Find the directional derivative of f(x,y,z)=yx+z^4 at the point (3,2,1) in the direction of a vector making an angle of 2π/3 with ∇f(3,2,1).
Answers
Answer:
Step-by-step explanation:
You don't need to know u . Since your function is differentiable everywhere.
We get that..
(5,1,−4)=∇(5,1,−4)⋅||||Duf(5,1,−4)=∇f(5,1,−4)⋅u||u||
But you also know that..
12=cos3=⋅∇(5,1,−4)||||||∇(5,1,−4)||⟹12=cosπ3=u⋅∇f(5,1,−4)||u||||∇f(5,1,−4)||⟹∇(5,1,−4)⋅||||=12||∇(5,1,−4)||=…∇f(5,1,−4)⋅u||u||=12||∇f(5,1,−4)||=…
And there you go!
I hope this helps! UwU
Related Questions
Nearly 100% of the observed occurrences of a random variable x that is normally distributed will fall within three standard deviations of the mean of the distribution of x. True False
Answers
Answer:
True
Step-by-step explanation:
Three standard deviation from the mean value of distribution of x comprises of 99.7 % of the values of a given set of data.
However, 68% of the data lies with in one standard deviation
while 95% percent of the data lies within two standard deviations
99.7% is approximately 100% of the observed occurrences.
Hence, given statement is true
Find the difference. (2/7x-6) - 1/7x-5) =
Answers
Answer:
(2/7*-6)-1/7*-5)
=-12/7--5/7
=7/7
=1
Step-by-step explanation:
i think the answer is positive
Please someone help me
Thanks
Answers
40/52 = 10/13
25/52
0
those were the answers of the wrong answer from above
Rearrange the equation
a= 1/2 (b- c)
to make b the subject.
Answers
I hope this helps.
Mr. Lew recorded the average length, in minutes, of phone calls received at work. He recorded the data in the box plots below. A box plot titled Professional Call Length in Minutes. A number line goes from 0 to 11. The whiskers range from 2 to 10, and the box ranges from 3 to 8. A line divides the box at 4. Professional Call Length in Minutes A box plot titled Personal Call Length in Minutes. A number line goes from 0 to 11. The whiskers range from 1 to 11, and the box ranges from 4 to 6. A line divides the box at 5. Personal Call Length in Minutes Which is an accurate comparison of the two data sets? Time spent on professional calls is typically shorter and more consistent than time spent on personal calls. Time spent on professional calls is typically shorter but less consistent than time spent on personal calls. Time spent on professional calls is typically longer but more consistent than time spent on personal calls. Time spent on professional calls is typically longer and less consistent than time spent on personal calls.
Answers
Answer:
D
Step-by-step explanation:
i did it
Answer:
A. Time spent on professional calls is typically shorter and more consistent than time spent on personal calls.
Step-by-step explanation:
E D G E N U I T Y 2020
In a sample of 10,000 observations from a normal population, how many would you expect to lie beyond three standard deviations of the mean? Group of answer choices About 100 About 127 None of them About 27
Answers
Around 27 of the observations are expected to lie beyond this interval.
Given data values of 10000 observations, 0.27 percent of 10000 is 0.27∗10000100=27. 0.27 ∗ 10000 100 = 27.
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
The numbers in between any two particular provided numbers are referred to as an interval. For instance, the interval containing 0, 5, and all values between 0 and 5 is the set of numbers x satisfying 0 x 5.
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What is the equation of the circle with center (-3.2, 2.1) and radius 4.3?
A. (x-2.1)^2 - (y + 3.2)^2 = (4.3)^2
B. (x + 3.2)^2 + (y - 2.1)^2 = 4.3^2
C. (x+ 2.1)^2 + (y- 3.2)^2 = 4.3^2
D. (x- 3.2)^2 + (y + 2.1)^2 = (4.3)^2
Answers
Thus, (x+3.2)2+(y+2.1)2=18.49 ( x + 3.2 ) 2 + ( y + 2.1 ) 2 = 18.49 is the equation of the circle with the center at (−3.2,−2.1) and a radius of r=4.3 .
When the centre and radius of a circle are known, how do you determine its equation?
Use the formula (x a) 2 + (y b) 2 = r 2 to determine a circle's equation when you are aware of its radius and centre. Here, stands for the circle's centre, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.
(x - h)2+ (y - k)2 = r2 is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.
We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.
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Of the people who fished at Clearwater Park today, 72 had a fishing license, and 8 did not. Of the people who fished at Mountain View Park today, 63 had a license, and 27 did not. (No one fished at both parks.)
Answers
| | Fishing License | No Fishing License |
| ------------- | -------------- | ------------------ |
| Clearwater | 72 | 8 |
| Mountain View | 63 | 27 |
To find the total number of people who fished at both parks, we can add up the number of people with a fishing license at each park:
72 + 63 = 135
Therefore, a total of 135 people fished at both parks today.
Will give brainliest answer
Answers
Answer:
Step-by-step explanation:
A(1) is the amount after 1 decade.
A(0.1) is the amount after 1 year.
Every year, the amount of CO₂ increases by a factor of 1.06^(0.1) ≅ 1.0058
Write the equation of the line that is parallel to the line y=−74x−2 through the point (4,-2).
Answers
Parallel lines have the same slope, so since the slope of the given line is -74, the slope of the line we want to find is also -74.
Substituting into point-slope form,
\(y+2=-74(x-4)\\\\y+2=-74x+296\\\\\boxed{y=-74x+294}\)
The 2007 BMW 335i Coupe is offered with a choice of 14 exterior colors, 5 interior colors, and 4 trims. How many combinations involving color and trim are available for the model?
Answers
Answer:
76 colors available
Step-by-step explanation:
Given
\(Exterior\ Colors = 14\)
\(Interior\ Colors = 5\)
\(Trims = 4\)
Required
Determine the possible combinations available
From the question, there is no distinction between the selection of external and internal color.
So:
\(Colors = 14 + 5\)
\(Colors = 19\)
The are 19 possible colors and 5 possible trims.
So, number of combination is answered using the following rule of product
\(Combination = Colors * Trims\)
\(Combination = 19 * 4\)
\(Combination = 76\)
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Answers
Answer:
B. 2:1
Step-by-step explanation:
The smaller rectangle is 2x1, the bigger one is 4x2.
We obtain similarity ratio by comparing any corresponding side of two similar objects, so we can either compare the long sides
4:2; this is equivalent to 2:1
or the short sides:
2:1
Either way, we arrive at similarity ratio of 2:1
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
Answers
The exponential function that can model the county population, y, x decades after Tiana was born, is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
\(y = a(b)^x\)
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 when y = 600000, hence:
\(y = 641000(0.99)^x\)
\(600000 = 641000(0.99)^x\)
\((0.99)^x = \frac{600000}{641000}\)
\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)
\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)
\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)
x = 6.6 decades.
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19. Write an ordered pair for the point in Quadrant II, that is 8 units away from the point Q
(0.75 -3.25) on a coordinate plane.
Answers
An ordered pair of point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)
In this question, we need to find an ordered pair for the point in Quadrant II, that is 8 units away from the point Q(0.75 -3.25) on a coordinate plane.
If we have a coordinate point (x, y) in Quadrant ||, if the coordinate is 8 units away, the resulting coordinate will be expressed as (x - 8, y + 8)
Given the point Q(0.75, -3.25) on the coordinate the plane, if a point in Quadrant II is 8 units away from this point, the resulting point will be (0.75 - 8, -3.25 + 8) which is (-7.25, 4.25)
Therefore, an ordered pair a point in Quadrant II is 8 units away from this point, the resulting point will be (-7.25, 4.25)
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During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.
Answers
The price of the bed after mark up is $475.00
What is discount?Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.
The first discount given is 25% , therefore the price of the bed before mark up is
25/100 × 800
= 25×8
= 200
the price before mark up = 800-200 = $600
Another 25% is given after the first sale, there the price of the bed after mark up is
25/100 × 600
=$ 125
price after markup = 600-125
= $475.00
therefore the price of the bed after markup is $475.00
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Mme potatana ask the children to count as a whole class from 1 to 20 Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count. in your view support the method that you find important to enhance the strong number sense. Provide appropriate examples for your chosen method.
Answers
The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.
In order to enhance strong number sense in children, there are various methods that can be used.
In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.
Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.
The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.
This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.
Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:
1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.
2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.
3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.
Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.
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Please help me, I will MARK AS BRAINLIEST.
Answers
Answer:
The third one
Step-by-step explanation:
-2(4+ x) + 3x = -4
Solve for X
Answers
Answer:
x = 4
Step-by-step explanation:
First expand the bracket.
- 8 - 2x + 3x = -4
Separate the terms and numbers.
-2x + 3x = -4 + 8
Simplify and solve for x.
x = 4
⇒I will start by multiplying out the bracket. 2 will multiply all the term in the brackets also considering their signs.
\(-2(4)-2(x)+3x=-4\\-8-2x+3x=-4\\\)
⇒The next step is to group like term together.
\(-2x+3x=-4+8\\\)
⇒Simplify the like terms
\(x=4\)
is y=4x+2 proportional?
Answers
Answer: yes
Step-by-step explanation:
What is (4 x 100) + 20.
Answers
Answer:
420 is the correct answer
Answer:
420
Step-by-step explanation:
Lucas ran 6 laps in 313.8 seconds. If he ran at the same speed for each lap, what was his time of each lap? Explain how you solved the problem
Answers
318.8/6=53.13
So he runs 53.13 seconds per lap.
you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm
Answers
The rectangular block of wax can make approximately 2 candles.
How do we determine the number of candles that could be made by that block of wax?To calculate the number of candles, we use the formula
V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm
V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm
1800 / 972 = 1.85
The above answer is based on the full question below;
you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.
The height of the candle is 12cm and the base width is 9cm
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Simplify the expression by combining like terms.
6x + 9 + 2x + 4
Does anyone know the answer?
Answers
Answer:
8x + 13
Step-by-step explanation:
"Like terms" means the same kind of algebraic expression...the 6x and the 2x are "like terms" because they both have an x in them. The 9 and the 4 are both constants, which means they are plain numbers. So 6x and 2x is 8x .
9+4 is 13 just like elementary school.
So all together,
6x + 9 + 2x + 4
6x + 2x + 9 + 4
8x + 13
We can rearrange the terms because the problem has all addition in between the terms.
Find the radius of a sphere whose volume is 12345mm
Answers
Answer:
14.34mm
Step-by-step explanation:
The formula for the volume of a sphere = 4/3nr³
where
n = 22/7
r = radius
give the volume of the sphere, we can determine the radius
12345 = 4/3 x 22/7 x r³
12345 = 88/21 x r³
divide both sides by 21/88
r³ = 2945.965909
take the cube root of both sides
r = 14.34 mm
Quadrilateral GHIJ is similar to quadrilateral KLMN. Find the measure of side NK.
Figures are not drawn to scale.
Answers
Answer:
NK = 14.4
Step-by-step explanation:
Given the following question:
We know that the two sides are similar
JI = 3, NM = 7.2
The scale factor is 2.4 since....
\(3\times2.4=7.2\)
Knowing the two sides are similar and if we multiply JI by 2.4, we get NM we can easily do the same for JG and NK.
JG = 6
\(6\times2.4=14.4\)
\(=14.4\)
NK = 14.4
Hope this helps.
clara is building a triangular garden. she wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long . what expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side ?
Answers
The expression to determine the perimeter of the triangle in terms of the shortest side (s) is 3s + 15.
To determine the perimeter of the triangle, we need to express the lengths of all three sides in terms of the shortest side (s).
The longest side is three more than twice the length of the shortest side. This can be expressed as 2s + 3.
The third side is twelve feet long.
Now, let's denote the lengths of the sides as follows:
Shortest side = s
Second side = 2s + 3
Third side = 12
To find the perimeter, we sum up the lengths of all three sides:
Perimeter = s + (2s + 3) + 12
Simplifying the expression:
Perimeter = s + 2s + 3 + 12
Perimeter = 3s + 15
Therefore, the expression to determine the perimeter of the triangle in terms of the shortest side (s) is 3s + 15.
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What is the measure of angle AED?
Answers
Answer:
Step by step explanation:
well this is simble you just do it
in how many ways can the letters of MCHNLRN be arranged
Answers
Answer:
2520
Step-by-step explanation:
There are 7 letters in MCHNLRN and they can be arranged into 7 ways:
7! = 5040 ways in total
However, the letter 'N' is repeated so we have to divide it by 2.
5040 ÷ 2 = 2520 ways
Answer:
2,520 ways
Step-by-step explanation:
MCHNLRN has 7 letters with one repetition.
therefore, =7!/2!
=2,520 ways
A fraternity charge $2.00 admission for dudes and $1.00 admission for ladies. They made $45 and sold 35 tickets how many ladies attended the party
Answers
After solving the equations, we know that a total of 25 ladies attended the party.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
So, take dudes as x and ladies as y.
Now, form the required 2 equations as follows:
2x + y = 45 ...(1)
x + y = 35 ...(2)
Work on equation (2):
x + y = 35
x = 35 - y
Now, substitute x = 35 - y in equation (1):
2x + y = 45
2(35-y) + y = 45
70 - 2y + y = 45
-y = -25
y = 25
Since ladies were charged $1 for each ticket, then 25 ladies attended the party.
Therefore, after solving the equations, we know that a total of 25 ladies attended the party.
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Alana runs 4 laps around the track in 10 minutes. If Alana runs 17 laps at the same rate how long does it take her
Answers
Answer:
42 minues 5 seconds to do 17 laps.
Step-by-step explanation:
it takes her 2 minuetes and 50 seconds to do 1 lap if you multiply 2.5x17=
42 munites and 5 secondesto do 17 laps
Answer:
It would take 42.5 min
Step-by-step explanation:
4/10 = 2.5(unit rate for every lap it takes 2.5 min)
17 x 2.5 = 42.5