3

2

Vx

1

1

2 3 4 5 6 7 8 9 10 11 12 X

Magnets

Using equivalent ratios, which statements are true about the cost per magnet? Check all that apply.

The cost of 2 magnets is $1.

The cost of 9 magnets is $3.

The cost of 10 magnets is $3.

The cost of 4 magnets is $2.

The cost of 6 magnets is $2.

The cost of 3 magnets is $1.

Next

Submit

Save and Exit

Mark this and retum

Answers

Answer 1

Answer:

The cost of 3 magnets is $1

The cost of 9 magnets is $3

The cost of 6 magnets is $2

Step-by-step explanation:

The cost of magnets is calculated using the equivalent ratio. If 3 magnets cost  $ then the multiple used for the calculations of more magnets is 3. The ratio for every magnet price is 1 : 3 which means every dollar will be equal to 3 magnets. The cost of 3 magnets is $1, the cost of 6 magnets is $2 and cost of 9 magnets is $3.


Related Questions

What are the slope and y-intercept of the equation 2x - 5y = -10?

Answers

Answer:

Step-by-step explanation:

y=2/5x+2

x= 5/2y-5

hopefully this works

Annie has 3/2 pounds of cookie dough. If she needs 1/16 of a pound of cookie dough to make one cookie, how many cookies can she make

Answers

Answer:

[tex]\boxed{\sf 24\ cookies}[/tex]

Step-by-step explanation:

1 cookie = 1/16 of a pound of cookie

If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16

=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]

=> [tex]\frac{3}{2} * 16[/tex]

=> 3*8

=> 24 cookies

Answer:

24 cookies

Step-by-step explanation:

3/2= 1.5 and 1/16= 0.0625

if you divide the amount of dough you have by the amount needed for each cookie you will have 24

1.5/0.0625=24

3. Solve for x2=81 C. 10​

Answers

Answer:

9

Step-by-step explanation:

9 x 9 = 81

Answer:

x = ±9

Step-by-step explanation:

x^2 = 81

Take the square root of each side

sqrt(x^2 ) = ±sqrt(81)

x = ±9

If f(x)=2x-6and g(x)=3x+9 find (f+g)(x)

Answers

Answer:

(f+g)(x) = 5x + 3

Step-by-step explanation:

(f+g)(x) is the sum (term by term) of f(x) and g(x):

(f+g)(x) = 2x - 6 + 3x + 9

Combining like terms, we get

(f+g)(x) = 5x + 3

Answer:

(f+g)(x)= 5x+3

Step-by-step explanation:

The question asks us to find (f+g)(x). In other words, the sum of f(x) and g(x).

f(x) + g(x)

We know that f(x)= 2x-6 and g(x)=3x+9. Therefore, we can substitute the expressions in.

(2x-6) + (3x+9)

Now, simplify by combining like terms. Add the terms with variables, then the terms without variables.

(2x+3x) + (-6+9)

Add 2x and 3x.

5x + (-6 + 9)

Add -6 and 9.

5x + 3

If f(x)=2x-6and g(x)=3x+9, then (f+g)(x) is 5x+3

Explain the difference between using the sine ratio to solve for a missing angle in a right triangle versus using the cosecant ratio. You must use complete sentences and any evidence needed (such as an example) to prove your point of view. (10 points)

Answers

Answer:

The sine ratio is the ratio between the opposite side over hypotenuse. The cosecant ratio is the ratio between the hypotenuse over the opposite side, therefore cosecant is the reciprocal of sine.

To find a missing angle using sine, you would need to use the inverse of sine. For example,  if the sine was  [tex]\frac{30}{40}[/tex], to find the angle you would need to find sin⁻¹ of  [tex]\frac{30}{40}[/tex] which is x =  sin⁻¹ (0.75). Therefore x equals approximately 49°.  

Express the product of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]

Answers

Answer:

Solution : 6 + 6i

Step-by-step explanation:

[tex]-3\left[\cos \left(\frac{-\pi }{4})\right+i\sin \left(\frac{-\pi }{4}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi }{2}\right)\right][/tex]

This is the expression we have to solve for. Now normally we could directly apply trivial identities and convert this into standard complex form, but as the expression is too large, it would be easier to convert into trigonometric form first ----- ( 1 )

( Multiply both expressions )

[tex]-6\sqrt{2}\left[\cos \left(\frac{-\pi }{4}+\frac{-\pi \:\:\:}{2}\right)+i\sin \left(\frac{-\pi \:}{4}+\frac{-\pi \:\:}{2}\right)\right][/tex]

( Simplify [tex]\left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] for both [tex]\cos \left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] and [tex]i\sin \left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] )

[tex]\left(\frac{-\pi }{4}+\frac{-\pi }{2}\right)[/tex] = [tex]\left(-\frac{3\pi }{4}\right)[/tex]

( Substitute )

[tex]-6\sqrt{2}\left(\cos \left(-\frac{3\pi }{4}\right)+i\sin \left(-\frac{3\pi }{4}\right)\right)[/tex]

Now that we have this in trigonometric form, let's convert into standard form by applying the following identities ----- ( 2 )

sin(π / 4) = √2 / 2 = cos(π / 4)

( Substitute )

[tex]-6\sqrt{2}\left(-\sqrt{2} / 2 -i\sqrt{2} / 2 )[/tex]

= [tex]-6\sqrt{2}\left(-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] = [tex]-\frac{\left(-\sqrt{2}-\sqrt{2}i\right)\cdot \:6\sqrt{2}}{2}[/tex]

= [tex]-3\sqrt{2}\left(-\sqrt{2}-\sqrt{2}i\right)[/tex] = [tex]-3\sqrt{2}\left(-\sqrt{2}\right)-\left(-3\sqrt{2}\right)\sqrt{2}i[/tex]

= [tex]3\sqrt{2}\sqrt{2}+3\sqrt{2}\sqrt{2}i:\quad 6+6i[/tex] - Therefore our solution is option a.

Which point is located at (5, –2)?

Answers

Answer: Point D

Explanation:

The origin is the center of the grid. This is where the x and y axis meet. The location of this point is (0,0).

Start at the origin and move 5 places to the right. Note how the x coordinate is 5 which tells us how to move left/right. Positive x values mean we go right.

Then we go down 2 spots to arrive at point D. We move down because the y coordinate is negative.

You could also start at (0,0) and go down 2 first, then to the right 5 to also arrive at point D. Convention usually has x going first as (x,y) has x listed first.

Answer:

Point D is located at (5, -2)

Step-by-step explanation:

The coordinates are in the form of (x,y) so that means the point has the x value of 5 and the y value of -2

For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is

Answers

Answer:

1.16

Step-by-step explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0)  =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) =  0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the  left until the first column is reached, we see that the value was 1.1.  similarly, we did the same in the  upward direction until the top row is reached, the value was 0.06.  The intersection of the row and column values gives the area to the two tail of z.   (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877

60feet to meters plaese with work

Answers

Answer:

60 Feet =  18.288 Meters

Step-by-step explanation:

foot = 12 inch = 0.3048 m

0.3047 × 60

18.288 meters

The cost in dollars y of producing x computer
desks is given by y = 40x + 4000
X
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $6200. (Hint: Find x when y = 6200.)
a. Complete the table.
х
100
200
300
y
b. For $6200,_ computer desks can be produced

Answers

Answer:

a.

y= 40x +4000

x= 100 --> y= 40(100)+4000= 4000+4000=8000

x=200 --> y= 40(200)+4000= 6000+4000= 10000

x=300 --> y= 40(300)+4000= 12000+4000= 16000

(in $)

b.

y= 40x+4000

6200= 40x+4000

6200-4000= 40x

2200= 40x

2200/40= x

55= x

(in unit)

Step-by-step explanation:

I hope this helps

if u have question let me know in comments ^_^

2. You are going to produce tennis shoes
that come in 3 different colors. In order to
decide how many to make in each color,
you conduct a survey. Of the 300 people
you survey, 75 said that they would
purchase the yellow shoes. If you are
going to make 10,000 pairs of shoes, how
many should be yellow?


Please help thank you

Answers

Answer:

Hey there!

[tex]\frac{75}{300}[/tex]=[tex]\frac{x}{10000}[/tex]

750000=300x

x=2500

They should make 2500 yellow shoes.

Hope this helps :)

A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within 2 of the population mean?

a. Since the mean is not given, there is no answer to this question.

b. -0.6826

c. 0.3413

d. 0.6826

e. -0.3413

Answers

Answer:

The correct option is  D

Step-by-step explanation:

From the question we are told that

    The standard deviation is  [tex]\sigma = 16[/tex]

     The sample size is  n =  64

The standard error of mean is mathematically evaluated as

        [tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

        [tex]\sigma _{\= x } = \frac{16 }{\sqrt{64} }[/tex]

        [tex]\sigma _{\= x } = 2[/tex]

Generally the probability that the sample mean will be within 2 of the population mean is mathematically represented as

              [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < \frac{ \= x - \mu }{\sigma_{\= x }} < \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]

Generally  [tex]\frac{ \= x - \mu }{\sigma_{\= x }} = Z (The \ standardized \ value \ of \ \= x )[/tex]

So

         [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < Z< \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]

         [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( -2 }{\sigma_{\= x }} < Z< \frac{ 2 }{\sigma_{\= x }} )[/tex]

substituting values

        [tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{-2 }{2} < Z< \frac{ 2 }{2} )[/tex]

        [tex]P( \mu - 2 < \= x < \mu + 2) = P(-1< Z< 1 )[/tex]

=>     [tex]P( \mu - 2 < \= x < \mu + 2) = P(Z < 1) - P(Z < -1)[/tex]

From the normal distribution table [tex]P(Z < 1 ) = 0.84134[/tex]

                                                          [tex]P(Z < - 1) = 0.15866[/tex]

=>  [tex]P( \mu - 2 < \= x < \mu + 2) = 0.84134 - 0.15866[/tex]

=>   [tex]P( \mu - 2 < \= x < \mu + 2) = 0.6826[/tex]

It takes amy 8 minutes to mow 1/6 of her backyard. At that rate how many more minutes will it take her to finish mowing her backyard

Answers

Answer:

40 minutes

Step-by-step explanation:

If it takes her 8 minutes to mow 1/6 of it, we can find the total amount of time it  will take by multiplying 8 by 6, since 1/6 times 6 is 1 (1 represents the whole lawn mowed)

8(6) = 48

The question asks for how many more minutes it will take, so subtract 48 by 8.

48 - 8 = 40

= 40 minutes

Answer:

40 minutes

Step-by-step explanation:

We can use ratios to solve

8 minutes          x minutes

------------------- = ----------------

1/6 yard                 1 yard

Using cross products

8 * 1 = 1/6 x

Multiply each side by 6

8*6 = 1/6 * x * 6

48 = x

48 minutes total

She has already done 8 minutes

48-8 = 40 minutes

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.
A. 68%
B. 99.7%
C. 47.5%
D. 34%

Answers

Answer:

C. 47.5%

Step-by-step explanation:

The  summary of the given statistics include:

mean =150000

standard deviation: 1200

The  objective is to use tributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: between $150,000 and $152,400

The z score formula can be use to calculate the percentage of the buyer who paid.

[tex]z = \dfrac{X - \mu}{\sigma}[/tex]

For the sample mean x = 150000

[tex]z = \dfrac{150000 - 150000}{1200}[/tex]

[tex]z = \dfrac{0}{1200}[/tex]

z = 0

For the sample mean x = 152400

[tex]z = \dfrac{152400 - 150000}{1200}[/tex]

[tex]z = \dfrac{2400 }{1200}[/tex]

z  = 2

From the standard normal distribution tables

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5% therefore option C is correct

This question is based on concept of  statistics. Therefore, correct option is C i.e. 47.5% of buyers who paid: between $150,000 and $152,400 if the standard deviation is $1200.

Given:

Mean is $150,000, and

Standard deviation is $1200.

We need to determined the percentage of buyers who paid: between $150,000 and $152,400 as per given mean and standard deviation.

By using z score formula can be use to calculate the percentage of the buyer who paid,

[tex]\bold{z=\dfrac{x-\mu }{\sigma}}[/tex]

As given in question sample mean i.e. X= 150,000

[tex]z=\dfrac{150000-150000}{1200} \\\\z= \dfrac{0}{1200}\\\\z=0[/tex]

Now for the sample mean X = 152,400 ,

[tex]z=\dfrac{152400-150000}{1200} \\\\\\z= \dfrac{24000}{1200}\\\\\\z=2[/tex]

By using standard normal distribution table,

P(150000 < X < 152400) = P(0 < z < 2 )

P(150000 < X < 152400) =P(z<2) -P(z<0)

P(150000 < X < 152400) =0.9772 -0.5

P(150000 < X < 152400) = 0.4772

P(150000 < X < 152400) = 47.7%  which is close to 47.5%

Therefore, correct option is C that is 47.5%.

For further details, please prefer this link:

https://brainly.com/question/23907081

The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]

a. 0
b. 1
c. 4​

Answers

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

you write a short story, but you want to make sure your work is protected before you post it online. what should you do to help protect your copyright?

Answers

Answer:

Hey there!

Here are a few steps:

Make sure your work is properly marked, because then it will be protected under law.

Register your work.

Keep or register supporting evidence.

Let me know if this helps :)

The area of a rectangular garden if 6045 ft2. If the length of the garden is 93 feet, what is its width?

Answers

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

Answer:

[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]

Step-by-step explanation:

The area of a rectangle formula is given as,

[tex]\mathrm{area = length \times width}[/tex]

The area and length are given.

[tex]6045=93 \times w[/tex]

Solve for w.

Divide both sides by 93.

[tex]65=w[/tex]

The width of the rectangular garden is 65 feet.

Find the minimum and maximum values of 3 sin^2x – 2 cos^2x + 9

Answers

838373838393 7373hshjd

Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separated list.) ln(x) = 1 /x − 3

Answers

Answer:

  x ≈ {0.653059729092, 3.75570086464}

Step-by-step explanation:

A graphing calculator can tell you the roots of ...

  f(x) = ln(x) -1/(x -3)

are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.

In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.

Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.

_____

A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,

I don’t understand this, may I get some help?

Answers

Answer
B. 8.0023 10(tiny 4)

Explain
In scientific notation, the goal is to get any select number between the numbers 1 and 10. To find the answer quickly, i find where the decimal is (in this case it would be at the end of the number because there are no decimal numbers) and count how many numbers it takes to get between 1 and 10 (diagram below to show what i mean)

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

80,023 written in scientific notation is [tex]8,0023[/tex] x [tex]10^4[/tex].

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 80,023

New Number: 8.0023

Step 2

New Number: 8 . 0 0 2 3

Decimal Count:   1 2 3 4

Now, to find b, count how many places to the right of the decimal.

There are 4 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10^b

a = 8.0023

b = 4

Now the whole thing:

8.0023 x 104

Step 4

Check your work:

10^4 = 10,000 x 8.0023 = 80,023

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

What is the relationship between factorising and expanding?

Answers

Answer:

The relation ship is both are opposites

Step-by-step explanation:

so what is factorising ???

factorizing is like this example : 4x+32 = 4(x+8)

so u take the expression make it factorized or shorter or in a way that you multiply them .

what is expanding well its the opposite

suck as  4(x+8)=4x+32

Simply. Who ever answers this will be marked Brainlist.

Answers

Answer:

Step-by-step explanation:

Hello,

[tex]r^3s^{-2}\cdot 8r^{-3}s^4\cdot 4rs^5\\\\=r^{3-3+1}s^{-2+4+5}\cdot 8\cdot 4\\\\\boxed{=32\cdot r\cdot s^7}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

What is the correct answer and how can this be solved?

Answers

Answer:

[tex]$\mathbf{\frac{1}{19} }[/tex]

Step-by-step explanation:

[tex]$$\bullet \Nth \ Term;\\$$$\frac{n+2}{2n^{2} +3n-2}[/tex]

[tex]$$\bullet U_{10} \ Term;\\\\$$\boxed{\frac{(10+2) }{2*10^{2} +3*10-2}= \frac{1}{19} }[/tex]

Answer:

[tex]\boxed{\displaystyle \frac{1}{19}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{n+2}{2n^2 +3n-2}[/tex]

Replace n with 10 to find the 10th term.

[tex]\displaystyle \frac{10+2}{2(10)^2 +3(10)-2}[/tex]

Evaluate.

[tex]\displaystyle \frac{12}{2(100) +30-2}[/tex]

[tex]\displaystyle \frac{12}{200 +30-2}[/tex]

[tex]\displaystyle \frac{12}{228}[/tex]

Simplify.

[tex]\displaystyle \frac{1}{19}[/tex]

What is the range of g?

Answers

Answer:

R: {y∈R | -1 ≤ y ≤ 5}

Step-by-step explanation:

the lowest point is -1 and the highest point is 5.

Will mark Brainliest! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?

Answers

Answer:

0.16

Step-by-step explanation:

Length = 5 unitsNumber of broken sticks= 3Equal lengths =  5 units/3

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

2/5*2/5 = 4/ 25 = 0.16

Answer is 0.16

If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?

Answers

We have

M(X) = (X + 5)/(X - 1)

N(X) = X - 3

So,

M(N(X)) =  [(X - 3) + 5]/[(X - 3) - 1]

M(N(X)) =  [X + 2]/[X - 4]

The M(N(X)) domain will be:

D = {X / X ≠ 4}

4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be

H(X) = 1/(X - 4)

A professional soccer player kicked a ball across the field. The ball’s height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground?

Answers

Answer:

Hey there!

You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.

Let  me know if this helps :)

Answer:

–3 meters per second

Step-by-step explanation:

An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5 and 10.5 respectively. How long is the island ?

Answers

Answer:

154.10 Feets

Step-by-step explanation:

Given the following :

Height (h) of cliff = 320 feet

Angle of depression of near side = 16.5°

Angle of depression of far side = 10.5°

Using trigonometry :

We can obtain x and y as shown in the attached picture :

Tanθ = opposite / Adjacent

Adjacent = height of cliff = 320 Feets

For the near side :

Tanθ = opposite / Adjacent

Tan (16.5°) = x / 320

0.2962134 = x / 320

x = 0.2962134 * 320

x = 94.788318 Feets

For the far side :

Tanθ = opposite / Adjacent

Tan (10.5°) = x / 320

0.1853390 = x / 320

x = 0.1853390 * 320

x = 59.308494 Feets

Length of island = (59.308494 + 94.788318) feet

= 154.10 Feets

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a function f, then

Answers

If there is such a scalar function f, then

[tex]\dfrac{\partial f}{\partial x}=4y^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}[/tex]

Integrate both sides of the first equation with respect to x :

[tex]f(x,y,z)=4xy^2+g(y,z)[/tex]

Differentiate both sides with respect to y :

[tex]\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}[/tex]

[tex]\implies\dfrac{\partial g}{\partial y}=4e^{4z}[/tex]

Integrate both sides with respect to y :

[tex]g(y,z)=4ye^{4z}+h(z)[/tex]

Plug this into the equation above with f , then differentiate both sides with respect to z :

[tex]f(x,y,z)=4xy^2+4ye^{4z}+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}[/tex]

[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=0[/tex]

Integrate both sides with respect to z :

[tex]h(z)=C[/tex]

So we end up with

[tex]\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}[/tex]

Help! Marking as brainlyest


What is the effect on the graph of the function () = 1/ when () is replaced with 1/2() + 7? A) compressed vertically and shifted 7 units up B) stretched vertically and shifted 7 units down C) compressed vertically and shifted 7 units left D) stretched vertically and shifted 7 units right

Answers

Answer:

Step-by-step explanation:

I used x instead of ()

The initial function is:

● x = 1

The function after the changes is

● (1/2)x + 7

The function was shifted 15 unit to the left

Other Questions
Consent of the client before completion of a trade made between the firm and a client must be made when A) an investment adviser will be acting in the capacity of a principal B) a broker-dealer will be acting in the capacity of a principal C) a broker-dealer will be acting as a contra party to the trade D) a broker-dealer will be acting in the capacity of an agent What does Lincoln encourage in his speech How are we supposed to find the Perimeter? A researcher wants to use a confidence interval to estimate the proportion of college students in his state who plan to vote in the 2020 presidential election. He plans to randomly sample 120 college students, and plans to construct a 95% or 99% confidence interval. Which of these confidence intervals will be wider, and why describe three major philosophical theories of law (1) Shipping along rivers is not as popular as it once was. (2) It is done by air and trucking on interstates. (3) Rivers still provide viable routes for shipping, but it is no longer the most feasible method for moving materials. (4) As rivers declined in popularity, other shipping methods took their place as the best ways to ship merchandise. Which sentence lacks a logical transition? Which of the following is a specific variant of a character? A.) A Class B.) A Trait C.) A Species What steps are needed for word to create an index If two firecrackers produce a sound level of 81 dBdB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? What is the oppisite of 0.7? how do you find the area of an open cylinder... what is the Formula?? please help When Jack was hired in 2011 at Ford Motor Company, he was offered $14 an hour. His best friend Sam started at the same plant doing the same job two years earlier making $28 an hour. This is an example of HURRY !!! PLEASE HELP!! Kellianne lined up the interior angles of the triangle along line p below.Which statements are true for line p? Check all that apply.It is a straight line with a measure of 360.It stays the same even if the angles in the triangle change.The line will not be straight if one of the angles in the triangle is changed to an obtuse angle.The line is only straight when one of the angles is a right angle.It represents the sum of the measures of the interior angles of the triangle.The line will not be straight if all the angles in the triangle are acute.It combines the three interior angles of the triangle to form a straight line.It is a straight line with a measure of 180 el deposito de gasolina en una estacion de servicio alcanza para 5 dias si se venden 1400 galones diarios cuantos galones diarios deben venderse para que el deposito cura 7 dias? A company sold equipment that originally cost $290,000 for $145,000 cash. The accumulated depreciation on the equipment was $145,000. The company should recognize a: Solve the equation for x. x+5-3=4 Math Question (10 Points): Lourdes hadn't bothered to study for the essay exam, joking that her motto was "fake it til you make it." Now as she stared in horror at the test booklet, the blank pages were doing the laughing, knowing she had no answers. What kind of figurative language is used? When arterial blood pressure falls the body compensates to raise the blood pressure. Explain this process. Figure ABCD is a rectangle Find the value of x