find equations of the following. 2(x − 9)2 (y − 5)2 (z − 2)2 = 10, (10, 7, 4) (a) the tangent plane (b) the normal line (x(t), y(t), z(t)) =
Answers
To find the equations of the tangent plane and normal line to the surface 2(x − 9)²(y − 5)²(z − 2)² = 10 at the point (10, 7, 4), we first need to find the partial derivatives of the surface at that point:
f_x = 4(x - 9)(y - 5)²(z - 2)²
f_y = 4(x - 9)²(y - 5)(z - 2)²
f_z = 4(x - 9)²(y - 5)²(z - 2)
Evaluating these partial derivatives at (10, 7, 4), we get:
f_x(10, 7, 4) = 4(10 - 9)(7 - 5)²(4 - 2)² = 32
f_y(10, 7, 4) = 4(10 - 9)²(7 - 5)(4 - 2)² = 128
f_z(10, 7, 4) = 4(10 - 9)²(7 - 5)²(4 - 2) = 256
So the equation of the tangent plane at (10, 7, 4) is:
32(x - 10) + 128(y - 7) + 256(z - 4) = 0
Simplifying this equation, we get:
8(x - 10) + 32(y - 7) + 64(z - 4) = 0
The normal vector to the tangent plane is therefore <8, 32, 64>. To find the equation of the normal line, we need a point on the line. Let's take the point (10, 7, 4) on the surface. Then the parametric equations of the normal line are:
x(t) = 10 + 8t
y(t) = 7 + 32t
z(t) = 4 + 64t
So the equation of the normal line is:
(x, y, z) = (10, 7, 4) + t<8, 32, 64>
or
x = 10 + 8t
y = 7 + 32t
z = 4 + 64t
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Related Questions
help asap will mark brainliest
Answers
Answer:
The first is not
Consider the two tables T1 and T2 shown.Show the results of the following operations: (9 points each. Total 36 points)
Table T1
P Q R
10 A 5
15 B 8
25 A 6
Table T2
A B C
10 B 6
25 C 3
10 B 5
T1 JOIN T1.P = T2.A T2
T1 (LEFT OUTER JOIN) T1.P = T2.A T2
T1 (RIGHT OUTER JOIN) T1.Q = T2.B T2
T1 JOIN (T1.P = T2.A AND T1.R = T2.C) T2
Answers
T1 LEFT OUTER JOIN T2 ON T1.P = T2.A T1.P T1.R T2.A T2.C10 B 6 NULL NULLNULL NULL NULL 7 C T2 JOIN (T1.P = T2.A AND T1.R = T2.C) T2 T1.P T1.R T2.A T2.CNULL NULL NULL NULL NULL NULL NULL NULL
Consider the two tables T1 and T2 and the operations performed on them. The results of the operations are shown above. In the first operation, a LEFT OUTER JOIN is performed on T1 and T2, where the join is made on the basis of T1.P = T2.A. In the second operation, a JOIN is performed on T1 and T2, where the join is made on the basis of T1.P = T2.A AND T1.R = T2.C. The keyword 'LEFT OUTER JOIN' has been bolded in the main answer, while 'JOIN' has been bolded in the supporting explanation.
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In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student chosen randomly from the class passed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
12
2
4
3
Answers
Answer:
20/27
Step-by-step explanation:
What is the Riemann Hypothesis?
Answers
I need help rn !! Please help me and explain
Answers
Answer:
A
Step-by-step explanation:
I=PRN
=4500×(4.75/100)×3
=$641.25
solve the initial value problem 7(t 1)dydt−5y=10t, for t>−1 with y(0)=14.
Answers
Initial value problem 7(t + 1)dy/dt−5y=10t, for t>−1 with y(0)=14 is y = 5(t + 1)^(14/7) + 9(t + 1)^(2/7).
To solve the initial value problem 7(t + 1)dy/dt−5y=10t, for t>−1 with y(0)=14, we will use the method of integrating factors.
Separate the variables and move the terms involving y to the left side of the equation.
7(t + 1)dy/dt - 5y = 10t
7(t + 1)dy/dt = 5y + 10t
dy/dt = (5y + 10t)/(7(t + 1))
Find the integrating factor by taking the exponential of the integral of the coefficient of y.
Integrating factor = e^∫(5/7(t + 1))dt = e^(5/7)ln(t + 1) = (t + 1)^(5/7)
Multiply both sides of the equation by the integrating factor.
(t + 1)^(5/7)dy/dt = (5y + 10t)(t + 1)^(-2/7)
Integrate both sides of the equation with respect to t.
∫(t + 1)^(5/7)dy/dt dt = ∫(5y + 10t)(t + 1)^(-2/7) dt
(t + 1)^(12/7)/12 = 5∫y(t + 1)^(-2/7) dt + 10∫t(t + 1)^(-2/7) dt
Solve for y and use the initial condition y(0) = 14 to find the constant of integration.
y(t + 1)^(-2/7) = (t + 1)^(12/7)/60 + C
y = 60(t + 1)^(14/7)/12 + C(t + 1)^(2/7)
y = 5(t + 1)^(14/7) + C(t + 1)^(2/7)
y(0) = 5(1)^(14/7) + C(1)^(2/7) = 14
C = 9
Substitute the value of C back into the equation to find the general solution.
y = 5(t + 1)^(14/7) + 9(t + 1)^(2/7)
Therefore, the solution to the initial value problem 7(t + 1)dy/dt−5y=10t, for t>−1 with y(0)=14 is y = 5(t + 1)^(14/7) + 9(t + 1)^(2/7).
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What transformation has changed the parent function f(x) = (0.5)x to its new appearance shown in the graph? exponential graph passing through point negative 3, 2 and negative 2, 1 a f(x) − 2 b f(x + 2) c f(x) + 1 d −1 • f(x)
Answers
Correct option is A, f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.
What modification has caused the parent function to change?The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.
In the picture below you can see the blue line is the graph of the function
f(x) = log(5x) and the green line is the graph of the function
g(x) = log[5(x + 4)] - 2
Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.
We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.
The function shifts to the left when you add a number to x;
The function moves to the right when you remove a number from x;
The function increases when you add a number to it;
The function decreases when you take a number away from it.
Then we get a function g(x) = log[5 (x + 4)] - 2.
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the time to complete a bridge varies inversely with the square root of the number of people working. if 9 people can complete the job in 75 days then how long would it take 25 people?
Answers
If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.
Let T be the time and L be the Labor (Number of people working on the bridge).
T ∞ 1/√L (Inverse relationship)
T = K/√L ----------------------------- (1)
Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.
According to the question,
Time (T) = 75 days and
labor (L) = 09
From the equation (1), we get,
T = K / √L
⇒ 75 = K/√9
⇒ 75= K/3
⇒ K= 225
First, the relationship between these variables is:
T = 225/√L
Therefore, how long it will take 25 people to do it means that we should look for the time.
T=225/√L
⇒ T= 225/√25
⇒ T= 225/5
⇒ T= 45 days.
therefore, 25 people needs 45 days to complete the job.
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consider two lists of numbers called list1 and list2. a programmer wants to determine how many different values appear in both lists. for example, if list1 contains [10, 10, 20, 30, 40, 50, 60] and list2 contains [20, 20, 40, 60, 80], then there are three different values that appear in both lists (20, 40, and 60).
Answers
To determine how many different values appear in both lists, you can use a set intersection.
Here's how you can do it in Python:
list1 = [10, 10, 20, 30, 40, 50, 60]
list2 = [20, 20, 40, 60, 80]
set1 = set(list1)
set2 = set(list2)
common_values = set1.intersection(set2)
print(len(common_values)) # Output: 3
In this code, we first convert each list to a set using the set() function. This eliminates any duplicate values in the list, leaving us with only the distinct values. We then use the intersection() method of set to get the common values between the two sets.
Finally, we use the len() function to determine the number of common values and print it out.
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simplify -3/5 + 13/55
Answers
Answer:
-4/11 or -0.36363
Step-by-step explanation:
;)
Answer:
-4/11
Step-by-step explanation:
-3/5 = -33/55
-33/55 + 13/55 = -20/55
Simplified: -4/11
Please mark me Brainliest :)
So, who is ready for the weekend?
Answers
Answer:
pls follow me now now I help
a model airplane is built using the scale 2 inches = 7 feet. how long is the actual plane of the model airplane is 1.5 feet long?
Answers
Answer:
63
Step-by-step explanation:
if 2 inches = 7 feet and the model plane is 1.5 feet, and that is 18 inches 18/2*7=63
1 inch is =12.
Greg’s parents bought a $350.00 savings bond when he was born. When he turns 3030, the bond’s value will have increased 125%. How much will the savings bond be worth on Greg’s thirtieth birthday?
Answers
Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
What is the percentage?In mathematics, a quantity or ratio known as A% stands for a percentage of 100.
There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.
To represent percentages, the symbol "%" is typically written after the number.
So, we know that:
The bond is $350.
The return is 125% when Greg turns 30.
Then, the amount after she turns 30 will be as follows:
350/100 * 125
437.5
Bonds value: 437.5 + 350 = $787.5
Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
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the two major forms of steganography are insertion and substitution. True or false?
Answers
Answer: True
Step-by-step explanation:
Can anybody help me solve this please!
Answers
Answer:
(-4,6)
Step-by-step explanation:
1. Easiest way
(x,y) of the dot.
. prove that if v is a vector space having dimension n, then a system of vectors v1, v2, . . . , vn in v is linearly independent if and only if it spans v .
Answers
A system of vectors v1, v2, . . . , vn in a vector space v of dimension n is linearly independent if and only if it spans v.
Let's first assume that the system of vectors v1, v2, . . . , vn in v is linearly independent. This means that none of the vectors can be written as a linear combination of the others. Since there are n vectors and v has dimension n, it follows that the system is a basis for v. Therefore, every vector in v can be written as a unique linear combination of the vectors in the system, which means that the system spans v.
Conversely, let's assume that the system of vectors v1, v2, . . . , vn in v spans v. This means that every vector in v can be written as a linear combination of the vectors in the system. Suppose that the system is linearly dependent. This means that there exists at least one vector in the system that can be written as a linear combination of the others. Without loss of generality, let's assume that vn can be written as a linear combination of v1, v2, . . . , vn-1. Since v1, v2, . . . , vn-1 span v, it follows that vn can also be written as a linear combination of these vectors. This contradicts the assumption that vn cannot be written as a linear combination of the others. Therefore, the system must be linearly independent.
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Consider a continuous-time Markov chain with three states 1, 2, 3, 4, 5 and transition rates q12=1, q13 = 2, q21 = 0, q23 = 3, q31 = 0, q32 = 0. (1) Write the system of ODEs for the corresponding transition probabilities Pᵢⱼ (t) . (2) Suppose that the initial state is 1. What is the probability that after the first transition, the process X(t) enters state 2?
Answers
the probability of transitioning from state 1 to state 2 after the first transition is:
P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3
To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.
Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.
The ODEs for the transition probabilities can be written as follows:
dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)
dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)
dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)
dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)
dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)
dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)
where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.
Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.
To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.
The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:
total_rate = q₁₂ + q₁₃
Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:
P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate
In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.
Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:
P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3
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The wages
w
(in £) Caroline earns is the number of hours she works
n
multiplied by her hourly rate
r
(in £ per hour). Enter a formula for Caroline's wages and enter the wage she would earn if she worked 20 hours at a rate of £7.20 per hour
Answers
Answer:
£ 144
Step-by-step explanation:
the formula would be :
w = n * r
finding the wages for 20 hours at a rate of 7.20 hours can be solved like this:
w = n *r
w = 7.20 * 20
w =£ 144
The length of the base of a parallelogram is 18 centimeters. the parallelogram has an area of 450 square centimeters.
what is the height of the parallelogram?
enter your answer in the box
Answers
Answer:
h = 25 cm
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the height )
given A = 450 and b = 18 , then
18h = 450 ( divide both sides by 18 )
h = 25
Answer:
h = 25cm
Step-by-step explanation:
4. What is the rate of change of the linear function that has a graph that passes
through the points (-1, 3) and (-2,-4)?
Answers
The rate of change of the function that has a graph that passes
through the points (-1, 3) and (-2,-4) is slope and is equal to 7.
The slope of a line is outlined because the amendment in y coordinate with relevancy the amendment in x coordinate of that line. cyber web amendment in y coordinate is Δy, whereas cyber web amendment within the x coordinate is Δx. The slope of a line is calculated victimisation 2 points lying on the line. Given the coordinates of the 2 points, we are able to apply the slope of line formula m = y₂ - y₁ / x₂ - x₁ where (x₁ ,y₁) are the coordinate of first point and (x₂ ,y₂) are the coordinate of second point.We have given two points (-1, 3) and (-2,-4) .
Rate of change of graph is given by slope
Using slope formula , we get
m = -4 - 3 / -2 - (-1)
m = -7 / -2 + 1
m = -7 / -1
m = 7
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Jamal will cut a piece of wood that is 212
2
1
2
feet long into 14
1
4
-foot sections. How many sections will result?
Group of answer choices
Answers
Answer:
no
Step-by-step explanation:
in each of the following describe the rate of change between the first and the second, assuming that the first coordinate is measured in minutes and the second coordinate is measured in feet. what are the units of your answer
Answers
Answer: no clue sonny boi but good luck
let x1...Xn ~ Poisson(λ) be iid and let θ = λ2.
find the maximum likelihood estimator of θ and compute the bias of this estimator (θ). is this estimator consistent?
Answers
The maximum likelihood estimator (MLE) of θ = λ² is θ-hat = (Σx_i/n)², and the bias of this estimator is E(θ-hat) - θ = (Σx_i/n)² - λ². This estimator is consistent as n→∞.
To find the MLE of θ, first find the MLE of λ (λ-hat), which is the mean of the observed values (Σx_i/n). Since θ = λ², the MLE of θ is θ-hat = (Σx_i/n)².
To compute the bias, find the expected value of θ-hat (E(θ-hat)) and subtract θ. E(θ-hat) = E((Σx_i/n)²) and θ = λ². Bias = E(θ-hat) - θ = (Σx_i/n)² - λ².
To determine if the estimator is consistent, observe that as n→∞, the bias converges to 0, making the estimator consistent.
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if the process mean and variance do not change over time, the process is considered to be
Answers
If the process mean and variance do not change over time, the process is considered to be stable. Stability is a crucial concept in statistical process control as it allows for the reliable and predictable performance of a process.
To determine whether a process is stable, statistical process control techniques are used to monitor the process over time and detect any changes in the mean or variance. Control charts are often used to display the process data and identify any trends or patterns that may indicate a change in the process.
If the process mean and variance remain within the control limits of the control chart and show no significant patterns or trends, the process is considered stable. Stable processes are desirable as they allow for consistent performance and can be easily maintained within established control limits.
However, if the process mean or variance shows a significant change, this indicates that the process is no longer stable. This could be due to a variety of factors such as changes in equipment, raw materials, or operator performance. In this case, action should be taken to identify and correct the cause of the instability to restore the process to a stable state.
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thirteen and thirteen thousandths decimal form
Answers
I need help with this practice I attempted this and got 13.96? Make sure your answer is rounded to the nearest hundredth
Answers
Law of Cosines
Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:
\(c^2=a^2+b^2-2ab\cos \theta\)We have a = 14, b = 9, θ = 71°. Substituting:
\(\begin{gathered} c^2=14^2+9^2-2\cdot14\cdot9\cos 71^o \\ c^2=196+81-252\cdot0.325568 \\ c^2=194.956825 \\ c=\sqrt[]{194.956825} \\ c=13.96 \end{gathered}\)The length of CD is 13.96
can someone do this for me please?! Just the answer pls
Answers
Answer:
1 is d
the square root of 36 = 6 which is the only equation with 36
2 is d
John's room is 12 feet by 8 feet. Spencer's room is 14 feet by 9 feet. How much larger is Spencer's room than John's room
Answers
Answer: 30 sq ft
Step-by-step explanation:
Let's calculate the area of both rooms.
John's room is 12x8 ft, so we can multiply to get the area. 12x8=96 ft squared.
Spencer's room is 14x9 ft, so we will do the same thing. 14x9= 126 ft squared.
Now, we can subtract 96 from 126 to find out how much larger Spencer's room is. 126-96= 30 ft squared.
hope this helped!
Determine the intercepts of the line.
Do not round your answers
Answers
Y intercept: (0 , -7/3)
How many 3/4 teaspoons of salt are in 1/3 of a teaspoon of salt?
Answers
Answer:
4/9
Step-by-step explanation:
Multiply each answer choice by 3/4 or 1/3 and they will all be wrong except for 4/9.
3 x 4 = 1/3
so 4/9