To descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), you should walk in the direction of the negative gradient vector, normalized to be a unit vector, which is approximately <0.640, 0.768>.
Explanation:To determine the direction in which you should walk to descend fastest from the point (5,4) on the surface z=15-(2x^2+3y^2), we can find the gradient of the surface at that point. The gradient vector will point in the direction of the steepest ascent, so the direction of the steepest descent is the opposite direction of the gradient vector.
First, calculate the partial derivatives of z with respect to x and y:
∂z/∂x = -4x
∂z/∂y = -6y
Next, evaluate these derivatives at the point (5,4):
∂z/∂x(5,4) = -4(5) = -20
∂z/∂y(5,4) = -6(4) = -24
The gradient vector at (5,4) is <-20, -24>. To get the direction of steepest descent, we take the negative of the gradient vector, which is <20, 24>.
Finally, normalize this vector to make it a unit vector (so it has a length of 1):
Length of gradient vector = √(20^2 + 24^2) = √(400 + 576) = √976 ≈ 31.24
The unit vector in the direction of steepest descent is <20/31.24, 24/31.24> ≈ <0.640, 0.768>.
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What you put on social media matters. Why does it matter and how will you ensure your social media postings reflect you professionally?
Answer:
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
As a professional what you put on social media matters a lot. Social Media postings show all what you are thinking or doing to hundreds, thousands, or even millions of people. If you are an artist you depend on those people (fans) to continue supporting you and your art so a single wrong post can turn a lot of people against you.
If you work for a company you are not only representing yourself through your posts but the company as well. This is because a company hires you for the person that you are therefore it is seen through the public eye that they share your way of thinking.
The best way for your postings to reflect you professionally, is to post only things relating to your own career and journey. While leaving out any opinions, personal information, and controversial topics.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
What is the probability that x is between $34 and $38?
The probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.
To find the probability that a random variable ( x) is between $34 and $38, we need to use the probability density function (PDF) if ( x) follows a continuous distribution. Let's assume ( x ) follows a normal distribution with a mean [tex](\( \mu \))[/tex] of $36 and a standard deviation [tex](\( \sigma \))[/tex] of $2.
Calculate the z-scores for $34 and $38:
[tex]\[ z_1 = \frac{34 - 36}{2} = -1 \][/tex]
[tex]\[ z_2 = \frac{38 - 36}{2} = 1 \][/tex]
Look up the z-scores in the standard normal distribution table:
[tex]\[ P(z_1 < Z < z_2) = P(-1 < Z < 1) \][/tex]
Find the probabilities corresponding to these z-scores:
[tex]\[ P(Z < 1) = 0.8413 \][/tex]
[tex]\[ P(Z < -1) = 0.1587 \][/tex]
Subtract the two probabilities:
[tex]\[ P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 \][/tex]
So, the probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.
2/3 x 5/8 in simplest form
Sarah polled 40 randomly selected students at her high school and found that 20% ( = 0.2) are happy with the quality of the cafeteria food. With a desired confidence level of 99%, which has a corresponding z*-score of 2.58, what is the approximate margin of error of Sarah’s poll? Remember, the margin of error, E, can be determined using the formula E = z*
What does it mean to say that lim n → ∞ an = ∞? the terms an become small as n becomes large. the terms an approach zero as n becomes large. the terms an become large as n becomes large. the terms an become small as n becomes small. the terms an become large as n becomes small?
The limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] means that the term [tex]a_n[/tex] becomes large as n becomes large
The limit of a function describes the behavior of such function as the independent variable approaches a certain value
Infinity [tex]\infty[/tex] represents a very large number
In the limit, both n and [tex]a_n[/tex] tend to infinity
The given limit is:
[tex]\lim_{n \to \infty} a_n = \infty[/tex]
The limit above describes the behavior of [tex]a_n[/tex] as n approaches infinity
As n approaches infinity [tex]a_n[/tex] also approaches infinity
Therefore, the description of the limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] is that the term [tex]a_n[/tex] becomes large as n becomes large
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The statement 'lim n → ∞ an = ∞' means that the terms an become large as n becomes large.
Explanation:The statement lim n → ∞ an = ∞ means that the terms an become large as n becomes large.
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How do I figure this out?
The perimeter of a college athletic field is 104 meters and the length is 16m more than the width find the length and width
The length and width of the rectangle will be 19 meters.
What is the perimeter of the rectangle?The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(L + W) units
The perimeter of a college athletic field is 104 meters and the length is 16 meters more than the width.
L = 14 + W
Then the length and width of the rectangle will be
P = 2(L + W)
104 = 2(14 + W + W)
52 = 14 + 2W
2W = 38
W = 19 meters
The length and width of the rectangle will be 19 meters.
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The weight of 1000 identical samples of a substance is 10 pounds. What is the weight of 10 samples?
Let f(x) = 3x+2 and g(x) = 7x+6. find f×x
Let a and b be events in a sample space s such that p(a) = 0.41, p(b) = 0.46 and p(a ∩
b.= 0.14. find p(a | b).
The conditional probability that event a will occur given that event b has occurred, denoted as p(a | b), is approximately 0.3 or 30%.
Explanation:The question is asking for the conditional probability of the event a given that event b has occurred, written as p(a | b). In probability theory, the formula for conditional probability is p(a | b) = p(a ∩ b) / p(b). Here, we already know that p(a ∩ b) = 0.14 and p(b) = 0.46. Substituting these values into the formula gives us:
p(a | b) = 0.14 / 0.46 = 0.304347826.
So, the probability of event a occurring given that event b has occurred is approximately 0.3 or 30%.
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Divide and give the answer in scientific notation.
8.4 x 10^7
----------------
3 x 10^3
Write the rate as a unit rate
A Jockey had 1053 wins in 31 years of riding
The unit rate is win per year
2+1.25f=10−2.75f solve for f
The value of f is 0.02.
What is an expression ?Expression is a formation of numbers and variables with mathematical operations.
According to the given question we have to solve for f or we can say we have to find the value of f for the given expression which is
2+1.25f=10−2.75f (lets multiply each term by 100 to remove
decimals )
∴ 200 + 125f = 1000 - 275f
125f + 275f = 1000 - 200
400f = 800
f = 800/400
f = 2.
As we have multiplied by 100 we have to divide by 100 we obtain the exact result.
So, 2/100 is = 0.02
f = 0.02.
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What is the distance between 0.5 to -1.5
on Monday 2/3 of the team practiced Tuesday 7/8 Wednesday 1/2 and Thursday 3/4 on which date were the most team members present at practice
which of the following represents the factorization of trinomal below
A video editor takes 15 hours to add a
If f(x) is the total number of bacteria present in a sample after x hours , which of the following statements best describes the meaning of f(2)=12
A. The total number of bacteria present in a sample after 12 hours is 2.
B. The total number of bacteria present in the sample after 6 hours is 12.
C. The total number of bacteria present in the sample after 2 hours is 12.
D. The total number of bacteria present in the sample after 6 hours is 12.
Answer: C. The total number of bacteria present in the sample after 2 hours is 12.
Step-by-step explanation:
The given statement : f(x) is the total number of bacteria present in a sample after x hours.
It means the independent quantity = Number of hours
i.e. The independent variable in the given situation = x
Also, the dependent quantity = Total number of bacteria
i.e. The dependent variable in the given situation = f(x)
Therefore, the meaning of "f(2)=12" is the total number of bacteris present in sample is 12 after 2 hours.
A family paid 23,100 as a down payment for a home if this represents 14% of the price of the home find the price of the home
find the percent of each number 30% of 35
A father is three times as old as his son, and the sum of their age is 76 years old. How old is the son?
Age of son = 19 years
Age of father = 57 years
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given,
A father is three times as old as his son
Sum of their age is 76 years
Let age of son is x, age of father = 3x
x + 3x = 76
4x = 76
x = 76/4
x = 19
Age of son = 19 years
Age of father = 3×19 = 57 years
Hence, 19 years is the age of son and
57 years is the age of father.
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I REALLY NEED HELP WITH MY CALC CORRECTIONS. THIS IS THE THIRD TIME IVE POSTED THIS. I NEED HELP ASAP PLS!! I HATE CALC 1
rewrite y^2(9y^2+4y-9) in standard form
a consumer purchased a computer after a 15% price reduction. if x represents the computer's original price, the reduced price can be represented by
Jane saved $ 800. Her sister has 10 times as much money. How much money does Jane's sister have? Use number or words to explain your answer.
Which of the following terms best describes the graph of the exponential function given below? F(x)=9*((1)/(7))^(x)
A. Linear
B.Decreasing
C.Increasing
D.Quadratic
Answer:
B. Decreasing
Step-by-step explanation:
We have been given formula of a function [tex]F(x)=9\cdot (\frac{1}{7})^x[/tex]. We are supposed to determine the type of our given function.
We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,
a = Initial value,
b = If [tex]b>1[/tex], then the function is growth function. If [tex]b<1[/tex], then the function is decay function.
Upon looking at our given function we can see it is in form of exponential function.
Upon comparing our given function with standard exponential function, we can see that the value of a is 9 and value of b is [tex]\frac{1}{7}[/tex].
Since [tex]\frac{1}{7}<1[/tex], therefore, our function is decreasing and option B is the correct choice.
Makayla's local movie theater has a moviegoer club that charges an annual registration fee of 25 dollars.However, movie tickets are discounted for members at 6 dollars per ticket, instead of 9 dollars per ticket.Let m equal the number of movie tickets Makayla purchases in a year. Write a function to model the amount of money Makayla spent going too the movies during the year she joined the club. C(m)=6x+25 The domain is best represented by: A)integers B)whole numbers C)rational numbers D)real numbers Algebra chestercat
A scientist placed 22.854 grams of sodium chloride in a beaker. He then added five times as much calcium chloride as sodium chloride. Finally, he divided the mixture evenly into four dishes.
How much of the mixture did each dish contain?
A .28.5675 g
B. 34.2810 g
C. 137.1240 g
D. 548.4960 g
Determine whether or not f is a conservative vector field. if it is, find a function f such that f = ∇f. if it is not, enter none. f(x, y) = (yex + sin y) i + (ex + x cos y) j
The vector field f(x, y) = (yex + sin y) i + (ex + x cos y) j is conservative because its curl vanishes everywhere. The function F such that ∇F = f is yex + cos y + C.
Explanation:To determine if the given function f(x, y) = (yex + sin y) i + (ex + x cos y) j is a conservative vector field, we need to see if the curl of the vector field vanishes everywhere. The curl of a vector field in two dimensions is the partial derivative of the j component with respect to x minus the partial derivative of the i component with respect to y.
For f(x, y), the partial derivative of the j component (ex + x cos y) with respect to x is ex + cos y, and the partial derivative of the i component (yex + sin y) with respect to y is ex + cos y. Both derivatives are equal, implying the curl is zero. Hence, f(x, y) is a conservative vector field.
Next, to find a function F such that ∇F = f, we need to integrate. The potential function, F, can be obtained by integrating the i component of f with respect to x (since it does not involve y), and the j component of f with respect to y (since it does not involve x): ∫yex dx + ∫sin y dy = yex + cos y + C. This is the function F such that ∇F = f.
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If rectangle ABCD is resized with a central point (−1, 1) and scale factor 3, what are the coordinates of D'?
A)(−3, 3)B)(−10, −5)C)(−5, −10)D)(−15, −15)