.
e = true
f = false
From the above work, we can conclude that the following statements are true:
b (The three points lie on a straight line)
c (A line through the points passes through the origin)
e (The graph shows a proportional relationship)
Hope this helps :)
Fiona wants to earn at least $100 this week. She makes $11 an hour babysitting. Choose the inequality that shows the number of hours Fiona needs to babysit in order to reach her goal.
h≥11
h>9
h>8
h≥9
Answers
The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.
What is inequality?
The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
Given that,
Fiona wants to earn at least \(\$\)100
She makes \(\$\)11/hour
in order to reach her goal = 100/11 = \(\$\)9.09 .
The inequality that shows the number of hours Fiona needs to babysit in order to reach her goal is h>9.
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A company expects that the number N(x) of a product sold during a week is related to the amount spent on advertising by the function N(x)=-6x3+180x²+2250x + 13,000, where x (with 0 ≤x≤25) is the amount spent on advertising in thousands of dollars. What is the point of diminishing returns?
The point of diminishing returns is
(Simplify your answer. Type an ordered pair. Do not use commas in the individual coordinates.)
Answers
The point of diminishing returns is (20.98, 21247.3).
The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.
Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.
The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:
0 = -18x² + 360x + 2250
Dividing by -18 simplifies the equation:
0 = x² - 20x - 125
Using the quadratic formula, we find the solutions to the equation:
x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)
x₁,₂ = 10 ± 5√5
Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.
To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:
N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8
N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8
From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.
To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).
Hence, the point of diminishing returns is approximately (20.98, 21247.3).
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What is -12x + 10 = - 14
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Step-by-step explanation:
- 12x + 10 = - 14
- 12x = - 14 - 10
- 12x = - 24
x = - 24 / - 12
x = 2
Hope it will help :)
Sausages come in packets of 12. Bread rolls come in packets of 9. Brian wants to buy enough packs of sausages and rolls so that there are an equal number of sausages and rolls. What is the minimum number of sausages and rolls he needs to buy?
lcm??????????
Answers
Answer:
LCM is 36
Step-by-step explanation:
9 x 4 = 36
12 x 3 = 36
PLEASE HURRY!
Choose all the points that are located on quadrant lV.
Choices:
(-3,-1/4). (6,-9). (-5,3). (2,-4). (-11,5). (7,1/4)
Sorry about the picture it’s not very clear:/
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Please answer............
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Answer:
A.)
1.) b = h(2)
2.) p = b - 3
B.) 10
C.) 5
Step-by-step explanation:
A.)
1.) The birch tree is twice the size of the orange tree so, birch = orange * 2
2.) The peach tree is 3m shorter than the birch so, peach = birch - 3meters
B.) b = 5(2)
C.) 8 = 4(2)
p = 8 - 3
Evan, Claire, Jaya and Tim are running a 3km relay race.
Evan ran 9/10 of a km
Claire ran 7/9 of a km
Jaya ran 2/3 of a km
What fraction of a km does Tim need to run to finish the race?
Try to answer ASAP please, thank you.
Answers
Answer:
Tim needs to finish 59/90
Step-by-step explanation:
Add together what Evan Claire and Jaya ran
9/10 + 7/9+ 2/3
The common denominator is 90
9/10 (9/9) +7/9 *10/10 + 2/3 *30/30
81/90 + 70/90 + 60/90
211/90
We need 3 km = 3 *90/90 = 270 /90
270/90 - 211/90 = 59/90
3
To solve 2x + 9 = 21, what is the first step?
А. Dividing each side by 2
B
Dividing each side by x
С
Subtracting 21 from each side
D
Subtracting 9 from each side
Answers
Answer: D. Subtracting 9 from each side
Step-by-step explanation:
Always start with numbers without variables first before doing anything with x. And make sure one side must not equal 0 unless you're doing polynomials.
Find the measure of angle 1
hurry
Answers
Answer:
112 degrees
Step-by-step explanation:
This is a quadrilateral, meaning 4 sides. The sum of the angles of a quadrilateral is 360 degrees. You are given the right angle, or 90 degrees, and the 46 degree angle at the bottom. Since the two lines on either side of the 46 degree angle represent parallelism, angles 1 and 2 are the same.
360 - (90+46) = 224.
224 / 2 = 112.
Answer:
\(m∠1 = 112\)
Step-by-step explanation:
\(m∠1 = m∠2\)
\(m∠1 + m∠2 + 90 + 46 = 360\)
\(m∠1 +m ∠2 + 136 = 360\)
\(m∠1 + m∠2 = 360 - 136\)
\(m∠1 + m∠2 = 224\)
\(m∠1 = \frac{224}{2} \)
\(m∠1 = 112\)
\(m∠2 = \frac{224}{2} \)
\(m∠2 =112\)
Pls show your work thank you will mark the Brainliest
Answers
Answer:
Step-by-step explanation:
Length of rectangle = \((5x + 4)\)
Width of rectangle = \((4x - 4)\)
∴Area of rectangle = Length × Width
= \((5x + 4)\) × \((4x - 4)\)
Expand the parenthesis using the Distributive Law:
\(5x(4x - 4) + 4(4x - 4)\)
\(= 20x^{2} - 20x + 16x - 16\)
Bring all the like terms together and simplify them in their lowest forms:
\(= 20x^{2} - 4x - 16\)
Use an algebraic approach to solve the problem.
Abby has 37 coins, consisting only of dimes and quarters, worth $5.65. How many dimes and how many quarters does she have?
Answers
Answer:
13 quarters and 24 dimes
Step-by-step explanation:
13*.25=3.25
24*.1=2.4
3.25+2.4=5.65