Please help! Will mark brainliest ! Thank you! Please explain so I can actually understand the question too :)

Answer:

a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]

b) The value of the integral is 18

Step-by-step explanation:

a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that

[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]

From here, we have that

[tex] yz = \frac{\partial f}{\partial x}[/tex]

if we integrate both sides with respect to x, we get that

[tex] f(x,y,z) = xyz+ g(y,z)[/tex]

where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is

[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]

This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form

[tex] f(x,y,z) = xyz+g(z)[/tex]

If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get

[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]

This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]

So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]

b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is

[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]

Answer:

4: 4[tex]\pi^2[/tex]

Step-by-step explanation:

2[tex]\pi[/tex] x 5 x [tex]x[/tex] = 10[tex]\pi x[/tex]

10[tex]\pi x[/tex] = 40[tex]\pi ^3}[/tex]

x = 4[tex]\pi^2[/tex]

Answer:

4π units

Step-by-step explanation:

v=lwh

40π^3=2π×5×h

40π^3=10π^2×h

h=40π^3/10π^2

h=4π units

mark brianliest if my answer suit your question please.

Answer:

D

Step-by-step explanation:

When there is an negative sign inside in a radical, then we remove that and put out of the radical classifying as "i". Then, reduce 63 into smallest form and we can write it as 9 and 7. 9 is a perfect square of 3 so we put it outside and the answer is D.

Answer:

54 square units

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]\frac{1}{2}[/tex] x base x height

The base is 12

The height is 9

So 1/2 x 12 x 9 = 54 square units

Answer:

17.3 Inches

Step-by-step explanation:

Given that the diagonal of a cube = 30 inches

For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]

Therefore:

[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]

Side Length of the cube is 17.3 Inches.

Answer:

17.3

Step-by-step explanation:

Edge 2020

Answer:

P(greater than 1.25 minutes) = 0.8611 (Approx)

Step-by-step explanation:

Given:

Waiting time = 0 - 9 minutes

Find:

Probability that selected passenger has a waiting time greater than 1.25 minutes.

Computation:

⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =

⇒  P(greater than 1.25 minutes) = [9-1.25] / 9

⇒ P(greater than 1.25 minutes) = [7.75] / 9

⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)

Answer:

[tex]\frac{56}{96}[/tex] is your answer

Step-by-step explanation:

[tex]\frac{7}{12}[/tex]=[tex]\frac{x}{96}[/tex]

to get to 96 you must multiply by 8

and since you did that for the bottom then you need to do the same for the top,

[tex]\frac{56}{96}[/tex] is your answer

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]

So it will take them approximately 51.43 minutes to complete the project together.

Answer:

\sqrt(12) hope this helped.

Answer:

Per hour: 2.40740740741

Step-by-step explanation:

you have to divided 65 and 27 so

65/27

which is 2.40740740741

Answer:

The hydro-static force [tex]F=245000N[/tex]

Step-by-step explanation:

given data

base = 3 m

height = 5 m

density of water = 1000 kg/m3

Acceleration due to gravity = 9.8

The area if the strip needs to be calculated using similar triangular formula as well as the hydrostatic force

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION

Answer:

The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]

Step-by-step explanation:

Solution

The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.

Thus,

Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.

Now,

If the company operates mine 1 for x1 days and mine​ #2 for x2 days

Then,

The total output becomes x₁v₁ +x₂v₂ which is the same output to  b = [296 2454]

Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]

So, the vector equation becomes  x₁v₁ +x₂v₂ = [296 2454]

Answer:

0-4: Make it 1 unit tall

5-9: Make it 5 units tall

10-14: Make it 4 units tall

15-19: Make it 1 unit tall

20-24: Make it 2 units tall

Step-by-step explanation:

0-4: 3 (1 number)

5-9: 5, 5, 7, 8, 8 (5 numbers)

10-14: 10, 11, 12, 13 (4 numbers)

15-19: 17 (1 number)

20-24: 22, 23 (2 numbers)

Answer:

  3/2

Step-by-step explanation:

The graph rises 3 feet for each 2 seconds to the right. The slope is ...

  rise/run = (3 ft)/(2 s) = (3/2) ft/s

The numerical value of the slope is 3/2 or 1.5. The associated units are feet per second.

Answer:

the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;

P(X) = 0.0043

P(X) = 0.43%

Step-by-step explanation:

The probability that a dentist recommend Colgate is;

P = 90% = 0.9

The probability that a dentist doesn't recommend Colgate is;

P' = 1 - P = 1 -0.9 = 0.1

Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;

8 will recommend and two will not recommend it.

P(X) = P^8 × P'^2

P(X) = (0.9)^8 × (0.1)^2

P(X) = 0.0043

P(X) = 0.43%

The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.

Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.

Probability of dentist, who recommend Colgate toothpaste = 0.9

Probability of dentist, who does not recommend Colgate toothpaste,

                                       = 1 - 0.9 = 0.1

When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend  Colgate toothpaste and 2 recommend other tooth paste.

Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,

                  [tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]

Learn more:

https://brainly.com/question/20046335

Step-by-step explanation:

=> The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid

=> The volume of a cone can be found by V = 1/3(Ab)(H) where Ab is base area and H is the height of the cone

The difference between both is that is it's base. A cone has a polygonal base while a pyramid has a tetragonal base

Answer:

The equation are

    [tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]

    [tex]y = \frac{12-z }{12} 8sin (2z)[/tex]

    z = z

Step-by-step explanation:

From the question we are told that

   The radius of the conical helix is  [tex]r= 8[/tex]

    The height of the conical helix is  [tex]h = 12[/tex]

    The angular frequency  is  [tex]w = 2[/tex]

The plot of the conical helix is  shown on the first uploaded image

 Generally  the parametric equation of a conical helix is mathematically represented as

for x -axis

     [tex]x =\frac{ h-z }{h} r cos (wz)[/tex]

substituting values

      [tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]

for  y-axis

     [tex]y = \frac{h-z }{h} rsin (wz)[/tex]

substituting values

      [tex]y = \frac{12-z }{12} 8sin (2z)[/tex]

for  z-axis

   z = z

Answer:

4

Step-by-step explanation:

T(n) = n² + 3

T(1) = 1² + 3 = 1 + 3 = 4

Answer:

100

Step-by-step explanation:

When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.

Answer:

100

Step-by-step explanation:

:3

Answer:

Step-by-step explanation:

We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.

The area is the product of length and width, so is ...

  A = (3x +5)(x) = 3x^2 +5x

To make the area 350, we can find the value of x from ...

  3x^2 +5x = 350

This can be solved a number of ways. One of them is "completing the square".

  3(x^2 +5/3x) = 350

We choose to divide by 3 and add the square of half the x-coefficient.

  x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2

  (x +5/6)^2 = 4225/36 . . . . simplify

  x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root

  x = 10  or  -11 2/3 . . . . subtract 5/6

The positive solution is the one of interest: x = 10.

The driveway is 10 ft wide and 35 ft long.

Answer:

54

Step-by-step explanation:

A = (9*12)/2

A = 9*6

A = 54

Answer:54

Step-by-step explanation:

multiply 9 and 12 then divide by 2 because a triangle is half of a square

Answer:

20 hours

Step-by-step explanation:

first calculate volume:

12x10x3=360

then divide by 18

360/18=20

So 20 hours in total

Answer: -8

Step-by-step explanation:

Answer:

No, because the​ z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual​ event, namely within 2 standard deviations of the mean of the sample means.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Unusual

If X is more than two standard deviations from the mean, x is considered unusual.

In this question:

[tex]\mu = 511, \sigma = 119, n = 55, s = \frac{119}{\sqrt{55}} = 16.046[/tex]

A random sample of 55 students from this school was​ selected, and the mean math SAT score was 528. Is the high school justified in its​ claim?

If Z is equal or greater than 2, the claim is justified.

Lets find Z.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{528 - 511}{16.046}[/tex]

[tex]Z = 1.06[/tex]

1.06 < 2, so 528 is not unusually high.

The answer is:

No, because the​ z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual​ event, namely within 2 standard deviations of the mean of the sample means.

The statement that could be made regarding the high school about the justification of its claim would be:

- No, because the​ z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual​ event, namely within 2 standard deviations of the mean of the sample means.

Given that,

μ = 511

σ = 119

Sample(n) = 55

and

s = [tex]119/\sqrt{55}[/tex]

[tex]= 16.046[/tex]

As we know,

The claim of the high school could be valid and justified only when

[tex]Z > 2[/tex]

To find,

The value of Z

So,

[tex]Z = (X -[/tex] μ )/σ

by putting the values using Central Limit Theorem,

[tex]Z = (528 - 511)/16.046[/tex]

∵ [tex]Z = 1.06[/tex]

Since [tex]Z < 2[/tex], the claim is not justified.

Learn more about "Standard Deviation" here:

brainly.com/question/12402189

Answer:

36 cm

Step-by-step explanation:

Since all measurements of the figure are the same, that means that this figure is a square.  To find the area of a figure multiply length by width.  Since this figure is a square and all sides are equal, we multiply 6 by 6 for an area of 36 cm.

Answer:

pic wont load

Step-by-step explanation:

Answer:

The quarter circle's area is 38.47 yard²

Step-by-step explanation:

The area of a full circle is pi * r ²

The area of a quarter circle is 1/4 * pi * r ²

Given:

Use 3.14 for pi

Round to the nearest hundredths.

Perimeter of quarter circle is 24.99 yards

For r you must leave it as 'r' because we do not know it for now...

1. Circumference of a full circle = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * r )

1/2 * 3.14 * r

1.57 * r

3 Since r = 'r'

We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.

4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch

1.57 * r + 2 * r = 24.99

( 1.57 + 2 ) * r = 24.99

3.57 * r = 24.99

Divide left and right of the = sign by 3.57

3.57 / 3.57 * r = 24.99 / 3.57

1 * r = 24.99 / 3.57

r = 7

The area of a quarter circle is 1/4 * pi * r ²

1/4 * pi * 7²

1/4 * 49 * pi

49/4 * pi

49/4 * 3.14

38.465

Round to the nearest hundredths gives 38.47 yard²

The quarter circle's area is 38.47 yard²

Answer:

x = 17 or x = ±7i

Step-by-step explanation:

x³ − 17x² + 49x − 833 = 0

x² (x − 17) + 49 (x − 17) = 0

(x² + 49) (x − 17) = 0

x = 17 or ±7i

One hundred thirty-nine billion, two hundred four million, five hundred thirty-nine thousand, nine hundred twelve.

Hope this helped!

Answer:

[tex]<38,52>[/tex]

Step-by-step explanation:

[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]

We are required to express 7u-5v+w in the form <a,b>.

[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]