Can someone please help me i literally am soo confused

Derivative Property [Multiplied Constant]:
\(\displaystyle (cu)' = cu'\)

Derivative Property [Addition/Subtraction]:
\(\displaystyle (u + v)' = u' + v'\)

Derivative Rule [Basic Power Rule]:

Integration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Rule [Fundamental Theorem of Calculus 1]:
\(\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)\)

Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:
\(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Del (Operator):
\(\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}\)

Div and Curl:

Divergence Theorem:
\(\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV\)

First, let's define what we are given:

\(\displaystyle \text{F} = x^2 \hat{\i} + y^2 \hat{\j} + z \hat{\text{k}}\)

Region D is the solid cube cut by coordinate planes and planes \(x = 2\). \(y = 2\), and \(z = 2\)

In order to use the Divergence Theorem, we first must find div F. We use partial differentiation and differentiation properties found under "Calculus" to attain div F:

\(\begin{aligned}\nabla \cdot \text{F} & = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial z}(z) \\& = 2x + 2y + 1 \\\textbf{div} \ \text{F} & = \boxed{2x + 2y + 1}\end{aligned}\)

∴ \(\displaystyle \boxed{ \textbf{div} \ \text{F} = 2x + 2y + 1 }\)

In order to find the outward flux of F across region D, we now must use the Divergence Theorem. Substitute our knowns into the Divergence Theorem Formula listed under "Multivariable Calculus":

\(\displaystyle \iiint_D \nabla \cdot \textbf{F} \, dV = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz\)

We can now evaluate the Divergence Theorem integral using basic + advanced integration techniques listed under "Calculus" and learned from "Multivariable Calculus":

\(\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dz \, dy \, dx \\& = \int\limits^2_0 \int\limits^2_0 {(2x + 2y + 1)z \bigg| \limits^2_0} \, dy \, dx \\& = 2 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dy \, dx \\& = 2 \int\limits^2_0 {\bigg( 2xy + y^2 + y \bigg) \bigg| \limits^2_0} \, dx \\\end{aligned}\)

\(\displaystyle\begin{aligned}\int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz & = 2 \int\limits^2_0 {4x + 6} \, dx \\& = 2 \bigg[ 2x^2 + 6x \bigg] \bigg| \limits^2_0 \\& = 2(20) \\& = \boxed{40} \\\end{aligned}\)

∴ the integrals evaluates to 40.

\(\displaystyle \int\limits^2_0 \int\limits^2_0 \int\limits^2_0 {2x + 2y + 1} \, dx \, dy \, dz = \boxed{40}\)

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Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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Answer:

Na+ and Cl- should be examples of an ion.

<Hope I answered your question>

Answer:

Na+ and Cl- should be examples of an ion.

Step-by-step explanation:

1800 meters of fencing is required to enclose a field.

Given that, the dimension of the field is 300 meters by 600 meters.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Now, the perimeter of the rectangular field=2(600+300)

=2×900=1800 meters.

Therefore, 1800 meters of fencing is required to enclose a field.

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The missing side of the right triangle is √57

To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

Let's assume the missing side is represented by the variable x.

According to the Pythagorean theorem:

(2√6\()^2 + x^2 = 9^2\)

Simplifying, we have:

\(4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57\)

Taking the square root of both sides, we get:

x = √57

Thus, the missing side of the right triangle is √57

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Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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Answer:

the answer to the question is 7

Answer:

Step-by-step explanation:

Point: 10,-9

k=-2

y=-2x+b

So: 9, -7

8,-5

7,-3

6,-1

5,1

4,3

3,5

2,7

1,9

0,11

y=-2x+11

Answer:

y + 9 = - 2(x - 10)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 2 and (a, b ) = (10, - 9 ) , then

y - (- 9) = - 2(x - 10) , that is

y + 9 = - 2(x - 10)

Answer:

12 dollars an hour

Step-by-step explanation:

The speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

To find the speed of the boat in still water and the speed of the current, let's follow these steps:

Step 1: Let x represent the speed of the boat in still water, and y represent the speed of the current. The speed downstream is (x + y) and the speed upstream is (x - y).

Step 2: Use the formula distance = time × speed to write two equations based on the given information.

Downstream: 9(x + y) = 189

Upstream: 63(x - y) = 189

Step 3: Simplify both equations:

Downstream: x + y = 21 (divide both sides by 9)

Upstream: x - y = 3 (divide both sides by 63)

Step 4: Solve the system of equations by adding the two simplified equations:

2x = 24

x = 12

Step 5: Plug the value of x back into either equation to solve for y:

12 + y = 21

y = 9

So, the speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.

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Answer:

50°

Step-by-step explanation:

Triangles have a sum of 180° when all angles/degrees are added. 68° is equal to angle B in the triangle to the right, and 62° is equal to angle D in the triangle to the right. Now you just need to find the remaining degree that gives you a sum of 180 when all three angles/degrees are added.

180°=68°+62+?

180°=130°+?

180°=130°+50°

180°=180°

Angle C is equal to 50°.

The probability that the hacker guesses the password on their first try is extremely low.

What is the probability that the hacker guesses the password on his first try?

There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are \(62^{9}\) possible passwords.

The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:

Probability = 1 / (\(62^{9}\))

Using a calculator, this can be simplified to approximately 1.2 x \(10^{-16}\)

Therefore, the probability that the hacker guesses the password on their first try is extremely low.

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Graphs are used to show relationships between related entities. See attachment for the graph that shows the relationship between the number of students and the number of buses.

Given that:

\(People = 45\\\)

\(Bus = 1\)

The given parameters can be represented as:

\((x_1,y_1) = (45,1)\)

Where:

\(x \to\) people

\(y \to\) bus

When there is nobody (i.e.  0 people), then the number of bus will also be 0. So, we have:

\((x_2,y_2) =(0,0)\)

To sketch the graph that represents the given relationship, we simply plot points (0,0) and (45,1) and connect both points

See attachment for the graph

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As a result of the inverse relationship between z and w, their product is constant.

There is an inverse relationship between two parameters when they are connected, where the value of one parameter tends to decrease as the value of the other parameter increases. It's often described as a "bad friendship" in conversation.

z * W is equal to 1.

The statement indicates that the constant's value is 2/3, so:

z * w = 2/3

The result of solving for any of the variables is:

either w = (2/3) / z or z = (2/3) / w

The following values fit that relation:

z w = (2/3) / z

-8/9 (2/3) / (-8/9)

= - (2/3) * (9/8) = -3/4

- 4/9 (2/3) / (-4/9)

= - (2/3) * (9/4) = - 3/2

- 2/9 (2/3) / (-2/9)

= - (2/3) * (9/2) = - 3

2/9 (2/3) / ( 2/9)

= (2/3) * (9/2) = 3

4/9 (2/3) / (4/9)

= (2/3) * (9/4) = 3/2

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The equivalent equation of  r sinθ = 10 in rectangular coordinates is y²  +   y⁴/x² - 100 = 0.

The rectangular coordinates is calculated from the polar equation as follows;

r sinθ = 10

the conversion from polar to rectangular coordinates;

r² = x² + y²

r = √(x² + y²) ----- (1)

y/x = tanθ  ------ (2)

r sinθ = 10

√(x² + y²)(y/x) = 10

(x² + y²)(y²/x²) = 100

y²  +   y⁴/x² = 100

y²  +   y⁴/x² - 100 = 0

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The point at which the lines k(x) = 5x - 1 and h(x) = -3x - 1 meet is (0, -1)

Given: k(x) = 5x - 1, h(x) = -3x - 1

We need to find the point(if any) at which these two lines k and h meets.

To find point of intersection(if any), we need to set the functions equal as at the point of intersection the (x, y) value will be same for both of the lines.

Therefore, k(x) = h(x)

=> 5x - 1 = -3x - 1

=> 8x = 0

=> x = 0

k(x=0) = 5 * 0  - 1 = -1

Hence the point at which the lines k(x) = 5x - 1 and h(x) = -3x - 1 meet is (0, -1)

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Answer:

B.) $300

Step-by-step explanation:

just multiply 15 by how many hours you have

Answer:

Step-by-step explanation:

21.

4(x + 7) - 2x

4x + 28 - 2x

2x + 28

answer: 2x + 28

22.

8(a + b) + 5(2a - 5b)

8a + 8b + 10a - 25b

18a - 17b

answer: 18a - 17b

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Jhon's solution is wrong

1. first mistake

when you see this

10^5/10^4

the right solution is 10^(5 - 4) = 10^1 or just 10

2. second mistake

6.4/7.2 he inverted the fraction which is wrong

you can only invert the fraction when the power is negative

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

now the correct answer is 6.4/7.2 x 10^5/10^4 = 0.88888888888888888888888888888889 x 10

or 0.9 x 10^1

or 8.9

Option • 12 is the answer .The number of treatments in the experiment is 12.

The understudy is directing a trial to comprehend the connection between microwave power and time on the quantity of unpopped bits in a pack of popcorn. There are three degrees of microwave power: low, medium, and high. Each sack of popcorn can be popped for either 3 minutes or 4 minutes, which provides us with a sum of double cross variables. To cover every one of the potential mixes of time and power, the understudy runs 12 distinct medicines (3 degrees of force x 2 degrees of time). Every treatment addresses one sack of popcorn that is popped for a particular time frame and with a particular power setting. The quantity of unpopped parts is recorded for every treatment, and the outcomes are utilized to make determinations about the impacts of microwave power and time on the quantity of unpopped pieces.

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The topsoil will be 4.05 inches deep

From the question, we are to determine how many inches deep the topsoil will be

From the given information,

The volume of the topsoil = 1 cubic yard

Convert to cubic feet

1 cubic yard = 27 cubic feet

∴ The volume of the topsoil = 27 cubic feet

Then,

The depth of the topsoil will be = 27/(8 ×10)

Depth of topsoil = 27/80

Depth of topsoil = 0.3375 foot

Now, convert to inches

1 foot = 12 inches

∴ 0.3375 foot = 0.3375×12 inches

= 4.05 inches

Hence, the topsoil will be 4.05 inches deep

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The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₁ + R₂ — R₂ on M, we have;

4(1) + (-5) = -1 {row 2 column 1}

4(0) + 2 = 2 {row 2 column 2}

4(3) + (-2) = 10 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

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Answer:

Step-by-step explanation:

5. (6.5 - 2)/(7 - 4) = 4.5/3 = 1.5

6. (8 - 8)/(-5 - 10)= 0/-15= 0

7. (-3 + .75)/(4 - 1) = -2.25/3 = -.75= -3/4

8. (2 + 7)/(18 - 18)= 9/0 = undefined

We write the linear function as f(x)=3.5x+1 for the graph.

Linear function means a linear equation. As per given statement, we need to write an equation for straight line. We are given four-point in the XY coordinate.

We use the formula line passes through two points. The required function

should be in the form f(x) =mx+b or y=mx+b

given points are (0,1) (1,4.5) , (-1,-2.5) (-2,-6)

slope of line passes through first two points is=m= (y₂-y₁)/(x₂-x₁)= 3.5

slop of last two points is = m= 3.5

hence, four points lies in the same straight line

the equation of line, y= 3.5x+b

as the line passes through (-2,-6)

                                  -6=3.5×(-2)+b

                                 b=1, b is a constant

         hence, the linear function is f(x)=y=3.5x+1

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Answer:

can you please send the picture as well because for this

(The length of the deck is shown in the figure.=??)

figure is needed ..

Answer:

$50.00 is the discount price

Answer:

Step-by-step explanation:

The total number of claim is the sum S of 1250 independent random variables,

each having poisson distribution with mean μ = 2

Since the  Variance of poisson distribution is equal to its mean ,

the standard deviation of this is

\(\sigma= \sqrt{2}\)

By the CLT is follow that S is approximately normal with mean 1250*2 =2500

and standard deviation \(\sqrt{1250} *\sqrt{2} =50\)

Hence, the probability to compute is

\(P(2350\leq S\leq 2600)=P(\frac{2450-2500}{50} \leq \frac{S-2500}{50} \leq \frac{2600-2500}{50} )\\\\=P(-1<2<2)\\\\=P(2\leq 2)-P(2\leq 1)\\\\=0.977249868-0.15365525\\\\=0.818594614\\\\=0.82\)