Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. R = 3 + 4 cos(θ), θ = phi/3
Answers
dy/dx = (3cos(φ/3) - 4sin(2φ/3)) / (-3sin(φ/3) - 4cos(2φ/3)). This is the slope of the tangent line to the given polar curve at the point specified by θ = φ/3.
To find the slope of the tangent line to the given polar curve at the specified point.
Given polar curve: R = 3 + 4cos(θ)
Point specified by: θ = φ/3
We'll first need to find the derivative dR/dθ:
1. Differentiate the given polar equation with respect to θ:
dR/dθ = -4sin(θ)
Now, we need to find the Cartesian coordinates (x, y) of the point specified by θ = φ/3. To do this, we'll use the following conversion formulas:
x = Rcos(θ)
y = Rsin(θ)
2. Plug in θ = φ/3 into the polar equation:
R = 3 + 4cos(φ/3)
3. Find the Cartesian coordinates x and y:
x = (3 + 4cos(φ/3))cos(φ/3)
y = (3 + 4cos(φ/3))sin(φ/3)
Now, we need to find the slope of the tangent line, dy/dx, at the given point:
dy/dx = (dy/dθ) / (dx/dθ)
4. Differentiate x and y with respect to θ:
dx/dθ = -3sin(φ/3) - 4cos(2φ/3)
dy/dθ = 3cos(φ/3) - 4sin(2φ/3)
5. Calculate dy/dx:
dy/dx = (3cos(φ/3) - 4sin(2φ/3)) / (-3sin(φ/3) - 4cos(2φ/3))
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Related Questions
chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
Answers
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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How many cans of paint are needed to cover an area of 2000?
Answers
The number of cans required to paint an area of 2000 square units is equal to 5 cans.
As given in the question,
Total area to be painted is equal to 2000 square units.
Area covered by one can of paint is equal to 400 square units
400 square units = 1 can of paint
⇒ 1 square units = ( 1 / 400 ) cans of paint
⇒ 2000 square units = ( 2000 / 400 ) cans of paint
⇒ 2000 square units = 5 cans of paint
Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.
The above question is incomplete, the complete question is:
How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?
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What is the degree of this polynomial?
5y^2+y+1
Answers
The average weekly unemployment benefit in Montana is $272. Suppose that the benefits are normally distributed with a standard deviation of $43. A random sample of 8 benefits is chosen in Montana. What is the probability that the mean for this sample is greater than $299?
Answers
From the given question we can extract all the necessary parameters to enable us to find the solution to the question.
We would therefore have the following parameters
\(\begin{gathered} \text{observed }value=X=299 \\ S\tan darddeviation=\sigma=43 \\ \text{sample}=n=8 \\ \text{average}=\mu=272 \end{gathered}\)This would be inserted into the formula given for the z score below
\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt[]{n}}}\)This would then be written as
\(\begin{gathered} z=\frac{299-272}{\frac{43}{\sqrt[]{8}}} \\ z=1.78 \end{gathered}\)We look up the z score on the probability table to get 0.9625. We then subtract from 1 to get the answer
\(p(z>1.78)=0.0375\)ANSWER=0.0375
Which point on the number line represents -4/5?
A
B
C
D
Answers
Answer:
A
Step-by-step explanation:
theare are 5 part from 0 to -1
since, the value from 0 to -1 is -1 then if we break it to 5 part, each part has value of -1/5
so, to be -4/5, -1/5 must be multiplied by 4, so we need to go to the 4th part from 0, so it A
Answer:
A
Step-by-step explanation:
I think the ans is A.
I hope it will help u
2(t+1)=10 what does t equal
Answers
Answer:
t = 4
Step-by-step explanation:
1. 2*t = 2t
2. 2*1 = 2
3. 2t+2 = 10
4. 10-2 = 8
5. 2t = 8
6. 8/2 = 4
7. t = 4
Answer:
t = 4
Step-by-step explanation:
2(t + 1) = 10
2t + 2 = 10
2t = 10 - 2
2t = 8
t = 8 ÷ 2
t = 4
-TheUnknownScientist
Consider the PDE au(x, t) = 4 d²u(x, t) 2 Ət əx² For each of BCs and ICs, solve the initial value problem. du(π,t) a) BCs: u(0,t)=0 = = 0 and əx IC: u(x,0) = x ANSWER: f(x)= n=1 u(2,t) = 0 and u(0,t)=0 u(x,0)=sin x ANSWER: f(x)=¹1_sin(2 + nx) na n=1 1+ 2 X b) BCs: IC: 8 (2n-1) T n+1 (-1)041 -4(2n-1)²t sin(2-nπ) nπ 1- 2 e sin (2n-1) 2 na sin X 2 -(nn)²t x -X
Answers
the solution for the initial value problem is: u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t) where λ = ± sqrt(-4n² / a), and n is a non-zero integer.
The given partial differential equation is:
au(x, t) = 4 * (d²u(x, t) / dt²) / (dx²)
a) BCs (Boundary Conditions):
We have u(0, t) = 0 and u(π, t) = 0.
IC (Initial Condition):
We have u(x, 0) = x.
To solve this initial value problem, we need to find a function f(x) that satisfies the given boundary conditions and initial condition.
The solution for f(x) can be found using the method of separation of variables. Assuming u(x, t) = X(x) * T(t), we can rewrite the equation as:
X(x) * T'(t) = 4 * X''(x) * T(t) / a
Dividing both sides by X(x) * T(t) gives:
T'(t) / T(t) = 4 * X''(x) / (a * X(x))
Since the left side only depends on t and the right side only depends on x, both sides must be equal to a constant value, which we'll call -λ².
T'(t) / T(t) = -λ²
X''(x) / X(x) = -λ² * (a / 4)
Solving the first equation gives T(t) = C1 * exp(-λ² * t), where C1 is a constant.
Solving the second equation gives X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) + C3 * cos(sqrt(-λ² * (a / 4)) * x), where C2 and C3 are constants.
Now, applying the boundary conditions:
1) u(0, t) = 0:
Plugging in x = 0 into the solution X(x) gives C3 * cos(0) = 0, which implies C3 = 0.
2) u(π, t) = 0:
Plugging in x = π into the solution X(x) gives C2 * sin(sqrt(-λ² * (a / 4)) * π) = 0. To satisfy this condition, we need the sine term to be zero, which means sqrt(-λ² * (a / 4)) * π = n * π, where n is an integer. Solving for λ, we get λ = ± sqrt(-4n² / a), where n is a non-zero integer.
Now, let's find the expression for u(x, t) using the initial condition:
u(x, 0) = X(x) * T(0) = x
Plugging in t = 0 and X(x) = C2 * sin(sqrt(-λ² * (a / 4)) * x) into the equation above, we get:
C2 * sin(sqrt(-λ² * (a / 4)) * x) * C1 = x
This implies C2 * C1 = 1, so we can choose C1 = 1 and C2 = 1.
Therefore, the solution for the initial value problem is:
u(x, t) = sin(sqrt(-λ² * (a / 4)) * x) * exp(-λ² * t)
where λ = ± sqrt(-4n² / a), and n is a non-zero integer.
Note: Please double-check the provided equation and ensure the values of a and the given boundary conditions are correctly represented in the equation.
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Kohl's is having a sale on Levi jeans for 1/3 off. Target is also having a sale on Levi jeans for 1/2 off. Who is having the better sale?
A) Kohl’s.
B) Target.
Answers
Answer:
Option B: Target.
Step-by-step explanation:
Kohl's sale
1/3 × 100= 33.3% off
While,
Target sale
1/2 × 100 = 50% off
Answer:
Target (option b/second option)
Step-by-step explanation:
We have to first convert the fraction rates into percentage rates. To change a fraction to a percentage, you can divide the numerator by the denominator then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.
1/2 = 50%
1/3 = 33.33%
Now reviewing this data, we see that a 50% decrease of a price is more than a 33.33% decrease.
find the perimeter, halla el perimetro
Answers
Answer:
28 cm
Step-by-step explanation:
The perimeter (P) is the sum of the sides
P = LE + EF + ( FG + HI + JK ) + ( GH + IJ + KL )
= 8 + 6 + 8 + 6
= 28 cm
A jewelry supply shop buys silver chains from a manufacturer for c dollars each, and then sells the chains at a 57-percent markup. Write the markup as a decimal, A expression for the retail price silver chain, a retail price of a silver chain purchased for 45 dollars, and how much was added to the original price of the chain
( if you answer all the questions i will mark you the Brainy-est. )
Answers
The amount added to the original price of the jewelery is the Markup price. Hence, the amount added is $16.34
Markup = 57% = 0.57Cost of jewellery = cRetail price = $45Retail price = cost of jewellery + Markup
$45 = c + 0.57c
45 = 1.57c
Divide both sides by 1.57
c = 45/1.57
c = $28.66
The Markup price = (Retail price - Original price)
Markup = $45 - $28.66 = $16.34Therefore, the amount added to the original price is $16.34
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In circle L, shown below, PQ is a chord of the circle which measures 42 cm. What is the length of PL?
Round to the nearest tenth digit.
Include all of the following in your work for full credit.
(a) length of segment PM
(b) what circle property did you use to find the length of PM
(c) what formula/theorem did you use to calculate the length of segment PL
(d) all math used to calculate the length of segment PL
Answers
a. Length of segment PM=21cm and length of segment PL = 24.6cm.
What is segment?In geometry, a segment is a part of a line that is bounded by two distinct endpoints and contains all the points between them. It can also be defined as the portion of a line that connects two points.
According to given information:(a) Using the given information, PQ=42cm and we can see that M is midpoint of PQ. Therefore we can use midpoint formula
PQ=PM+MQ
42=2PM
PM=42/2
PM=21
(b) We used the property that the perpendicular bisector of a chord passes through the center of the circle, which means that LP is the perpendicular bisector of PQ.
(c) We used the Pythagorean theorem again to solve for PL.
\(PL^2 = PM^2 + LM^2\\\\PL^2 = 21^2 + 13^2\\\\PL^2 = 610\\\\PL = \sqrt{(610)\)
PL ≈ 24.6 cm
(d)
\(PM^2=PL^2-LM^2= 610-169=441\\\\PM=21\)
Using the fact that LP is the perpendicular bisector of PQ, we can split PQ in half to get two segments of length 21. Then, using the Pythagorean theorem in right triangle LPL', where L' is the midpoint of PQ, we can solve for PL.
PL ≈ 24.6 cm
Therefore, the length of PL is approximately 24.6 cm.
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A pizza is to be cut into thirds. Each of these thirds is to be cut into sixths. What fraction of the pizza is each of the final pieces
Answers
Answer:
1/18
Step-by-step explanation:
The pizza is 1 piece
1 divided by 3 = 1/3
1/3 divided by 6 = 1/18
this is because dividing by a whole number is the same thing as multiplying by its reciprocal
therefore the final piece is 1/18 of the original pizza
Work out the size of angle x
Answers
Answer:
as the sum of 2 opposite interior angles is equal to the sum of the exterior angle.
So here, X is the exterior angle.
and the measure of 2 opposite interior angles are 82° and 29°
Answer:
hope it helps.stay safe healthy and happy.
Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier?
Answers
Answer:
9 / 13
Step-by-step explanation:
From the question :
Let :
Hostel students = h
Day students = d
Students with A grade = a
P(h) = 60% = 0.6
P(d) = 40% = 0.4
P(hostel with A grade) ; P(A / H) = 0.3
P(day with A grade) ; P(A / D) = 0.2
The probability that a student picked at random withbA grade is an hostel student is given as :
Probability of being an hostel student gun he has A :
P(H | A) = (P(A/H) * P(H)) ÷ P(A/H) * P(H) + P(A/D) * P(D))
P(H | A) = (0.3 * 0.6) ÷ ((0.3*0.6) + (0.2*0.4))
P(H | A) = 0.18 ÷ (0.18 + 0.08)
P(H | A) = 0.18 ÷ 0.26
P(H | A) = 9 / 13
studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
Answers
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = \(\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}\)
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
\(\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \]\)
Where:
\(\(\lambda\)\) is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
\(\(\lambda = 5\)\)
\(\(k = 0\)\), back to the formula as
\(\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \]\)
Calculating the probability as
\(\[ P(X = 0) = e^{-5}\)
\(= 0.0067379\)
Therefore, the probability is 0.0067379 or 0.67%.
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expand the following:
a) 8(×-2y)
Answers
Answer:
8x-16y
Step-by-step explanation:
8*x-8*2y
8x-16y
Answer.
8x - 16y
Explained in the picture atteached:
a zoo has a total of 8 lions and tigers. the number of tigers are one less than twice the number of lions. write a system of equations that represents the number of lions and tigers
A. L + T = 2
T=L-8
B. L-T=8
T=2L-1
C. L+T =8
T=2L-1
D. L+T =8
T= 2L +1
Answers
Step-by-step explanation:
Let the number of lions be represented by L
Let the number of tigers be represented by T
A zoo has a total of 8 lions and tigers :
\(L + T= 8\)
The number of tigers are one less than twice the number of lions. :
\(T = 2L -1\)
What would be coordinates of the image(13,570)
Answers
25.20 ÷ -0.5
How do I write out how I divided it?
Answers
Answer:
You can write it like 25.20 x -2 = -50.40
Step-by-step explanation:
Social scientists gather data from samples instead of populations because
a. samples are much larger and more complete.
b. samples are more trustworthy.
c. populations are often too large to test.
d. samples are more meaningful and interesting
Answers
Social scientists gather data from samples instead of populations because c. populations are often too large to test.
Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.
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A variable needs to be eliminated to solve the system of equations
below. Choose the correct first step.
–9x – 10y = -42
-9x + 7y = 60
Answers
Answer:
The first step would be to subtract the two equations.
2. Write an algebraic expression for the total number of minutes in h hours and 20 minutes.
3. Write an algebraic expression for the total number of hours in 2 hours and x minutes.
4. Write an algebraic expression for the total number of hours in y hours and 45 minutes.
Answers
Answer:
The expressions are:
2. \(60h+20\ minutes\)
3. \(2+\frac{x}{60}\ hours\)
4. \(y+0.75\ hours\)
Step-by-step explanation:
The given expressions have to be converted into algebraic expressions.
So,
2. Write an algebraic expression for the total number of minutes in h hours and 20 minutes.
Here,
h is a variable that can have any value but the 20 minutes will remain same with any number of hours.
If h is for hour, the number of minutes in h hours will be: \(60*h = 60h\)
And there are also 20 minutes so the algebraic expression is:
\(60h+20\ minutes\)
3. Write an algebraic expression for the total number of hours in 2 hours and x minutes.
In order to convert minutes into hour, the minutes are divided by 60
So converting x minutes into hour means
\(x\ minutes = \frac{x}{60}\ hours\)
There are 2 hours already so the expression will be:
\(2+\frac{x}{60}\ hours\)
4. Write an algebraic expression for the total number of hours in y hours and 45 minutes.
Converting 45 minutes to hours by dividing by 60
\(45\ minutes = \frac{45}{60}\ hours = 0.75\ hours\)
The expression is:
\(y+0.75\ hours\)
Hence,
The expressions are:
2. \(60h+20\ minutes\)
3. \(2+\frac{x}{60}\ hours\)
4. \(y+0.75\ hours\)
Work out the size of angle x.
Answers
Answer:
x = 46°
Step-by-step explanation:
Angles on a straight line sum to 180°.
Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:
⇒ 180° - 130° = 50°
The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:
⇒ 180° - 96° = 84°
The interior angles of a triangle sum to 180°. Therefore:
⇒ 50° + 84° + x = 180°
⇒ 134° + x = 180°
⇒ 134° + x - 134° = 180° - 134°
⇒ x = 46°
Therefore, the size of angle x is 46°.
what two integers does the square root of 58 fall between?
Answers
Answer:
7 and 8
Step-by-step explanation:
Answer:
7 and 8Step-by-step explanation:
The first step is to find the √58.
The answer is 7.61577310586.
Since this is between 7 and 8, the correct answer is 7 and 8.
can u help me with this asap
Answers
5x + 3 > 4x + 7
x > 4
Shaded part should be greater than 4
It would be number line A
Answer:
the answer is the first one
Step-by-step explanation:
please help urgently i am not sure what to do
Answers
Step-by-step explanation:
5 * 5²
= 5 ^ (1 + 2)
= 5³
Hope it will help
A spinner is split in to six equal sections with the sections colored as labeled in the drawing
Emily rolls a number cube labeled 1-6 and spins the spinner
What is the probability of Emily rolling a 5 and spinning a yellow?
Answers
Answer: 1/18
Step-by-step explanation:
Answer:
the answer is 1/36
Step-by-step explanation:
because 1/6 times 1/6 is equal to 1/36
!!Will mark Brainliest!! The points in the table lie on a line. What is the slope of the line?
Answers
Answer:
-7/6
Step-by-step explanation:
It cost $110 to plant watermelons on an acre of farmland. How much would it cost to only plant 2/3 of the acre?
Answers
No solve this you have to multiply the cost per acre by the total are you want to plant:
\(110\cdot\frac{2}{3}=73.3\)It'll cost $73.3 to plant 2/3 of the acre.
Which ordered pair is a solution to the following system of inequalities?
y < –x2 + x
y > x2 – 4
(0, –1)
(1, 1)
(2, –3)
(3, –6)
Answers
Answer: (0,-1)
Step-by-step explanation:
Let's start with the first inequality, \(y < -x^{2}+x\). To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.
A) \(-1 < -0^{2}+0 \longrightarrow -1 < 0 \longrightarrow \text{ True}\)B) \(1 < -1^{2}+1 \longrightarrow 1 < 0 \longrightarrow \text{ False}\)C) \(-3 < -2^{2}+2 \longrightarrow -3 < -2 \longrightarrow \text{ True}\)D) \(-6 < -3^{2}+3 \longrightarrow -6 < -6 \longrightarrow \text{ False}\)Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).
A) \(-1 > 0^{2}-4 \longrightarrow -1 > -4 \longrightarrow \text{ True}\)C) \(-3 > 2^{2}-4 \longrightarrow -3 > 0 \longrightarrow \text{ False}\)Therefore, the answer is (A) (0, -1).