What is the probability of the event where we randomly select a permutation of the letters A,B,C,D,E,F,G where B immediately precedes D.

The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

Learn more about force from this link:

https://brainly.com/question/12785175

#SPJ11

======================================================

Explanation:

Check out the diagram below. Locate -2 on the horizontal x axis. Draw a vertical line through this value. Mark where the vertical line crosses the curve. Call this point P. Then draw a horizontal line through point P to have it cross the y axis. This horizontal line crosses at y = 1

In short, x = -2 leads to y = 1

So that is why f(-2) = 1

This is another way of saying f(x) = 1 when x = -2.

Note: y = f(x) since both are outputs of a function

Answer: 2224000

Step-by-step explanation:

246 is double twice 82 (x4)

That means 139000 would be double four times

139000*2*2*2*2=139000*16=2224000

Hope that helps! Please make me Brainliest!

Answer:

1, 3, 9, 27, 81, is a geometric sequence.

Step-by-step explanation:

A geometric sequence is basically a sequence of numbers that's multiplied by or divided one specific set number each time.

0, 2, 6, 12, 72, does not have a set number it is multiplied or divided by each time.

4, 9, 14, 19, 24, adds 5 each time, it doesn't multiply

Answer:

D - 1, 3, 9, 27, 81, . . .

Step-by-step explanation:

Answer:

The first three have clear answers, which are

0.19 0.165 47.625

The last one can't be divided.I don’t know how many decimal places to keep, so I list its value.

0.2201565557729941

Answer:

Step-by-step explanation:

Area of a triangle is   A = height x base / 2

So plug in what you know.

42 = (14 x b)/2  get rid of the 2 by multiplying both sides by 2 which gives:

84 = 14 x b       get rid of the 14 by dividing both sides by 14

b = 84/14

b=6 cm

Area measures the 2 dimensional space a figure takes. The base of the considered triangle is 6 cm long.

Suppose that the considered triangle has base 'b' units and height 'h' units.

Then, its area will be:

\(A =\dfrac{1}{2} \times b \times h \: \rm unit^2\)

For this case, we are given that:

Then, from the formula for area of a triangle, we get:

\(A = b \times h \: \rm unit^2\\\\42 = \dfrac{1}{2}\times{b}\times{14}\\\\42 = b \times 7\\\\\text{Dividing both the sides by 7}\\\\\dfrac{42}{7} = \dfrac{b \times 7}{7}\\\\6 = b\\\\b = 6 \: \rm cm\)

Thus, the base of the considered triangle is 6 cm long.

Learn more about area of a triangle here:

https://brainly.com/question/14503701

The simplification of the given expression will be  \((-3x^2-15x-30)\).

Given expression is

\(-3(x+2)^2 -3+3x\)

By applying  \((a+b)^2=a^2+2ab+b^2\)  we get

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

Multiplying by -3 into the whole bracket we get

\(-3x^2-18x-27-3+3x\)

\(-3x^2-18x-30+3x\)

\(-3x^2-15x-30\)

Thus the simplification of the given expression will be  \((-3x^2-15x-30)\)

To know more about Simplification follow

https://brainly.com/question/723406

Answer:

B. –3x^2 – 15x – 30

Step-by-step explanation:

Answer:

4 * pi

Step-by-step explanation:

Given r = 10

Formula for the circumference of this full circle is:

2 * r * pi

2 * 10 * pi = 20 * pi

Given one (biggest) part = 16 * pi of this circle.

The other (smaller) part must therefore be:

20 * pi - 16 * pi

4 * pi

The volume generated by rotating the given region about the y-axis is V = ∫[0 to 25/2] A(y) dy. Evaluating this integral will give us the desired volume.

We are given the region bounded by y = 25/2, y = 0, and x = 4, which forms a rectangle in the xy-plane. To find the volume generated by rotating this region about the y-axis, we can consider a vertical line parallel to the y-axis at a distance x from the axis. As we rotate this line, it sweeps out a disk or washer with a certain cross-sectional area.

To determine the cross-sectional area, we need to consider the distance between the curves y = 25/2 and y = 0 at each value of x. This distance represents the thickness of the disk or washer. Since the rotation is happening about the y-axis, the thickness is given by Δy = 25/2 - 0 = 25/2.

Now, we can express the cross-sectional area as a function of y. The width of the region is 4, and the height is given by the difference between the curves, which is 25/2 - y. Therefore, the cross-sectional area can be calculated as A(y) = π * (4^2 - (25/2 - y)^2).

To find the total volume, we integrate the cross-sectional area function A(y) over the range of y values, which is from y = 0 to y = 25/2. The integral represents the sum of all the infinitesimally small volumes of the disks or washers. Thus, the volume generated by rotating the given region about the y-axis is V = ∫[0 to 25/2] A(y) dy. Evaluating this integral will give us the desired volume.

To learn more about integral click here, brainly.com/question/31059545

#SPJ11

Answer:

---------------------------------------------

the answer is D 1/3

I just check Ed it

Answer:

Step-by-step explanation:

\(log_{10}(2000xy)-(log_{10}x})(log_{10}y)=4\\\\log_{10}(2000(xy))-log_{10}(xy)=4\\\\log_{10}(2000)+log_{10}(xy)-log_{10}(xy)=4\\\\log_{10}(2(1000)=4\\\\log_{10}2+log_{10}(1000)=4\\\\log_{10}2+log_{10}(10^3)=4\\\\log_{10}2+3log_{10}(10)=4\\\\log_{10}2\approx0.3\\\\Hence,\\\\log_{10}2+3\neq 4\)

\(log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\\\\log_{10}(2(yz))-log_{10}(yz)=1\\\\log_{10}2+log_{10}(yz)-log_{10}(yz)=1\\\\log_{10}2\neq 1\)

\(log_{10}(zx)-(log_{10}z)(log_{10}x)=0\\\\log_{10}(zx)-log_{10}(zx)=0\\\\0\equiv0\)

The chromosome number 25 is not a possible number produced in an allotetraploid formed from species I (2n = 22) and species II (4n = 28).

In an allotetraploid, the chromosome number is usually the sum of the chromosome numbers of the two parent species. In this case, species I has 2n = 22 and species II has 4n = 28. When these two species combine to form an allotetraploid, the expected chromosome number would be 2n + 4n = 6n = 50. However, the given options are between 25 and 30.

To calculate the possible chromosome numbers, we can consider different combinations of chromosomes from the two species. In an allotetraploid, chromosomes can pair up during meiosis, resulting in different combinations. Possible chromosome numbers for the allotetraploid would be:

- For species I: 2n = 22

- For species II: 4n = 28

Possible combinations for the allotetraploid:

- Species I (2n) + Species II (2n) = 22 + 22 = 44

- Species I (2n) + Species II (4n) = 22 + 28 = 50

- Species I (4n) + Species II (2n) = 44 + 22 = 66

- Species I (4n) + Species II (4n) = 44 + 28 = 72

Therefore, the chromosome number 25 is not a possible number produced in an allotetraploid formed from species I and species II.

Learn more about allotetraploid here: brainly.com/question/33277548

#SPJ11

Answer:

14 stacks

Step-by-step explanation:

Given :

There are 70 red colored blocks

There are 84 green colored blocks

The ratio of green blocks to red blocks is \($84/70 = 1.2$\)

Therefore, the ratio of g : b = 1.2 : 1

or                                  g : b = 6 : 5

Therefore, in order to calculate the number of stacks , we divide 84 by 6 and we get 14.

So we will get 14 block stacks to be made of 6 green blocks and 5 red blocks.

The derivative dy/dx of the equation ysin(x^2) = xsin(y^2) is given by (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

In the given equation, y and x are both variables, and y is implicitly defined as a function of x. To find dy/dx, we differentiate each term using the chain rule and product rule as necessary.

Differentiating the left-hand side of the equation, we apply the product rule to ysin(x^2). The derivative of ysin(x^2) with respect to x is dy/dxsin(x^2) + ycos(x^2)*2x.

Differentiating the right-hand side of the equation, we apply the product rule to xsin(y^2). The derivative of xsin(y^2) with respect to x is sin(y^2) + x*cos(y^2)2ydy/dx.

Now we have two expression for the derivative of the left and right sides of the equation. To isolate dy/dx, we can rearrange the terms and solve for it.

Taking the derivative of ysin(x^2) = xsin(y^2) with respect to x using implicit differentiation yields:
dy/dxsin(x^2) + ycos(x^2)2x = sin(y^2) + xcos(y^2)2ydy/dx.

By rearranging the terms, we can solve for dy/dx:
dy/dx * (sin(x^2) - 2yxcos(y^2)) = sin(y^2) - y*cos(x^2)*2x.

Finally, we can obtain the value of dy/dx by dividing both sides by (sin(x^2) - 2yxcos(y^2)):
dy/dx = (sin(y^2) - ycos(x^2)2x) / (sin(x^2) - 2yxcos(y^2)).

Learn more about implicit differentiation here brainly.com/question/31568657
#SPJ11

1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

To know more about the method of unitary, here

https://brainly.com/question/24587372

#SPJ1

Answer:

5=4x+13

4x+13=5

4x=5-13

4x= -8

x = -8÷4

x = -2

# be careful£

Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.

To determine the total distance Ronaldo's family drove, we need to add the distance from their house to the gas station and the distance from the gas station to the store. We can write this as:

\(4 6/10 km + 2 30/100 km\)

To add these two distances, we need to find a common denominator for the fractions. The smallest common denominator for 10 and 100 is 100, so we can convert the first distance to an equivalent fraction with a denominator of 100:

\(4 6/10 km = 4 60/100 km = 4.60 km\)

Then we can add the two distances:

\(4.60 km + 2.30 km = 6.90 km\)

Therefore, Ronaldo's family drove a total of 6.90 kilometres to get from their house to the store.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ9

\(\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=na^2\cdot \tan\left( \frac{180}{n} \right) ~~ \begin{cases} n=sides\\ a=apothem\\[-0.5em] \hrulefill\\ n=8\\ a=15 \end{cases}\implies A=(8)(15)^2\tan\left( \frac{180}{8} \right) \\\\\\ A=1800\tan(22.5^o)\implies A\approx 745.6\)

Make sure your calculator is in Degree mode.

Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

Step-by-step explanation:

It should be 33.49 sorry if I’m a little off!

Because if we take two obtuse triangles, then their sum will exceed 180°. We know, sum of all angles of a triangle is 180° and so a triangle couldn't be formed.

Answer:

i think its 17

Step-by-step explanation:

Answer:

388.79 (nearest hundredth)

Step-by-step explanation:

Given sequence:  324, 54, 9, ...

Therefore:

\(a_1=324\)

\(r=\textsf{common ratio}=\dfrac{54}{324}=\dfrac16\)

Sum of a finite geometric series:

\(S_n=\dfrac{a_1-a_1r^n}{1-r}\)

Sum of the first 6 terms → n= 6:

\(\begin{aligned}S_6 & =\dfrac{324-324(\frac16)^6}{1-\frac16}\\ & =\dfrac{324-\frac{1}{144}}{1-\frac16}\\ & =\dfrac{9331}{24}\\ & = 388.79\:\textsf{(nearest hundredth)}\end{aligned}\)

So

\(\\ \rm\Rrightarrow S_n=\dfrac{a-ar^n}{1-r}\)

\(\\ \rm\Rrightarrow S_6=\dfrac{324-324(1/6)^6}{1-1/6}\)

\(\\ \rm\Rrightarrow S_6=\dfrac{324-\dfrac{1}{12^2}}{\dfrac{5}{6}}\)

\(\\ \rm\Rrightarrow S_6=\dfrac{9331}{24}=388.79\)

Answer:

Infinite solution

Step-by-step explanation:

each is 1/3 when divided

The equation to determine how many bags Trisha brought is: T = 180 - (4 + 6)

We know that the total number of clementines is 180, Sal brought 4 bags and Joe brought 6. To determine how many bags Trisha brought, we need to determine the total number of bags that Sal and Joe brought together. We can do this by combining the two numbers together (4 + 6). This will give us a total of 10 bags. To determine how many bags Trisha brought, we need to subtract the total number of bags that Sal and Joe brought (10) from the total number of clementines (180). This gives us an answer of 170. This means that Trisha brought 170 clementines, or 7 bags. Therefore, the equation to determine how many bags Trisha brought is: T = 180 - (4 + 6).

Learn more about equations here:

https://brainly.com/question/29657988

#SPJ4

Answer:

(2xy)²

Step-by-step explanation:

please mark me as brainliest