find the normal vector to the level curve f(x, y) = c at p. f(x, y) = 1 − 5x − 10y c = 1, p(0, 0)
Answers
This vector is perpendicular to the level curve f(x, y) = 1 at p(0, 0), so it is the normal vector to the level curve at p.
To find the normal vector to the level curve f(x, y) = c at p, we need to find the gradient of f at p, which is a vector that is perpendicular to the level curve at p.
In this case, we have f(x, y) = 1 − 5x − 10y and c = 1, so the level curve is given by the equation f(x, y) = 1 − 5x − 10y = c = 1.
To find the gradient of f at p(0, 0), we take the partial derivatives of f with respect to x and y and evaluate them at p:
∂f/∂x = -5 and ∂f/∂y = -10
Therefore, the gradient of f at p is the vector:
grad f(p) = (-5, -10)
This vector is perpendicular to the level curve f(x, y) = 1 at p(0, 0), so it is the normal vector to the level curve at p.
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Related Questions
what is the quotient of the expression
\( \frac{21a {}^{3} b - 14ab {}^{2} + 7ab}{7ab} \)
Answers
How many times does 5 go into 1,200??
Answers
240 times.
Explanation:
24 times because,
If you divide 5 with 12k that's,
= 1200/5
= 240
Hence proved, 240 times.
We need to survey a sample of the 300 passengers on a full flight from Cincinnati to London. We randomly generate 30 seat numbers and survey the passengers who sit there. What best describes the sampling technique being used
Answers
The sampling technique being used in this scenario is known as "Systematic Sampling."
Systematic sampling involves selecting every kth element from a population after starting at a random initial element. In this case, the researchers are randomly generating 30 seat numbers, which serves as the starting point. They then survey the passengers who are sitting in those specific seats, selecting every 10th passenger (assuming there are 300 passengers on the flight).
By systematically selecting passengers based on their seat numbers, the researchers ensure that the sample is representative of the entire population of passengers on the flight.
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solve the given inequality 11x-20<_13
Answers
Answer:
x ≤ 3
Step-by-step explanation:
11
x
−
20
≤
13
Step 1: Add 20 to both sides.
11
x
−
20
+
20
≤
13
+
20
11
x
≤
33
Step 2: Divide both sides by 11.
11
x
11
≤
33
11
\(\huge{ \mathfrak{ Answer }}\)
\(11x - 20 \leqslant 13\)\(11x \leqslant 20 + 13\)\(x \leqslant 33 \div 11\)\(x \leqslant 3\)\( \#TeeNForeveR\)
Alyssa starts with $40 and saves $10 each week. Bill has $24 and saves $12 each week. For numbers 5a. – 5c., determine whether each statement is True or False. Write "True" or "False" for each statement. a. Bill will never have more money than Alyssa. b. Bill's savings can be represented by the equation = 12 + 24 where x is the number of weeks and y is his savings. c. Alyssa and Bill will have the same amount of money at Week 6.
Answers
Answer: See explanation
Step-by-step explanation:
Alyssa starts with $40 and saves $10 each week. This can be written as:
= 40 + 10x
Bill has $24 and saves $12 each week. This can be written as:
= 24 + 12x
where, x = number of weeks
a. Bill will never have more money than Alyssa.
False.
From the 9th week, Bill will have more money than Alyssa. To check goes below.
Alyssa = 40 + 10x = 40 + 10(9) = 40 + 90 =$130
Bill = 24 + 12x = 24 + 12(9) = 24 + 108 = $132
b. Bill's savings can be represented by the equation = 12 + 24 where x is the number of weeks and y is his savings.
False.
Bill savings can be represented by:
= 24 + 12x
where, x = number of weeks
c. Alyssa and Bill will have the same amount of money at Week 6.
False.
Alyssa = 40 + 10x
= 40 + 10(6)
= 40 + 60
= $100
Bill = 24 + 12x
= 24 + 12(6)
= 24 + 72
= $96
PLEASE HELP I AM BEGGIN YOU EXTRA POINTS AND BRAINLIEST PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Karsik borrowed $8,500 from a bank. During a period of five years, he paid a total of $2,125 in interest. What was the simple annual interest rate that the bank charged Karsik for his loan?
0.05%
0.5%
5%
7.7%
Answers
Answer:
5%
Step-by-step explanation:
2,125 interest/5 years=425 interest/year
425/8500=.05 or 5%
Answer:
the real answer is 4.25
Step-by-step explanation:
hope this helps
by the way to calculate the interest you have to divide the total interest by how many days or years then put in percent form example 2.125 divided by 5 wich equals 4.25
LOGIC, Use the model universe method to show the following invalid.
(x) (AxBx) (3x)Ax :: (x) (Ax v Bx)
Answers
The conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).
To show that the argument is invalid using the model universe method, we need to find a counterexample where the premises are true, but the conclusion is false.
Let's consider the following interpretation:
Domain of discourse: {1, 2}
A(x): x is even
B(x): x is odd
Under this interpretation, the premises "(x)(A(x) ∧ B(x))" and "(∃x)A(x)" are true because all elements in the domain satisfy A(x) ∧ B(x), and there exists at least one element (e.g., 2) that satisfies A(x).
However, the conclusion "(x)(A(x) ∨ B(x))" is false since there exist elements (e.g., 1) that satisfy B(x) but not A(x).
In this counterexample, the premises are true, but the conclusion is false, demonstrating that the argument is invalid using the model universe method.
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Which of these is a reason you might use a credit union instead of a bank? (flocabulary)
A
They often don’t have any fees associated with their accounts.
B
They often have higher interest rates on savings accounts.
C
They often have higher interest rates on loans.
D
They are out to make a profit on your money.
Answers
Two window washers start at the heights shown. One is rising, the other is descending. How long does it take for the two window washers to reach the same height? Explain.
Answers
Answer:
After 18.32 seconds washer men will be at the same height.
Step-by-step explanation:
Given question is incomplete; here is the complete question.
Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11 inches per second) one is rising one is descending. How long does it take for the two window washers to reach the same height? Explain
Two window washers are moving in opposite directions.
First window washer is at 21 ft and rising with the speed of 8 inches per second.
Second window washer is at 50 feet and descending with the speed of 11 inches per second.
Since 1 feet = 12 inches
Therefore, 21 feet = 21×12 = 252 inches
Similarly, 50 feet = 50 × 12 = 600 inches
Let both the window washer takes 't' time to be at the same height.
Height of the first window washer after t seconds = (252 + 8t) feet
Height of the second window washer after t seconds = (600 - 11t) feet
Since both are at the same height after time 't',
(252 + 8t) = (600 - 11t)
8t + 11t = 600 - 252
19t = 348
t = 18.32 seconds
Therefore, after 18.32 seconds washer men will be at the same height.
Which of the following gives and example of an equation that is non-linear?
A y=2x+1
B y=15/x
C y=10x
D y=x/5
Answers
The answer is A. y=2x+1
A is the only equation in which the numbers are not naturally written,but there is another numbering being either taken or added to the situation (+1). B and D both are divided which is linear, and C is multiplying which is also linear. This only leaves us with A.
Hope this helps. & don't forget to drink water <3
(b) Use the defining formula to compute the sample standard deviation s_ Recall the defining formula used to compute the sample standard deviation $ where x is a F = member of the data set, x is the mean, and n is number of data values Before using the formula, we must determine x and n There are five values in the data set 1, 2, 4, 7, 8, so n Calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values: 1 + 2 + 4 + 7 + 8 22 Step 3 In order to use the defining formula for sample standard deviation, it is helpful to first calculate (x each data value in the data set 1, 2, 4, 7, 8. for Use the values in the data set and the previously determined mean, x = 4.4,to complete the following table_ 4.4 4.4 4.4 4.4 4.4 X-* ~3.4 0.4 3.6 11.56 5.76 6.76 (iX?
Answers
The standard deviation is 4.95.
The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.
A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean. The standard deviation and the mean together can tell you where most of the values in your frequency distribution lie if they follow a normal distribution.
Dataset: 1,2,4,7,8
So, n = 5 (because the sample size is 5)
We calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values:
X = 1+2+4+7+8/5
X=22/5 = 4.4
So, the average is 4.4
For standard deviation calculation,
$ = \({\sqrt{(x-X)^2/n-1} }\)
Thus, the standard deviation is 4.95.
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Consider the parent function f(x) = x^2 and the transformed function f(x) =- 5(x - 4)^2 – 8. Identify the
transformations.
Answer
Answers
Given:
The parent function is
\(f(x)=x^2\)
Consider the transformed function is g(x) instead of f(x) because both functions are different.
\(g(x)=-5(x-4)^2-8\)
Step-by-step explanation:
We have,
\(f(x)=x^2\)
\(g(x)=-5(x-4)^2-8\)
It can be written as
\(g(x)=-5f(x-4)-8\) ...(i)
The translation is defined as
\(g(x)=kf(x+a)+b\) .... (ii)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<|k|<1, then the graph compressed vertically by factor k and if |k|>1, then the graph stretch vertically by factor k.
If k is negative, then f(x) is reflected across the x-axis to get g(x).
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
On comparing (i) and (ii), we get
\(a=-4<0\), f(x) shifts 4 units right.
\(b=-8<0\), f(x) shifts 8 units down.
\(k=-5\), it is negative so f(x) reflected across the x-axis.
\(|k|=|-5|=5>1\), so f(x) stretched vertically by factor 5.
Therefore, the function f(x) reflected across the x-axis, stretched vertically by factor 5 and shifted 4 units right 8 units down to get g(x).
The perimeter of a rectangle is 224 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
Answers
We conclude that the length of the rectangle is 17 ft, and the width of the rectangle is 95ft.
How to find the length and width of our rectangle?
Remember that for a rectangle of width W and length L, the perimeter is:
P = 2*(L + W)
Here we know that the perimeter is 224 ft, and we know that the length length is an odd integer, then:
L = (2n + 1)
The width is 5 times the next odd integer, then:
W = 5*(2n + 3)
Where n is an integer number. Replacing all that in the perimeter equation, we get:
224 = 2*( (2n + 1) + 5*(2n + 3))
Now we just need to solve this for n.
224/2 = ( (2n + 1) + 5*(2n + 3))
112 = (2n + 1) + 5*(2n + 3) = 2n + 1 + 10n + 15 = 12n + 16
112 - 16 = 12n
96 = 12n
96/12 = n = 8
Then the length is:
L = (2n + 1) = (2*8 + 1) = 17
And width:
W = 5*(2n + 3) = 5*(19) = 95
We conclude that the length of the rectangle is 17 ft, and the width of the rectangle is 95ft.
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Answer:
the length is 17, the width is 95
Step-by-step explanation:
i just got this right on delta
75+ In an academy, there are two batches of students studying for their Green Belt exam. Both batches are instructed to study for 16 hours to prepare for the exam without any variation. You have recorded the time it took for each individual to prepare for the Green Belt exam. To identify the variance in the performance of these two batches, you carry out a 2-Variance test. The results are shown in the given diagram. You have to identify if the variance in study time between the two batches is significantly different. Assume the data is normally distributed. . Testa Method Test normal) Lerene's Test any continua Teat DEL DF2 Statistie Value 1919 0.42 131 0.063 0.074 Since the p-value of F test is greater than 005, it is concluded with 95% confidence that the variance in study time of Batch 1 is significantly different than the variance in study time of Batch 2. Since the p-value of Levene's test is greater than 005, it is concluded with 95% confidence that the variance in study time of Batch 1 is significantly different than the variance in study time of Batch 2. 2. . Since the p-value of F test is greater than 0.05, it is concluded with 95% confidence that the variance in study time of Batch 1 is NOT significantly different than the variance in study time of Batch 2. Since the p-value of Levene's test is greater than 0.05, it is concluded with 95% confidence that the variance in study time of Batch 1 is NOT significantly different than the variance in study time of Batch 2.
Answers
The F-test is used to compare two population variances and determine if they are significantly different from each other. When conducting an F-test, the null hypothesis states that the two population variances are equal, and the alternative hypothesis states that the variances are different.
In the given diagram, the F-statistic is calculated as 1.919 with a p-value of 0.063. Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the variance in study time of Batch 1 is NOT significantly different than the variance in study time of Batch 2. Therefore, option (2) is the correct answer.
The Levene's test is used to determine if the variances of two populations are equal or not. If the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the variances are equal. In the given diagram, the Levene's test statistic is calculated as 0.42 with a p-value of 0.74. Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the variance in study time of Batch 1 is NOT significantly different than the variance in study time of Batch 2. Therefore, option (4) is incorrect.
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identify an intercept
Answers
Answer:
Step-by-step explanation:
An x- intercept would be -6 and a y-intercept would be -6 also.
Can anyone please help me to do this with steps
Answers
9514 1404 393
Answer:
x = 45°
Step-by-step explanation:
We presume you want the measure of angle x.
Long arc BAD is intercepted by inscribed angle BCD and by inscribed angle BDE. Hence angle BDE has the same measure as angle BCD.
x + 70° = 115°
x = 45° . . . . . . subtract 70°
_____
It doesn't matter where point C is on short arc BD—the measure of angle C is the same regardless. This is still true even if point C moves to be on top of point D, so that angle BCD and angle BDE are indistinguishable.
What is the surface area of a sphere with a radius of 21 units
Answers
Hope this helps
Answer: 5541.77
Simplifying the equation below! Please help.
Answers
Answer:
that would be -11
Step-by-step explanation:
it is asking for the absolute value of -7-4 however absolute value is always positive once you solve that you have a negative symbol on the outside that turns ur answer negative
Answer:
- 3
Step-by-step explanation:
- | -7+4|
Determine inside the absolute value first
-7+4 = -3
Replace inside the absolute value
- |-3|
The absolute value means take the non negative value
|-3| =3
- 3
Select the correct answer.
What does the concept of historical cost involve in accounting?
O A. valuing business resources at their current market price
OB
O B. valuing business resources at their purchase price
O c.
recording all expenses in the book of accounts
D.
recording all income in the book of accounts
OE.
valuing intangible assets in terms of money
Answers
The concept of historical cost in accounting involves valuing business resources at their purchase price. This is further explained below.
What is the historical cost?Generally, historical cost is a value of measure used in accounting that records the value of an asset on the balance sheet at its original cost when purchased by the firm.
In conclusion, valuing business resources at their purchase price is what historical cost is about.
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Answer:
b. valuing business resources at their purchase price
Step-by-step explanation:
Hours Rented (h) Cost ($) 1. Determine whether the relationship between the two quantities described in the table is linear. If so, find the constant rate of change. If not, explain your reasoning. 2 50 1. 4 100 6 150 8 200 Is the relationship linear? (type (type YES or NO) What is the constant rate of change (slope)?
Answers
Answer: I think it is either 25$ an hour or no the change from cost to hours is not constant
Step-by-step explanation:
Hope that helpssss !!!!!!!!!!! *-*
what does a correlation coefficient of 0 indicate?
Answers
Answer:
no linear relationship exists between the two variables being compared
Step-by-step explanation:
The following table shows the number of candy bars bought at a local grocery store and the
total cost of the candy bars:
Candy Bars 3
5
Total Cost $6.65
8
$10.45 $16.15
12
$23.75
15
$29.45
20
$38.95
25
$48.45
Based on the data in the table, find the slope of the linear model that represents the cost
of the candy per bar: m =
Answers
Answer:
The slope of a linear model can be calculated using the formula:
m = Δy / Δx
where:
Δy = change in y (the dependent variable, in this case, total cost)
Δx = change in x (the independent variable, in this case, number of candy bars)
This is essentially the "rise over run" concept from geometry, applied to data points on a graph.
In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.
Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).
Δy = $48.45 - $6.65 = $41.8
Δx = 25 - 3 = 22
So the slope m would be:
m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar
This suggests that the cost of each candy bar is $1.9 according to this linear model.
Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.
The difference between twice a number and 7 is 15. Find the number
Answers
Answer:
is there options to choose from
Answer:
The number could be 4 or 2
Step-by-step explanation:
there are two possible solutions since the difference can be calculated in two ways
HELP! I’ll MARK BRAINLIEST
contestants indoor run-and-bike-a-thon run for a specified length of time, then bike for a specified length of time. Jason ran at an average speed of 5.2 mi/H and biked at an average speed of 20.2 mi/H, go in a total of 14.6 miles. Seth ran at an average speed of 10.4 mi/H and bite at an average speed of 18.8 mi/H, going a total of 17.8 miles. For how long do contestants run and for how long do they bike? Round to the nearest hundred if necessary.
Answers
Answer:
they ran 5 and 2 and half hour
Step-by-step explanation:
they ran 5 and 2 and half hour
what value of (m) makes this equation true
Answers
Answer:
-71
Step-by-step explanation:
(M+3)/4=-17
M+3=-17*4
M+3=-68
M=-68-3
M=-71
Someone plz help me with this
Answers
Answer:
1. (5,2)
2. (8,10)
3. (6, -10)
4. (-4, -8)
5. (-10, 0)
6.(-8,7)
7. (-6,-9)
8.(9,-6)
9. (5,-6)
10.(6,-6)
*NEED HELP??!!! The regression equation y = 3. 648 • 1. 182x approximates the cost to go on a safari, y, given the number of years since it opened in 2005, x. Which is the best estimate for the cost of a vehicle to drive through the safari in 2011?
A) $ 25. 87
B) $ 22. 95
C) $ 10. 74
D) $ 9. 95
I got C on this but im not for sure. If its the right answer or what /:
Answers
The best estimate for the cost of a vehicle to drive through the safari in 2011 is $22.95, which corresponds to option B. Therefore, your answer is correct.
The given regression equation is y = 3.648 * 1.182x, where y is the cost to go on a safari and x is the number of years since it opened in 2005. To estimate the cost of a vehicle to drive through the safari in 2011, we need to find the value of y when x = 6 (since 2011 is 6 years after 2005).
So, we substitute x = 6 into the regression equation:
y = 3.648 * 1.182x
y = 3.648 * 1.182^6
y ≈ 22.95
Therefore, the best estimate for the cost of a vehicle to drive through the safari in 2011 is $22.95, which corresponds to option B. This means that if the number of years since the safari opened was 6 in 2011, then the estimated cost for a vehicle to drive through it would be approximately $22.95, according to the given regression equation.
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HELPPP!!!
2 to the power of 5 x 2 to the power of 3
I do know that the answer is 256 but
I don't know HOW to find it!
Answers
Step-by-step explanation:
I use a thing call
P-parenthesis
E-exponents
M D-Multiplication and division (Left to right)
A S- Addition and Subtraction (left to right)
We need to wait to use the exponents so 5x2=10, Add the 2 power to ten so 10^2.=100. 100^3.
A basketball team played 15 games and won 80% of them. If the team expects to play 30 games in all, how many more games must it win to finish the season with a 90%
winning percentage?
A. 12
B. 14
C. 15
D. 27
Answers
Answer:
They have alrady won 12 games (80% of 15) and need to win 15 more.
Step-by-step explanation:
Karl’s math class is playing a number game. Each student is given a number card containing the numbers 1 to 6. The rules of the game are that each student must put a cross through two numbers on the card and hand it in to the teacher. The teacher has a bag containing six balls numbered 1 to 6. When all the number cards have been handed in the teacher draws out two balls from the bag. Every student who had chosen the same two numbers shown on the balls wins a prize. If there are 30 students in Karl’s class, how many students are likely to win a prize? Describe your reasoning
Answers
By finding the probability, we can expect that 2 out of the 30 students will win the prize.
How many of the 30 students will win the prize?
First, we should get the probability of winning this game.
Here the students select two numbers out of 6, just to make the calculations let's say that these numbers are 1 and 2.
Now, we need to get these two numbers in two balls. The probability of getting the ball with the number 1 out of the 6 balls is:
p = 1/6
The probability of getting the ball with the number 2 out of the remaining 5 balls (because we already got one) is:
q = 1/5
The joint probability is then:
P = 2*(1/6)*(1/5) = 1/15.
Where the factor 2 comes to take in account the permutations, for the case where we first draw the number 2 and then the number 1.
Then the expected number of students that will win is equal to the probability times the total number of students:
(1/15)*30 = 2
So out of the 30 students, we can expect that 2 will win.
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