Use the Chain Rule to find ∂z/∂s and ∂z/∂t.
z = (x − y)7, x = s2t, y = st2
∂z
∂s
= ∂z
∂t
=
Answers
The value of ∂z/∂s and ∂z/∂t using the chain rule is 7st\((x-y)^6\)(2 - t²) and 7s²\((x-y)^6\) - 14st\((x-y)^6\) respectively.
The chain rule is a useful technique for finding partial derivatives of composite functions. It allows us to break down a complex function into simpler components and compute the derivatives of each component separately.
In this case, we applied the chain rule to find the partial derivatives of z with respect to s and t by first finding the partial derivatives of z with respect to x and y, and then applying the chain rule to x and y.
To find ∂z/∂s and ∂z/∂t using the chain rule, we first need to find the partial derivatives of z with respect to x and y:
∂z/∂x = 7\((x-y)^6\)
∂z/∂y = -7\((x-y)^6\)
Next, we can use the chain rule to find ∂z/∂s and ∂z/∂t:
∂z/∂s = (∂z/∂x) × (∂x/∂s) + (∂z/∂y) × (∂y/∂s)
= 7\((x-y)^6\) × 2st - 7\((x-y)^6\) * t²
= 7st\((x-y)^6\)(2 - t²)
∂z/∂t = (∂z/∂x) × (∂x/∂t) + (∂z/∂y) × (∂y/∂t)
= 7\((x-y)^6\) × s² - 7\((x-y)^6\) * 2st
= 7s²\((x-y)^6\) - 14st\((x-y)^6\)
Therefore, ∂z/∂s = 7st\((x-y)^6\)(2 - t²) and ∂z/∂t = 7s²\((x-y)^6\) - 14st\((x-y)^6\).
Learn more about chain rules at
https://brainly.com/question/28972262
#SPJ4
Related Questions
for a bill totalling $5.65, the cashier received 25 coins consisting of nickels and quarters. how many nickels did the cashier receive?
Answers
Answer: 3 Nickles.
Step-by-step explanation:
22 quarters adds up to $5.50
The remaining 15c is accounted by the last 3 coins, which are nickles.
LED, Inc. manufactures and sells LED light bulbs, which they guarantee will last at least 2,000 hours of continuous use. LED's engineers randomly select 16 bulbs, plug them in, and record the amount of time they are on before burning out. They find out that the sample mean is 1988 hours with a standard deviation of 32 hours. You can assume the population time before burning out is normally distributed. Suppose the company wants to test the following hypotheses:H0:μ≥2,000vsH1:μ<2,000What distribution would you use to look up the p-value for this set of hypothesis?a. t(32)b. zc. t (15)d. t (23)
Answers
The distribution we would use to look up the p-value is option (c) t(15).
Since the population standard deviation is unknown and the sample size is less than 30, we should use a t-distribution to look up the p-value.
The test statistic can be calculated as
t = (sample mean - hypothesized population mean) / (sample standard deviation / √(sample size))
Substitute the values in the equation
t = (1988 - 2000) / (32 / √(16))
Do the arithmetic operation
t = -3
The degrees of freedom for the t-distribution would be (sample size - 1), which is 15 in this case.
Therefore, the correct option is (c) t(15).
Learn more about t-distribution here
brainly.com/question/13624214
#SPJ4
11. Daisy is calculating her assets. She has $10,000 in gold and silver jewelry, and $50,000 in her savings. She has paid $20,000 of her $150,000 house. She has also pain
$10,000 of the $45,000 car she bought last year.
O $285,000
O $80,000
O $255,000
O $90,000
Answers
Answer:
C is the answer because if u add all the numbers up and subtract how much she has paid so far u get 255,000
Answer: $90,000
Step-by-step explanation: just did the test
Calculate the volume of the solid obtained by rotating the region bounded by the parabola 28 y = x² and the square root function y= √28x around the x-axis
Answers
The volume of the solid obtained by rotating the region bounded by the parabola 28y = x² and the square root function y= √28x around the x-axis is 392π/3.
To find the volume of the solid, we use the method of cylindrical shells.
Consider a vertical strip of thickness dx at a distance x from the y-axis. The strip has height (y₂ - y₁) where y₂ is the value of the square root function and y₁ is the value of the parabola.
From the equation of the square root function, we have:
y₂ = √(28x)
From the equation of the parabola, we have:
y₁ = x²/28
Therefore, the height of the strip is:
(y₂ - y₁) = √(28x) - x²/28
The circumference of the cylindrical shell at x is:
2πr = 2πy₁ = 2π(x²/28)
Thus, the volume of the shell is:
dV = 2π(x²/28) * [√(28x) - x²/28] dx
To find the total volume, we integrate dV from x = 0 to x = 28:
V = ∫₀²⁸ 2π(x²/28) * [√(28x) - x²/28] dx
Simplifying and evaluating the integral, we get:
V = 392π/3
To know more about volume of the solid, refer here:
https://brainly.com/question/12649605#
#SPJ11
In one area along the interstate, the number of dropped wireless phone connections per call follows a Poisson distribution. From four calls, the number of dropped connections is 2 0 3 1 (a) Find the maximum likelihood estimate of 2. (b) Obtain the maximum likelihood estimate that the next two calls will be completed without any ac- cidental drops.
Answers
The solution involves calculating the likelihood function, maximizing it, and using the estimated value to find the probability of no dropped connections in the next two calls.
(a) To find the maximum likelihood estimate of λ, the mean number of dropped connections per call, we need to use the Poisson distribution to calculate the likelihood function L(λ) for the given data. The Poisson distribution is given by:
P(X = x | λ) = (λ^x * e^(-λ)) / x!
where X is the random variable representing the number of dropped connections per call, λ is the parameter representing the mean number of dropped connections per call, and x is the observed number of dropped connections in a call.
The likelihood function for four calls with observed numbers of dropped connections 2, 0, 3, and 1 can be expressed as:
L(λ) = P(X = 2 | λ) * P(X = 0 | λ) * P(X = 3 | λ) * P(X = 1 | λ)
= (λ^2 * e^(-λ)) / 2! * (e^(-λ)) / 0! * (λ^3 * e^(-λ)) / 3! * (λ^1 * e^(-λ)) / 1!
= (λ^6 * e^(-4λ)) / 6
Taking the derivative of L(λ) with respect to λ, setting it equal to zero, and solving for λ.
d/dλ [L(λ)] = d/dλ [(λ^6 * e^(-4λ)) / 6]
= [(6λ^5 * e^(-4λ) - 4λ^6 * e^(-4λ)) / 6]
Setting this derivative equal to zero, we get:
2λ - 3λ^2 = 0
λ = 0 or λ = 2/3
Since λ = 0 is not a valid solution for a Poisson distribution, the maximum likelihood estimate of λ is λ = 2/3.
Therefore, the maximum likelihood estimate of the mean number of dropped connections per call is 2/3.
(b) To obtain the maximum likelihood estimate that the next two calls will be completed without any accidental drops, we can use the estimated value of λ = 2/3 to calculate the probability of no dropped connections in each of the next two calls, using the Poisson distribution:
P(X = 0 | λ = 2/3) = (2/3)^0 * e^(-2/3) / 0! = e^(-2/3) ≈ 0.5134
P(both calls have no drops | λ = 2/3) = P(X = 0 | λ = 2/3)^2 ≈ 0.2637
Therefore, the maximum likelihood estimate that the next two calls will be completed without any accidental drops is approximately 0.2637.
To know more about Poisson distribution, visit:
brainly.com/question/30388228
#SPJ11
Please help me!!!!!!!!
Answers
Answer:
Step-by-step explanation:
If 5x+3/2=6-2/3x, what is the value of X
Answers
Answer:
x=12/17
Step-by-step explanation:
hope this helps
Partially factored form: f(x) = (x − 3)(x 3)(x2− 4x 5) use the quadratic formula to identify the zeroes of x2 − 4x 5. x =
Answers
Answer:
2 ± i
Step-by-step explanation:
by 5, I assume you mean +5
x² - 4x + 5 = 0
x = (-b±(√(b²-4ac)) / 2a
x = (4 ± (√(16 - 20)) / 2
x = (4 ± (√(-4)) / 2
√-4 = √4√-1 which is 2i
x = (4 ± 2i) / 2
x = 2 ± i
State what each variable may be so that the equation is true. You must have at least one negative number. Explain how you chose the values for a and b. 2^a • 2^b = 2^0
Answers
We can solve \(2^{a}\) x\(2^{b}\) = \(2^{0}\) by recognizing that \(2^{0}\)equals 1 and simplifying the equation to \(2^{a+b}\) = 1.
EquationsTo solve \(2^{a}.2^{b}=2^{0}\) for a and b, we must first recognize that 2^0 equals 1, which means that the equation can be rewritten as \(2^{a}.2^{b}=1\). Therefore, we can simplify the equation to \(2^{a+b}\) = 1.
Since 2 raised to any negative power is a fraction, we need at least one of the exponents to be negative.
We could also choose other values that make either a or b negative, such as a = -2 and b = 2, or a = -3 and b = 3. The key is to have one negative exponent and one positive exponent so that their sum equals zero.
In summary, we can solve \(2^{a}.2^{b}=1\)by recognizing that \(2^{0}\) equals 1 and simplifying the equation to \(2^{a+b}\) = 1. We must have at least one negative exponent to satisfy the equation, and we can choose various values for a and b as long as their sum equals zero.
To know more about Exponents, click here,
https://brainly.com/question/5497425
#SPJ1
if you run 2 1/2 miles each day how far are you going
Answers
Answer:
2 1/2 miles
Step-by-step explanation:
my teacher
20 or 30 points-
I need help
Answers
Answer:
Step-by-step explanation:
03. as a percent is 30%
1.5% as a decimal is 0.75
3/4 x 80 is 60.
4 2/3 divided by 1/2 is 1.5...
Answer:
27 = 30%
28 = 0.15
29 = 60
30 = 14
Step-by-step explanation:
When you convert a decimal to a percentage, if it is set up with "0." in front, then just swap the number behind the decimal and put it in front of the zero and add a percentage sign. When converting a percentage to a decimal, you reverse the process. Then the others are simple multiplication and division! Remember, when you're dividing a fraction, use the process "KCP" (keep change flip) where you keep the first fraction in the equation, change the division sign to a multiplication sign, and flip the next fraction. (ex. 1/2 flipped to 2/1.) Then just multiply.
How much water can this container hold? Express your answer in terms of pi.
A: 3,888pi in^3
B: 243pi in^3
C: 7,776pi in^3
D: 972pi in^3
Answers
The amount of water that the container can hold will be equal to 972pi in³ that is option D is correct.
A sphere may be defined as the 3-D hollow figure. It has a diameter, surface area and a fixed volume. The formula for the volume of the sphere is equal to
Volume of Sphere = 4/3(πr³)
where r is the radius of the sphere.
According to the figure the diameter of the spherical container is 18 in. Now the radius of the spherical container will be half of the diameter that is
Radius = Diameter/2
Radius = 18 in/2
Radius = 9 in
Now the amount of water that the container can hold will be equal to the volume of the spherical container that is
Volume = 4/3(πr³)
Volume = 4/3(π)(9in³)
Volume = 972π in³ which is the required answer.
Learn more about Volume at:
brainly.com/question/12336476
#SPJ4
d/dx(pu δ) = d/dx (rd δ/dx)
Integrate the 1D steady state convection diffusion equation over a typical cell. Use the nomenclature from class.
Answers
The first term on the left-hand side represents the flux of the quantity D(pu δ) across the cell boundaries, and the second term represents the change of this flux within the cell.
To integrate the 1D steady-state convection-diffusion equation over a typical cell, we can start with the given equation:
D/dx(pu δ) = d/dx (rd δ/dx)
Here, D is the diffusion coefficient, p is the velocity, r is the reaction term, u is the concentration, and δ represents the Dirac delta function.
To integrate this equation over a typical cell, we need to define the limits of the cell. Let's assume the cell extends from x_i to x_i+1, where x_i and x_i+1 are the boundaries of the cell.
Integrating the left-hand side of the equation over the cell, we have:
∫[x_i to x_i+1] D/dx(pu δ) dx = D∫[x_i to x_i+1] d(pu δ)/dx dx
Using the integration by parts technique, the integral can be written as:
= [D(pu δ)]_[x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx
Similarly, integrating the right-hand side of the equation over the cell, we have:
∫[x_i to x_i+1] d/dx (rd δ/dx) dx = [rd δ/dx]_[x_i to x_i+1]
Combining the integrals, we get:
[D(pu δ)][x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx = [rd δ/dx][x_i to x_i+1]
This equation can be further simplified and manipulated using appropriate boundary conditions and assumptions based on the specific problem at hand.
To know more about integrate refer to-
https://brainly.com/question/31744185
#SPJ11
how many samples of size n=2 can be drawn from this population
Answers
The samples of size n = 2 that can be drawn from this population is 28
How many samples of size n=2 can be drawn from this populationFrom the question, we have the following parameters that can be used in our computation:
Population, N = 8
Sample, n = 2
The samples of size n = 2 that can be drawn from this population is calculated as
Sample = N!/(n! * (N - n)!)
substitute the known values in the above equation, so, we have the following representation
Sample = 8!/(2! * 6!)
Evaluate
Sample = 28
Hence, the number of samples is 28
Read more about sample size at
https://brainly.com/question/17203075
#SPJ1
Complete question
A finite population consists of 8 elements.
10,10,10,10,10,12,18,40
How many samples of size n = 2 can be drawn this population?
Find the value of b in the rhombus below.
Answers
Answer:
26
Step-by-step explanation:
A rectangle’s perimeter and its area have the same numerical value. The length of the rectangle is 6. What is the width of the rectangle in units?.
Answers
Answer:
Step-by-step explanation:
Formula
P = 2*w + 2*L
Area = L*w
Givens
Area = P
L = 6
Create equation and Solve
LW = 2w + 2L
6w = 2w + 2*6
6w = 2w + 12 Subtract 2w from both sides
6w - 2w = 12 Combine
4w = 12 Divide by 4
4w/4 = 12/4
w = 3
Check
Area = 6*3 = 18
Perimeter = 2*3 + 2*6
Perimeter = 6 + 12 Combine
Perimeter = 18
It does check.
what are the dimensions of a storage tank
Answers
Answer:
Step-by-step explanation:
550 48 6-0 3/16 3/16 800
1000 48 10-10 3/16 3/16 1300
1100 48 11-11 3/16 3/16 1400
1500 48 15-8 3/16 3/16 1650
65 9-0 3/16 3/16 1500
2000 65 11-10 3/16 3/16 2050
2500 65 14-10 3/16 3/16 2275
3000 65 17-8 3/16 3/16 2940
4000 65 23-8 3/16 3/16 3600
5000 72 23-8 1/4 1/4 5800
84 17-8 1/4 1/4 5400
7500 84 26-6 1/4 1/4 7150
96 19-8 1/4 1/4 6400
10000 96 26-6 1/4 5/16 8540
120 17-0 1/4 5/16 8100
12000 96 31-6 1/4 5/16 10500
120 20-8 1/4 5/16 9500
15000 108 31-6 5/16 5/16 13300
120 25-6 5/16 5/16 12150
20000 120 34-6 5/16 5/16 15500
25000 120 42-6 3/8 3/8 22300
30000 120 51-3 3/8 3/8 28000
1.If you invest $100 at an interest rate of 15%, how much will you have at the end of 8 years?
Answers
Answer:
$1500 is the answer para po maka tulong akoStep-by-step explanation:
sana maka tulong
what is the GCF of 42 and 54?
Answers
Answer:
6!
Step-by-step explanation:
42 and 54 have a GCF of 6. To find the biggest common factor of 42 and 54, factor every digit (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and select the greatest factor that divides both 42 and 54 exactly, i.e., 6.
Q1-) Consider a manufacturing system with two machines. Suppose that when both ma- chines are available, one is in use and the other is on standby. The probability that a machine in use fails during a day is p. When it fails its repair may start only the next day if the single repair facility is available. It takes two days to repair a failed machine. We can use a Markov Chain model to describe the evolution of this system. Let Xn = (i, j), n ≥ 0 denote the states of the Markov chain, where i is the number of machines in working condition and j is the number of elapsed repair days of a machine at the repair facility at the beginning of the n'th day. The corresponding transition probability matrix is (2,0) (1,0) (1,1) (0,1) (2,0) [1-p P 0 0 (1,0) 0 0 1-p Р P= (1,1) 1-p 0 0 P (0,1) 0 1 0 0 For parts (a)-(c) do not assume a specific value for p, leave your answer in terms of p. (a) Given Xo = (1, 1), what is the probability that only one machine is in working condition after two days? (b) Find the expected number of days until both machines are down, given that currently both machines are operational. (c) Find the steady state probabilities. (d) Suppose the revenue of the manufacturing system is R TL per day if any one of the machines is in operating condition and currently p = 0.3. What will be the percentage change in the long run average benefit per day if a major technological improvement is achieved that changes p from 0.3 to 0.2?
Answers
(a) To find the probability that only one machine is in working condition after two days, we need to determine the probability of transitioning from state (1, 1) to state (1, 0) after two days.
From the transition probability matrix, we see that to transition from (1, 1) to (1, 0) in one day, both machines need to remain operational, which has a probability of (1 - p) * (1 - p) = (1 - p)^2.
Therefore, the probability of transitioning from (1, 1) to (1, 0) after two days is ((1 - p) * (1 - p))^2 = (1 - p)^4.
(b) To find the expected number of days until both machines are down, given that currently both machines are operational, we need to consider the transition probabilities from state (2, 0) to state (0, 1).
From the transition probability matrix, we see that to transition from (2, 0) to (0, 1) in one day, both machines need to fail, which has a probability of p * p = p^2.
Therefore, the expected number of days until both machines are down, given that both machines are currently operational, is 1 / (p^2).
(c) To find the steady-state probabilities, we need to solve the equation πP = π, where π is the row vector of steady-state probabilities and P is the transition probability matrix.
Solving this equation will give us the steady-state probabilities for each state (i, j). Since the given matrix is not provided, it is not possible to calculate the exact steady-state probabilities without the specific values of the transition probabilities.
(d) To determine the percentage change in the long-run average benefit per day if p changes from 0.3 to 0.2, we would need to know how the revenue R TL is related to the probability p. Without this information, it is not possible to calculate the percentage change.
To learn more about probability : brainly.com/question/31828911
#SPJ11
y=-1/3x -1
Y=2x+2 Solve the systems of equations
Answers
This system of equations has been solved graphically and its solution is equal to the ordered pair (-1.29, -0.57).
What is a point of intersection?In Mathematics, a point of intersection is the location on a graph where two (2) lines intersect, or cross each other, which is typically represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection of the lines on the graph;
y = 2x + 2 ........equation 1.
y = -1/3x - 1 ........equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-1.29, -0.57).
Read more on a graph here: brainly.com/question/4546414
#SPJ1
The solution to the system of equations is
x = -9/7 and y = -4/7What are system of equations?A system of equations is a pair of two linear equations
How to solve the system of equations?Given the system of equations
y = -x/3 - 1 and
y = 2x + 2
We proceed to solve the system of equations as follows.
Since we have the equations
y = -x/3 - 1 and
y = 2x + 2
Eqating both expressions, we have that
-x/3 - 1 = 2x + 2
adding 1 from both sides, we have
-x/3 - 1 + 1 = 2x + 2 + 1
-x/3 + 0 = 2x + 3
-x/3 = 2x + 3
Subtracting 2x from both sides, we have that
-x/3 - 2x = 2x - 2x + 3
(-x - 6x)/3 = 0 + 3
-7x/3 = 3
Multiplying both sides by 3, we have
-7x = 3 × 3
-7x = 9
Dividing both sides by -7, we have
x = 9/-7
x = -9/7
Substituting x = -9/7 into y = 2x + 2, we have that
y = 2x + 2
y = 2(-9/7) + 2
= -18/7 + 2
= (-18 + 14)/7
= -4/7
So,
x = -9/7 and y = -4/7Learn more about system of equations here:
https://brainly.com/question/13729904
#SPJ1
Find the product of the complex numbers. express your answer in trigonometric form.
Answers
The product of the complex numbers in trigonometric form computed as:
\(\(z_1 \cdot z_2 = r_1 r_2 (\cos(\theta_1 + \theta_2) + i \sin(\theta_1 + \theta_2))\)\)
To find the product of two complex numbers in trigonometric form, we can multiply their magnitudes and add their arguments. Let's denote the complex numbers as follows:
Number 1: \(\(z_1 = r_1(\cos \theta_1 + i \sin \theta_1)\)\)
Number 2: \(\(z_2 = r_2(\cos \theta_2 + i \sin \theta_2)\)\)
The product of these complex numbers can be computed as:
\(\(z_1 \cdot z_2 = r_1 r_2 (\cos(\theta_1 + \theta_2) + i \sin(\theta_1 + \theta_2))\)\)
In this form, \(\(r_1\) and \(r_2\)\) represent the magnitudes of the complex numbers, and \(\(\theta_1\) and \(\theta_2\)\) represent their arguments.
Please provide the values of the complex numbers you want to multiply, and I'll calculate their product in trigonometric form for you.
Learn more about complex numbers here:
https://brainly.com/question/20566728
#SPJ11
Convert the angle in radians to degrees. Round to two decimal places.
Answers
To convert radians to degrees we have to multiply the angle by the factor
\(\frac{180}{\pi}\)Then
\(3(\frac{180}{\pi})=171.89\)Therefore in degrees the angle is 171.89°.
15a2+12b-9a2 Solve with step by step please
Answers
Answer:
(assuming the 2 was an exponent, if I am wrong don't use this answer) 6a^2 + 12b
Step-by-step explanation:
Add like terms
6a^2 + 12b
Tom has 13 new magazines to read. Let M be the number of magazines he would have left to Read after reading R of them. Write an equation relating to M to R. Then graph your equation using the axis below
Answers
The equation that relates M to R is M = 13 - R
How to determine the equation that relates M to R?From the question, we have the following parameters:
Total number of new magazines = 13Number of magazines read = RNumber of magazines left = MThe total number of new magazines is the sum of the number of magazines read and the number of magazines left
This is represented as
Total number of new magazines = Number of magazines read + Number of magazines left
Substitute the known values in the above equation
13 = R +M
Make M the subject
M = 13 - R
Hence, the equation is M = 13 - R
See attachment for the graph
Read more about linear equations at
https://brainly.com/question/13738662
#SPJ1
egan's flower bed has a length of 6 feet and a width of six eighths feet. Which of the following is true?
Question 13 options:
The area of the flower bed is equal to 8 square feet.
The area of the flower bed is larger than 8 square feet.
The area of the flower bed is equal to 6 square feet.
The area of the flower bed is smaller than 6 square feet.
Answers
6 times 6/8 will be 36/8, which is also 4 4/8. That’s smaller than 6 feet, so your answer is D
plsssssss help me
I will give u 10 points
Answers
Therefore...
The slope is 1/3.
Hope this helps :)
Let me know if there are any mistakes!!
Plz help brainiest to the correct answer!
Answers
#1
Current temperature=0°C
Temperature before 1 hour
\(\\ \sf{:}\dashrightarrow 0+3°C=3°C\)
#2
Temperature before 3h
\(\\ \sf{:}\dashrightarrow 0+3(3)=0+9=9°C\)
#3
Temperature before 4.5h
\(\\ \sf{:}\dashrightarrow 0+4.5(3)=13.5°C\)
1,000 liters equals 1 ________.
Answers
Answer:
cubic meter (m³)
Step-by-step explanation:
N/A
The angle \theta_1θ
1
theta, start subscript, 1, end subscript is located in Quadrant \text{IV}IVstart text, I, V, end text, and \cos(\theta_1)=\dfrac{9}{19}cos(θ
1
)=
19
9
cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 9, divided by, 19, end fraction .
What is the value of \sin(\theta_1)sin(θ
1
)sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?
Express your answer exactly.
\sin(\theta_1)=sin(θ
1
)=sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals
Answers
I guess that we know that the angle θ is in the fourth quadrant, and we know that:
cos(θ) = 9/19
now we want to find the value of sin(θ).
To do it, we can remember that for a point (x, y), such that we can define an angle β between the positive x-axis and a ray that connects the origin with the point (x, y), we can write the relations:
tan(β) = x/y
sin(β) = y/√(x^2 + y^2)
cos(β) = x/√(x^2 + y^2)
Because the angle is in the fourth quadrant, we know that:
x > 0
y < 0.
And we also know that:
cos(θ) = 9/19
then we have:
x = 9
√(x^2 + y^2) = √(9^2 + y^2) = √(81 + y^2) = 19
Solving the above equation we can find the value of y, that we need to remember, is negative:
√(81 + y^2) = 19
81 + y^2 = 19^2
y^2 = 19^2 - 81 = 280
y = √280 = -16.7
Now that we know the value of y, we can replace that in the sine equation to get:
sin(θ) = -16.7/19 = -0.879
If you want to learn more, you can read:
https://brainly.com/question/19830127