can someone please help me find the slope on khan academy? and please provide an explanation if possible

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Answer to question 1 is D

answer to question 2 is A

Answer is f(x, y, z) = xy + y² - xz - yz + C

Given field, F is F = (y - z) i + (x + 2y - z) j - (x + y) k

To find potential function f,

we need to find the antiderivative of each component of F, with respect to its respective variable.

The antiderivative of the x-component is

∫ (y - z) dx= xy - xz + C1

The antiderivative of the y-component is

∫ (x + 2y - z) dy= xy + y² - yz + C2

The antiderivative of the z-component is:

∫ -(x + y) dz= -xz - yz + C3

Therefore, potential function f is

f(x, y, z) = xy + y² - xz - yz + C.

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Answer:

[tex]P(A) = \frac{3}{10}[/tex]

Step-by-step explanation:

Given

[tex]S = \{11,12,13,14,15,16,17,18,19,20\}[/tex]

Required

The probability of having a multiple of 3

Let the event of having a multiple of 3 be represented as: A

So:

[tex]A = \{12,15,18\}[/tex]

[tex]n(A) = 3[/tex]

So, the probability is:

[tex]P(A) = \frac{n(A)}{n(S)}[/tex]

Where

[tex]n(S) = 10[/tex] i.e. the sample size

So:

[tex]P(A) = \frac{n(A)}{n(S)}[/tex]

[tex]P(A) = \frac{3}{10}[/tex]

Answer:

x= 11/7 + 3y/7

Step-by-step explanation:

Answer:

y=11 -7/3x

Step-by-step explanation:

subtract the 7

bring the seven to the other side

then divide by 3

Option (d) W = 162 is the correct answer.

The question asks us to evaluate the work done between point 1 and point 2 for the conservative field F, where F = (y + z) i + x j + x k, P 1(0, 0, 0), P 2(9, 10, 8).

Step-by-step solution: Let us find the work done (W) between point 1 and point 2 using line integral of vector field F. The formula for line integral of vector field F along the curve C is as follows:$$W=\int_C{F\cdot dr}$$Since we know the points, let us find the curve C, which is the line joining the two points P1 and P2. Let P1 be the initial point and P2 be the final point. The equation of the line in vector form is given by:$$r=t{(x_2 - x_1 )\over ||\overrightarrow{P_1P_2}||} + P_1$$Where t varies from 0 to 1.Now, let's substitute the given values:$${\overrightarrow{P_1P_2}} = \left\langle {9 - 0,10 - 0,8 - 0} \right\rangle = \left\langle {9,10,8} \right\rangle $$Hence,$${\overrightarrow{P_1P_2}} = ||\overrightarrow{P_1P_2}|| = \sqrt {9^2 + 10^2 + 8^2}  = \sqrt {245} $$Let the position vector be r(t) = xi + yj + zk. Then, the vector dr = dx i + dy j + dz k.Substitute r(t) and dr in the formula of line integral. Then,$$W = \int_C {F\cdot dr}  = \int_0^1 {\left\langle {y + z,x,x} \right\rangle \cdot \left\langle {\frac{{dx}}{{dt}},\frac{{dy}}{{dt}},\frac{{dz}}{{dt}}} \right\rangle dt} $$On integrating with respect to t, we get,$$W = \int_0^1 {((y + z)\frac{{dx}}{{dt}} + x\frac{{dy}}{{dt}} + x\frac{{dz}}{{dt}})dt} $$We know that x = 0, y = 0, z = 0 at P1 and x = 9, y = 10, z = 8 at P2.Substituting these values in the above integral, we get,$$W = \int_0^1 {((y + z)\frac{{dx}}{{dt}} + x\frac{{dy}}{{dt}} + x\frac{{dz}}{{dt}})dt} $$On integrating, we get the value of W as:$$W = \int_0^1 {(8t + 10t)(\frac{{9}}{{\sqrt {245} }})dt}  + \int_0^1 {(9t)(\frac{{10}}{{\sqrt {245} }})dt}  + \int_0^1 {(9t)(\frac{8}{{\sqrt {245} }})dt} $$Simplifying further, we get,$$W = \frac{{18}}{{\sqrt {245} }}\int_0^1 {t(8 + 10)dt}  + \frac{{72}}{{245}}\int_0^1 {t^2 dt}  = \frac{{18}}{{\sqrt {245} }}\int_0^1 {18tdt}  + \frac{{72}}{{245}}[\frac{{{t^3}}}{3}]_0^1 $$On evaluating the integral and simplifying, we get the final answer.$$W = \frac{{81}}{{\sqrt {245} }}$$

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Answer:

yes cs its a orange juice

Step-by-step explanation:

Answer:

taking back the answer spot that is rightfully mine!

Step-by-step explanation:

The most cost-efficient container is the Rectangular Prism.

1. Rectangular Prism:

Volume: V = lwh = 10 x 5 x 15 = 750 cubic units

Cost: C = $0.01 x 750 = $7.50

Cost per unit volume: C/V = $7.50 / 750 = $0.01 per cubic unit

2. Rectangular Pyramid:

Volume: V = (1/3) x lwh = (1/3) x 10 x 5 x 15 = 250 cubic units

Cost: C = $0.02 x 250 = $5.00

Cost per unit volume: C/V = $5.00 / 250 = $0.02 per cubic unit

3. Cylinder:

Volume: V = πr²h = π x 5² x 15 ≈ 1178.1 cubic units

Cost: C = $0.015 x 1178.1 = $17.67

Cost per unit volume: C/V = $17.67 / 1178.1 ≈ $0.015 per cubic unit

Now, comparing the cost per unit volume for each container:

a. Rectangular Prism: $0.01 per cubic unit

b. Rectangular Pyramid: $0.02 per cubic unit

c. Cylinder: $0.015 per cubic unit

The container with the lowest cost per unit volume is the Rectangular Prism, with a cost of $0.01 per cubic unit.

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Answer:

See below.

Step-by-step explanation:

y^2 - 6y + 9 can be changed correctly into y^2 - 2(y)(3) + 3^2.

Up to here, it's correct.

The right side above shows a polynomial that is the square of a binomial.

It factors into (y - 3)^2.

The correct factorization is (y - 3)^2.

The incorrect factorization of the student's solution is the product of a sum and difference.

The product of a sum and a difference is the correct factorization for a difference of squares.

For example, y^2 - 9 is the same as y^2 - 3^2 and is a difference of squares.

It factors into (y + 3)(y - 3), a product of a sum and a difference.

Answer:

Minimum: (2,4)

Step-by-step explanation:

h(x)=3([tex]x^{2}[/tex]-4x)+16

=3([tex]x^{2}[/tex]-4x+4-4)+16   (- For the balance of equation, and attention 1)

=3[tex](x-2)^{2}[/tex]-3*4+16

=3[tex](x-2)^{2}[/tex]+4

1. [tex](a-b)^{2}=a^{2} -2ab+b^{2}[/tex]

2. The formula for the vertex form is y = [tex]a(x-h)^{2}+k[/tex], the vertex is (h,k)

Answer:

6x

Step-by-step explanation:

12x^3, 6xy, and 18x can all be evenly divided by 6x

Answer:

wtfrick- that's so confusing

Step-by-step explanation:

sorry I don't have an answer wish this was a comment

The integral ∫ 1/ (z-a)(z-b) dz over the circle Cr, where a and b are complex numbers and |a| < R < |b|, evaluates to 2πi/(a-b).

To show this, we can use the Residue theorem. Since the function 1/(z-a)(z-b) has two simple poles at z=a and z=b within the region enclosed by the circle Cr, we can evaluate the integral by summing the residues at these poles.

The residue at z=a is given by Res(a) = 1/(b-a), and the residue at z=b is given by Res(b) = -1/(b-a). By the Residue theorem, the integral is equal to 2πi times the sum of the residues.

Therefore, ∫ 1/ (z-a)(z-b) dz = 2πi * (1/(b-a) - 1/(b-a)) = 2πi/(a-b).

This result shows that the integral over the circle Cr simplifies to a complex constant determined by the difference between a and b.

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Answer:

numbers less than 5 are 1,2,3,4 and equal to 5 is 5.

probability of less than 5 is 4/16

while equal to 5 is 1/16

or means additions; so its 4/16 +1/16=5/16

Let L be the linear operator in R2 defined by L(x) = (3x1 - 2x2, 9x1 - 6x2)T. The bases of the kernel and image of L are to be determined. To find the bases of the kernel and image of L, we first recall the definitions of kernel and image of a linear operator. Definition of Kernel: Let T be a linear operator on a vector space V. Then the kernel of T, denoted as ke T, is the subspace of V that consists of all vectors that are mapped to the zero vector of the range of T. Definition of Image: Let T be a linear operator on a vector space V. Then the image of T, denoted as im T, is the subspace of the range of T consisting of all vectors that are mapped by T to some vectors in the range of T. The kernel and image of L are given as follows. Kernel of L: For L(x) = (3x1 - 2x2, 9x1 - 6x2)T to be zero vector, we must have 3x1 - 2x2 = 0 and 9x1 - 6x2 = 0, which implies that x1 = (2/3)x2.

Therefore, a typical element of the kernel of L can be expressed as (x1, x2)T = (2/3)x2(1, 3)T, where x2 is a scalar. Hence, a basis for the kernel of L is {(1, 3)T}. Image of L: The image of L is the subspace of R2 consisting of all vectors that can be expressed in the form L(x) = (3x1 - 2x2, 9x1 - 6x2)T, where x is any vector in R2. It follows that any vector in the image of L is of the form (3x1 - 2x2, 9x1 - 6x2)T = x1(3, 9)T + x2(-2, -6)T. Therefore, a basis for the image of L is {(3, 9)T, (-2, -6)T}.Hence, the bases of the kernel and image of L are as follows. Kernel: {(1, 3)T}Image: {(3, 9)T, (-2, -6)T}.

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Answer:

24

Step-by-step explanation:

added all the sides hope this helps

The subset of items that should be carried is (2, 4) and (4, 2).

The last 9 digits of my mobile number are 904202527.

So, when I sort them in descending order, I get 975422000.

Therefore, W (backpack capacity) = 9. N = 4 items as follows: (Wi, vi) = (3, 7), (1, 5), (2, 4), (4, 2).

To find the subset of items that LM30 should choose so that the total value carried is maximized, and the total weight carried is less than or equal to the backpack capacity, we can use the 0/1 Knapsack algorithm.

Here are the steps:

Step 1: Create a table with (N+1) rows and (W+1) columns.

Step 2: Initialize the first row and first column with 0.

Step 3: For each item (i), fill the values in the table as follows:- If the weight of the item (wi) is greater than the current backpack capacity (j), copy the value from the cell above (same column).- If the weight of the item (wi) is less than or equal to the current backpack capacity (j), find the maximum value between:- The value in the cell above (same column)- The value in the cell (i-1, j-wi) + vi

Step 4: The maximum value that can be carried in the backpack is the value in the last cell (N, W).

Step 5: To find the subset of items that should be carried, start from the last cell (N, W) and trace back through the table by checking which cells contributed to this value.

For our case, the table would look like this:

Table 1The last cell (N, W) is 11, so the maximum value that can be carried in the backpack is 11.

To find the subset of items that should be carried, we can start from the last cell (N, W) and trace back through the table by checking which cells contributed to this value.

We can see that the cells (2, 6) and (4, 2) contributed to this value.

Therefore, the subset of items that should be carried is: (2, 4) and (4, 2).

Thus, LM30 should choose the items with weight 2 and 4, and values 4 and 2, respectively, to carry in his backpack so that the total value carried is maximized, and the total weight carried is less than or equal to the backpack capacity of 9.

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Answer:

5 o clock

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

(24^2)+(30^2)

Answer:

54yd^2

Step-by-step explanation:

you need to break up the figure into 2 different boxes. One 3 x 10 and one    6 x 4 which adds up to 30 + 24 = 54.

Answer:

21?i think

Step-by-step explanation:

Answer:

40.95

Step-by-step explanation:

P = 1500 + 75 = 1575

I = Prt

I = 1575(1.3%)(2)

I = 40.95

Answer:

They are both correcte

Step-by-step explanation:

Imagine a pizza with 6 slices

Half of 6 slices is 3 slices, or 3/6

If you simplify 3/6, you will get 1/2

So, both fractions are equal, but in different forms.

For better context see images below!

Answer:

120

equation: 40+8(10)=120

Step-by-step explanation:

The math for this is $40 initial plus $8x the 10 weeks which equals 80 so

40+80=120

The given differential equation is given by `dy/dx = V*y` and the initial condition is `y(x) = Yo`.

The solution of the differential equation is given by `y(x) = Yo*e^(V*x)`.

Using this formula and the initial condition `y(x) = Yo`,

we get `Yo = Yo*e^(V*x)`.

This implies that `e^(V*x) = 1` or `V*x = 0`.

Thus `x = 0` is the only value of x on which `y(x) = Yo` for any value of `V`.

Now, we are given `y(x) = (1 + x^2)/(x^2 + Yo)` which is valid only if `Yo > 0` (as given). We need to find the largest interval on which the solution is defined. This means that we need to find the largest interval of x-values for which the given expression for `y(x)` makes sense. Since the denominator of the expression `y(x) = (1 + x^2)/(x^2 + Yo)` is `x^2 + Yo`, the expression is defined only if `x^2 + Yo > 0`. As `Yo > 0`, this inequality holds for all values of `x`. Thus, the solution is defined for all `x` in the real line. Therefore, the largest interval on which the solution is defined is `(-∞, ∞)`.

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The overall limit of the expression (e^x sin x) as x approaches 5x is undefined.

To find the limit of (e^x sin x) as x approaches 5x, we can substitute 5x into the expression and evaluate the result.

lim (e^x sin x)    (substituting 5x for x)

x→5x

= lim (e^(5x) sin (5x))

x→5x

Now, let's analyze the behavior of the function as x approaches 5x. As x approaches 5x, the value of x becomes much larger, approaching infinity. In this case, we can examine the limits of the individual components.

1. Limit of e^(5x) as x approaches infinity:

lim e^(5x) = ∞

x→∞

Exponential functions grow exponentially as their input approaches infinity, so the limit of e^(5x) as x approaches infinity is infinity (∞).

2. Limit of sin (5x) as x approaches infinity:

lim sin (5x) = DNE

x→∞

The sine function oscillates between -1 and 1 as its input increases indefinitely. Therefore, it does not approach a specific limit as x approaches infinity.

Combining these results, we have:

lim (e^(5x) sin (5x))

x→∞

Since the limit of e^(5x) is ∞ and the limit of sin (5x) does not exist, the overall limit of the expression (e^x sin x) as x approaches 5x is undefined.

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The equations Verdita could use to represent the data sets include the following:

A. Data Set A: y = 4x-2

Data Set B: y = x +4

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of data set A;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 6)/(1 + 1)

Slope (m) = 8/2

Slope (m) = 4

At data point (1, 2) and a slope of 4, a linear equation for data set A can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 4(x - 1)

y = 4x - 2

At data point (0, 4) and a slope of 1, a linear equation for data set B can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 4 = 1(x - 0)

y = x + 4

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

134-(-80)=134+80=214