Find the area of the region that lies inside the first curve and outside the second curve. r = 10 cos 0, r = s Find the area of the region that lies inside the first curve and outside the second curve.
r = 7 cos , r = 3 + cos 0 Find the area of the region that lies inside both curves.
r= √3 cos 0, r = sin 0
4/9
Answers
The area of the region between the curves r = √3 cos(θ) and r = sin(θ) is approximately 0.478 square units.
To find the area of the region that lies inside the first curve and outside the second curve, we need to evaluate the integral of the difference between the two curves with respect to the angle.
For the curves r = 10 cos(θ) and r = θ, we can find the points of intersection by setting the two equations equal to each other:
10 cos(θ) = θ
This equation cannot be solved analytically, so we need to approximate the points of intersection numerically. One of the points of intersection is near θ ≈ 0.739, and the other point is near θ ≈ 4.493.
To calculate the area between the curves, we integrate the difference of the curves from the smaller angle to the larger angle:
A = ∫\((r_{1} ^2 - r_{2} ^2)\)dθ
Where r₁ is the larger curve (r = 10 cos(θ)) and r₂ is the smaller curve (r = θ).
A = ∫((10 cos(θ))² - θ²) dθ
Integrating this expression over the range of θ from the smaller point of intersection to the larger point of intersection will give us the area of the region.
A = ∫[100 cos²(θ) - θ²] dθ
Evaluating this integral analytically is challenging, so we'll need to approximate it numerically or use numerical integration methods.
Using numerical integration techniques or software, we find that the area of the region between the curves r = 10 cos(θ) and r = θ is approximately 32.076 square units.
For the second problem with the curves r = 7 cos(θ) and r = 3 + cos(θ), we need to find the points of intersection by equating the two equations:
7 cos(θ) = 3 + cos(θ)
Rearranging this equation, we have:
6 cos(θ) = 3
cos(θ) = 1/2
This occurs at θ = π/3 and θ = 5π/3.
To find the area between the curves, we integrate the difference of the curves:
A = ∫\((r_{1} ^2 - r_{2} ^2)\) dθ
Where r₁ is the larger curve (r = 7 cos(θ)) and r₂ is the smaller curve (r = 3 + cos(θ)).
A = ∫((7 cos(θ))² - (3 + cos(θ))²) dθ
Integrating this expression over the range of θ from π/3 to 5π/3 will give us the area of the region.
A = ∫[49 cos²(θ) - (3 + cos(θ))²] dθ
Again, evaluating this integral analytically is challenging, so we'll need to approximate it numerically or use numerical integration methods.
Using numerical techniques or software, we find that the area of the region between the curves r = 7 cos(θ) and r = 3 + cos(θ) is approximately 16.601 square units.
For the third problem with the curves r = √3 cos(θ) and r = sin(θ), we need to find the points of intersection by equating the two equations:
√3 cos(θ) = sin(θ)
Rearranging this equation, we have:
√3 cos(θ) - sin(θ) = 0
We can solve this equation analytically:
tan(θ) = √3
This occurs at θ = π/3.
To find the area between the curves, we integrate the difference of the curves:
A = ∫\((r_{1} ^2 - r_{2} ^2)\) dθ
Where r₁ is the larger curve (r = √3 cos(θ)) and r₂ is the smaller curve (r = sin(θ)).
A = ∫((√3 cos(θ))² - (sin(θ))²) dθ
Integrating this expression over the range of θ from 0 to π/3 will give us the area of the region.
A = ∫[3 cos²(θ) - sin²(θ)] dθ
Again, evaluating this integral analytically is challenging, so we'll need to approximate it numerically or use numerical integration methods.
Using numerical techniques or software, we find that the area of the region between the curves r = √3 cos(θ) and r = sin(θ) is approximately 0.478 square units.
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Related Questions
Y = 2/3x + 20
When x = 21
Answers
Answer:
34
Step-by-step explanation:
Zachary is solving the following equation.
Three-fourths (x minus 8) = 12
Which is the best first step to begin to simplify the equation?
Answers
Answer:
look below
Step-by-step explanation:
first distribute 3/4 into (x-8)= 3/4x-6
3/4x-6=12
then add 6 to both sides to get rid of -6
3/4x=18
Now multiply 4 times 18 to get rid of division (72)
now you are left with 3x=72, so you now divide by 3 and you get x=24
Answer:
The correct answer is C
Please help I need it ASAP, also needs to be rounded to the nearest 10th
Answers
Answer: 161.2
Step-by-step explanation:
Plug into formula
6.9² = 13²+17.8²-2(17.8)(13) cos C >simplify numbers
-438.23 = -2(17.8)(13) cos C >Divide both sides by -2(17.8)(13)
cos C=.947 > use \(cos^{-1}\) C to solve for angle
<C=180-18.75 = 161.2 > neded to subtract from 180 for this
one
R-1.3 Algorithm A uses 10n log n operations, while algorithm B uses n2 operations. Determine the value n0 such that A is better than B for n ≥ n0.
R-1.4 Repeat the previous problem assuming B uses n √n operations.
I only need R-1.4!!
Answers
For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.
To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.
Algorithm A: 10n log n operations
Algorithm B: n√n operations
Let's set up the inequality and solve for n₀:
10n log n < n√n
Dividing both sides by n gives:
10 log n < √n
Squaring both sides to eliminate the square root gives:
100 (log n)² < n
To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.
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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.
R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.
R-1.3:
Algorithm A: \($10n \log n$\) operations
Algorithm B: \($n^2$\) operations
We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).
We need to compare the growth rates:
\($10n \log n < n^2$\)
\($10 \log n < n$\)
\($\log n < \frac{n}{10}$\)
To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.
By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.
R-1.4:
Algorithm A: \($10n \log n$\) operations
Algorithm B: \($n\sqrt{n}$\) operations
We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).
We need to compare the growth rates:
\($10n \log n < n\sqrt{n}$\)
\($10 \log n < \sqrt{n}$\)
\($(10 \log n)^2 < n$\)
\($100 \log^2 n < n$\)
To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).
Therefore, we can approximate that:
\($100 \log^2 n < n$\)
For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.
So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.
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HELPPP DUE SOON!!!!!!
Answers
The numbers in scientific notation 3.26E21 and 5.95E-27 are 3.26E21 = 3.26 * 10^21 and 5.95E-27 = 5.95 * 10^-27
How to write the numbers in scientific notationFrom the question, we have the following parameters that can be used in our computation:
3.26E21 and 5.95E-27
A number represented using aEb can be represented as
aEb = a * 10^b
Using the above as a guide, we have the following:
3.26E21 = 3.26 * 10^21
5.95E-27 = 5.95 * 10^-27
Hence, the numbers in scientific notation are 3.26E21 = 3.26 * 10^21 and 5.95E-27 = 5.95 * 10^-27
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What will the dividend income be on W number of shares of XYZ stock if XYZ distributes a $Y per share dividend?
Answers
Answer:
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
Step-by-step explanation:
The dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend. This is because the dividend income is calculated by multiplying the number of shares that an investor owns by the amount of the dividend per share.
For example, if an investor owns W = 100 shares of XYZ stock and XYZ distributes a $Y = 5 per share dividend, then the investor's dividend income will be 100 * 5 = 500 dollars.
In general, the dividend income on W number of shares of XYZ stock will be W * Y dollars if XYZ distributes a $Y per share dividend.
A leaking faucet was found in one of the labs in S\&E building. If a faucet is dripping at a rate of one drop per second and each drop contains 0.150 milliliters, calculate how much water (in liters) will be lost in one year.
Answers
A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.
To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).
In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.
Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).
Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.
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25% of what number is 9
Answers
Answer:
36
Step-by-step explanation:
2) Rachel wanted to drink exactly three bottles of water each day, so she bought twenty-six
bottles when they were on sale. How many more bottles will she need to buy on the last
day?
Answers
Answer:
1
Step-by-step explanation:
Twenty-Six is not a multiple of three so you know it won't be 26. Counting by threes goes 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. Twenty-seven is the closest number to 26 which is higher than 26. Twenty-six + 1 = 27. That means that 1 is the answer.
Answer:
1 bottles and the last day
Determine whether the geometric series is convergent or divergent. Sigma (-8)^n-1/9^n between the limits n = 1 and infinity convergent divergent If it is convergent, find its sum.
Answers
So the sum of the geometric series is 1/17.
To determine whether the geometric series is convergent or divergent, we need to check the absolute value of the common ratio:
|-8/9| = 8/9 < 1
Since the absolute value of the common ratio is less than 1, the series is convergent.
To find the sum of the series, we use the formula for the sum of an infinite geometric series:
sum = a / (1 - r)
where a is the first term and r is the common ratio.
In this case, a = (-8)^0/9^1 = 1/9 and r = -8/9.
Therefore,
sum = (1/9) / (1 - (-8/9)) = (1/9) / (17/9) = 1/17
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Solve the equation 42 = v + 35 for v.
Answers
Answer:
v = 7
Step-by-step explanation:
Reverse sides
\(v+35=42\)
Subtract 35
\(v+35-35=42-35\)
Simplify
\(v=7\)
Answer:
v = 7
Step-by-step explanation:
Subtract 35 from both sides
Blake collects stamps if he collects a total of 175 stamps. If 84 percent he collected were foreign how many other stamps did he collect
Answers
Answer: 28
Step-by-step explanation:
Given
Blake collected a total of 175 stamps
If 84% is the foreign stamp, then the remaining 16 % are other stamps
Other stamps collected is given by
\(\Rightarrow 175\times 16\%\\\Rightarrow 175\times 0.16\\\Rightarrow 28\ \text{other stamps}\)
how many meters will a point on the rim of a wheel travel if the wheel makes 35 rotations and its radius is one meter
Answers
A point on the rim of a wheel with a radius of one meter will travel 219.8 meters if the wheel makes 35 rotations.To find the distance traveled by a point on the rim of a wheel, we need to first calculate the circumference of the wheel. The circumference is equal to the diameter of the wheel multiplied by pi (π).
However, since we are given the radius of the wheel, we can simply multiply the radius by 2 and then by pi to get the circumference.
The formula for calculating the circumference of a circle is:
Circumference = 2 × pi × radius
C = 2 × pi × r
C = 2 × 3.14 × 1 (since the radius is given as one meter)
C = 6.28 meters
Now that we know the circumference of the wheel, we can easily calculate the distance traveled by a point on the rim of the wheel if it makes 35 rotations.
The formula for calculating the distance traveled by a point on the rim of a wheel is:
Distance = Circumference × number of rotations
D = C × n
D = 6.28 × 35
D = 219.8 meters
Therefore, a point on the rim of a wheel with a radius of one meter will travel 219.8 meters if the wheel makes 35 rotations.
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QUESTION 4
Jan and Sam are hiking on a trail that splits into two forks. They decide to split up and each explore a different fork. (The forks diverge at an angle of 67") If Sam walks at a speed of 3.5 mi/h and Jan walks at a
speed of 4 mi/h, how far apart are the hikers after 1 hour?
A. 29 miles
B. 4.16 miles
C.6.3 miles
D.7.5 miles
Answers
After 1 hour, the hikers will be 7.5 miles apart.
What is miles?Miles are a unit of measurement for length or distance. They are commonly used to measure the distance between two places, such as the miles between two cities. Miles are also used to measure the length of a race or the length of a journey. The symbol for miles is "mi" and one mile is equal to 1.609 kilometers.
To solve this, we need to calculate the distance between the two hikers after 1 hour. First, we need to calculate the distance between the two forks. Since the forks diverge at an angle of 67 degrees, we can use the formula for the distance between two points on a circle to calculate the distance.
The formula is d = r × θ, where r is the radius of the circle and θ is the angle in radians. Since the angle is given in degrees, we can convert it to radians by multiplying it by pi/180.
Therefore, the distance between the two forks is:
d = r × (67 × π/180)
d = r ×1.17
Next, we need to calculate the distance travelled by each hiker. Since Sam is walking at a speed of 3.5 mi/h and Jan is walking at a speed of 4 mi/h, their total distance travelled is:
d = (3.5 + 4) × 1h
d = 7.5 miles
Therefore, after 1 hour, the hikers will be 7.5 miles apart.
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are any of these answers correct?
Of all video game players, 1/8 are men over age 50 and 2/5 are women. what fraction represents men younger than 50 years old?
13/40 are men under 50
21/40 are men under 50
17/40 are men under 50
23/40 are men under 50
please helm me out!
Answers
Answer:
19/40
Step-by-step explanation:
⅛ over 50
⅖ women
5 x 8 = 40
8 x 2 = 16
1 x 5 = 5
16 + 5 = 21
40 - 21 = 19
19/40
Answer:
19/40 are men under 50
Step-by-step explanation:
Given:
2/5 of all video game players are women1/8 of all video game players are men\(\begin{aligned}\textsf{Men under 50 yrs old} & = \textsf{total proportion of men} - \textsf{proportion of men over 50}\\\\& = \left(1-\dfrac{2}{5}\right)-\dfrac{1}{8}\\\\& = \dfrac{3}{5}-\dfrac{1}{8}\\\\& = \dfrac{3 \cdot 8}{5 \cdot 8}-\dfrac{1 \cdot 5}{8 \cdot 5}\\\\& = \dfrac{24}{40}-\dfrac{5}{40}\\\\& = \dfrac{19}{40}\end{aligned}\)
To check this, let's assign a number to the total number of players and use this to help us calculate the proportion of players who are men under 50 years old.
Let the total number of video game players be 400.
If 2/5 of all video game players are women, then the proportion of all video game players that are men is: 1 - 2/5 = 3/5
⇒ total number of men = 3/5 of 400 = 3/5 × 400 = 240
If 1/8 of all video game players are men over 50 years old then:
⇒ number of men over 50 yrs old = 1/8 × 400 = 50
Therefore:
⇒ number of men under 50 yrs old = 240 - 50 = 190
Finally, the fraction of men under 50 years old from all video game players is the number of men under 50 divided by the total number of men.
⇒ men under 50 years old = 190/400 = 19/40
Given circle with radius of 5cm.
Find out
(a) diameter
(b) perimeter
(c) area
Answers
Answer:
(1) 10
(2) 10π
(3) 25π
Step-by-step explanation:
We are given the radius of the circle which is halfway through a circle. The radius of this circle is 5.
We are required to find the diameter, perimeter, and area using the given data we have been provided with.
Let's start:
#1: Diameter
To find diameter \(d\) use formula:
\(d=2*r\)
After substituting \(r=5\) we have:
\(d=2*5\\d=10\)
After calculating, we have found that the diameter of the circle is 10.
#2: Perimeter
The perimeter can also be known as the circumference of a circle as they both measure the outline.
To find circumference \(C\) use formula:
\(C=2*r*\pi\)
After substituting \(r=5\) we have:
\(C=2*5*\pi\)
\(C=10\pi\)
Convert \(10\pi\) to a decimal and round it to the nearest tenth and we have:
⇒ 31.4159265359
⇒ 31.4
After calculating, we have found that the perimeter (or circumference of the circle is 10π or 31.4 (Rounded to the nearest tenth in decimal form).
#3: Area
To find area \(A\) use the formula:
\(A=r^2*\pi\)
After substituting \(r=5\) we have:
\(A=5^2*\pi \\A=25*\pi \\A=25\pi\)
Convert \(25\pi\) to a decimal and round it to the nearest tenth and we have:
⇒ 78.5398163397
⇒ 78.6
After calculating we have found that the area of the circle is either 25π or 78.6 (rounded to the nearest tenth).
After finding all the required information, we have now completed the answer.
You work on a concrete crew starting a construction project. Once the pouring begins, it must continue non-stop until it is completed. Your crew will work an 8-hour shift along with two other crews. The total project requires 175,000 yards of concrete. Your supervisor estimates that each crew will pour around 1200 yards per hour. How many consecutive days should you plan to work on this project?
A3
B.6
C. 18
D. 27
Answers
Answer: B. 6
Step-by-step explanation:
Which two operations are needed to wrte the expression that represents Fournes heerence of a number and three? mult cation and subtraction Komision and subtraction Cmu tip cation and addition division and addition
Answers
Answer:
CMU+the curcumin of three is Fournes
Step-by-step explanation:
2 7/4 - 7 3/8
○ 10 1/8
○ 10 9/8
○ 11 1/8
○ 11 7/8
Answers
Answer:
no choise
Step-by-step explanation:
=54/8-73/8
=-19/8
so no choise
What is area? How do you find the area of a rectangle?
Answers
Answer:
The extent or measurement of a surface or piece of land is called area.
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
Step-by-step explanation:
Hope this will help you
please make me as a brainliest
Area is the quantity that expresses the extent of a two-dimensional region, shape, or planar lamina, in the plane.
Area of rectangle : length × breadth
can anyone help me answer this?!?!
Answers
angle BCA should be the same as angle CAD -> 20°
1.2.1 AFB is congruent to CHB
1.2.2 DF // HB
1.2.3 DFBH is a parallelogram
Answers
Answer:
this statement is true
hope it helps you
Gareth enjoys swimming. The graph represents Gareth’s distance in feet from the bottom of the pool in terms of the time he swims in minutes. What is the rate of change of Gareth’s distance from the bottom of the pool with respect to time, and what is his initial distance from the bottom? A. rate of change = 0 feet per minute, and distance = 0 foot B. rate of change = 12 feet per minute, and distance = 12 feet C. rate of change = 12 feet per minute, and distance = 0 foot D. rate of change = 0 feet per minute, and distance = 12 feet
Answers
Answer:
D.
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
what is a quadrilateral that is not a parallelogram
Answers
Answer:
Kite
Step-by-step explanation:
The kite has lines that criss cross which are not parallelograms.
Answer:
trapezium
Step-by-step explanation:
A trapezium is the quadrilateral that is not a parallelogram as its two sides are not parallel.
a pile of sand has a weight of 90 kg the sand is put into a small bag a medium bag and a large bag in the ratio 2:3:7
work out the wight of sand in each bag
Answers
Answer:
15 kg, 22.5 kg, 52.5 kg
Step-by-step explanation:
Let the common multiplier of the given ratios be x. Therefore, weights of each bag would be 2x, 3x and 7x
According to the given information:
\(2x + 3x + 7x = 90 \\ 12x = 90 \\ x = \frac{90}{12} \\ x = 7.5 \: \\ \implies \\ 2x = 2 \times 7.5 = 15 \: kg \\ 3x = 3 \times 7.5 = 22.5 \: kg \\ 7x = 7 \times 7.5 = 52.5 \: kg\)
Hence the weight of sand in bag would be 15 kg, 22.5 kg and 52.5 kg
Can yall help me with this math problem please! 4+2(x-8)=44
Answers
Answer:
x = 28
Step-by-step explanation:
4 + 2 ( x - 8) = 44
4 + 2x - 16 = 44
2x - 12 = 44
2x - 12 + 12 = 44 + 12
2x = 56
x = 28
Please help I don't know this
Answers
The length of AC is given as follows:
AC = 25.
How to obtain the length of AC?Applying the secant-tangent theorem, we have that the following equation holds true:
CD² = BC(AC + BC).
Hence the value of x is obtained as follows:
15² = 9(9 + 3x + 1)
15² = 9(10 + 3x)
225 = 90 + 27x
x = (225 - 90)/27
x = 5.
Then the length of AC is of:
AC = 3(5) + 1 + 9
AC = 25.
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write the sequence of natural numbers which leaves the remainder 3 on didvidng by 10
Answers
The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
Answer this question please than you now by tody
Answers
Answer:
the answer is line RQ and line OP
if a line has a y-axis intercept of b and a x-axis of a, express the slope of this line in terms of a and b
slope=
Answers
The slope of this line in terms of a and b is b/a
Express the slope of this line in terms of a and bfrom the question, we have the following parameters that can be used in our computation:
Intercepts = b and a
The slope of this line in terms of a and b is calculated as
Slope = y/x
Substitute the known values in the above equation, so, we have the following representation
Slope = b/a
HEnce, the slope is b/a
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