work out the value of z in the question below. give your answer to 1dp. tan 33°= 8/z

1) The line integral value is : ∫F dr = 6

2) The line integral value is : ∫F dr = 6

3) The line integral value is : ∫F dr = 6

Here we are given:

\(F.dr = (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)

where\(\vec{F}\) is a conservative field

So,

f(x, y , z) = \(\int\limits (3x + 2y)dx + (2x -2z)dy + (3x -2y)dz,\)

f(x , y , z) = (3zx +2yx) + (2xy - 2zy) + (3xz - 2yz) + c(x , y , z)

\(f(x, y, z) = (6xz + 4xy - 4yz) + c(x, y, z)\)

Now substitute the values of x , y ,z ,

1)

Line segment from (0, 0 , 0) to (1,1 ,1)

∫F dr = f(1,1,1) - f(0,0,0)

= |6 + 4 - 4 |- |0 + 0 - 0|

∫F dr = 6

2)

Line segment from (0,0,0) to (0,0,1) to (1,1,1)

First we take (0,0,0) to (0,0,1)

\(\int _c \vec{F}.\vec{dr}=f(0,0,1)-f(0,0,0) =[6(0)(1)+4(0)(0)-4(0)(1)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\)

∫F dr = 0

\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+6 [F.dr = 6\)

3)

Line segment from (0,0,0) to (1,0,0) to (1,1,0) to (1,1,1)

First we take (0,0,0) to (1,0,0)

\(\int _c \vec{F}.\vec{dr}=f(1,0,0)-f(0,0,0) =[6(1)(0)+4(1)(0)-4(0)(0)]-[6(0)(0)+4(0)(0)-4(0)(0)] =[0+0-0]-[0+0-0]\int _{c}\vec{F}.\vec{dr}=0\)

Next we take (1,0,0) to (1,1,0)

\(\int _c \vec{F}.\vec{dr}=f(1,1,0)-f(1,0,0) = [6(1)(0) + 4(1)(1) − 4(1)(0)] - [6(1)(0) + 4(1)(0) — 4(0)(0)] = [0+4-0] - [0+0-0]\int _{c}\vec{F}.\vec{dr}=4\)

Lastly we take (1,1,0) to (1,1,1)

\(F.dr = f(1,1,1) ƒ(1,1,0) = [6(1)(1) +4(1)(1) − 4(1)(1)] - [6(1)(0) + 4(1)(1) — 4(1)(0)] =[6+4-4]-[0+4-0]\int _{c}\vec{F}.\vec{dr}=2\)

Adding the three results we get

\(\Rightarrow \int _{c}\vec{F}.\vec{dr}=0+4+2\\\\\int\limits F.dr = 6\)

Therefore we see that the Line integral for the three cases comes out to be same between the initial and final points since it is independent of the path taken.

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y = e is the equation of the tangent line to the given curve at the specified point , y = \(e^{x}\) / x , (1, e)

Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.

The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).

thus , y' =  \(\frac{e^{x}-xe^{x} }{x^{2} }\)

y'(1) = 0 = m

Our slope is indicated by the horizontal line.

y−\(y_{1}\)=m(x−\(x_{1}\))

Our line will simply be our y-coordinate because our slope(m) is 0:

e

Therefore:

The tangent line's equation is y=e.

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3. She can multiply the bottom equation by –4 and then add the equations to solve for h is correct . The solution to the system of linear equations is g = 22, h = 7.

The correct statement that explains how Kasi could find a solution to the system of linear equations using elimination is:

She can multiply the bottom equation by –4 and then add the equations to solve for h.

To solve the system of equations using elimination, Kasi wants to eliminate one of the variables, either g or h, by adding or subtracting the equations in a way that cancels out one of the variables.

In this case, she can eliminate g by multiplying the top equation by 1 and the bottom equation by 4, which gives:

-4g - 15h = -17 (equation 1)

-4g + 20h = 52 (equation 2)

Then, if she adds the two equations, the term -4g will cancel out:

-4g - 15h = -17

(-4g + 20h = 52)

0g + 5h = 35

Simplifying the last equation gives:

5h = 35

And dividing both sides by 5, she gets:

h = 7

Now, Kasi can substitute h = 7 into one of the original equations, say the second one, to solve for g:

-g + 5h = 13

-g + 5(7) = 13

-g + 35 = 13

-g = -22

g = 22

Therefore, the solution to the system of linear equations is:

g = 22, h = 7

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Answer:

45x

Step-by-step explanation:

Plz mark brainliest

Answer:

The screenshot of my test is below

Step-by-step explanation:

The inverse function is \(f^{-1} (x)\)=(x+3)/9.

The given function is f(x)=9x-3.

Steps for finding the inverse of a function f(x).

Now, y=9x-3

Interchange x and y. That is x=9y-3.

Solve for y.

That is, 9y=x+3

⇒y=(x+3)/9

⇒\(f^{-1} (x)\)=(x+3)/9

Therefore, the inverse function is \(f^{-1} (x)\)=(x+3)/9.

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Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

To find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 3θ, 0 ≤ θ ≤ 2.9, with a straight line segment, we need to break down the problem into two parts: the area enclosed by the spiral and the area enclosed by the straight line segment. Answer : Total Area ≈ (2.9)^3 + 37.905

1. Area enclosed by the spiral:

The equation r = 3θ represents a spiral. We can use polar coordinates to find the area enclosed by the spiral. The formula for the area enclosed by a polar curve is given by A = (1/2) ∫[θ1, θ2] r^2 dθ.

In this case, the spiral is given by r = 3θ and the range of θ is 0 to 2.9. Therefore, the area enclosed by the spiral is:

A_spiral = (1/2) ∫[0, 2.9] (3θ)^2 dθ

Simplifying the expression:

A_spiral = (1/2) ∫[0, 2.9] 9θ^2 dθ

A_spiral = (1/2) * 9 * ∫[0, 2.9] θ^2 dθ

Integrating:

A_spiral = (1/2) * 9 * [θ^3/3] evaluated from 0 to 2.9

A_spiral = (1/2) * 9 * [(2.9)^3/3 - 0^3/3]

A_spiral ≈ 9 * [(2.9)^3/9]

A_spiral ≈ (2.9)^3

2. Area enclosed by the straight line segment:

Since the straight line segment connects the ends of the spiral, it forms a triangle. The area of a triangle can be calculated using the formula A_triangle = (1/2) * base * height.

The base of the triangle is the distance between the two ends of the spiral, which is equal to the radius at θ = 2.9: r = 3(2.9) ≈ 8.7.

The height of the triangle is the difference in radii at the ends of the spiral: height = 3(2.9) - 0 = 8.7.

Therefore, the area enclosed by the straight line segment is:

A_line_segment = (1/2) * 8.7 * 8.7 = 37.905

Finally, to find the total area enclosed by the closed curve, we add the area of the spiral and the area of the straight line segment:

Total Area = A_spiral + A_line_segment

Total Area ≈ (2.9)^3 + 37.905

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Answer:

A relation is...

A set of points that pair input values with output values.

Is the following graph a function?

Yes

Step-by-step explanation:

Answer:

184.26 i dont exacaly know but i think it is just let me know if im right or wrong

Step-by-step explanation:

There are different consecutive ways that the flowers can be planted:

3,9,15,21 and so on.

Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written sequentially, where the difference between the numbers is fixed and no number in between is skipped.

Given that:

Roses plants in 1st, 2nd, row are:

3,9 ,.....

Since difference between consecutive terms is same:

It is an AP

We have to find number of row in the flower bed:

Lets assume there are n rows in the flowers bed.

We know that:

    aₙ = a + (n-1)d

and d = 9-3 = 6

Therefore, the next numbers can be:

3,9,15 ,21 ......

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Answer:

333

Step-by-step explanation:

1/3x5= 1.66

Answer:

333

Step-by-step explanation:

i need points lol

The simple interest earned on $1,272 deposited in a bank for 20 years at 3% annual interest rate is $764.40.

To calculate the simple interest earned on a principal amount deposited in a bank, we use the formula:

Simple Interest = (Principal) x (Rate) x (Time)

where the rate is the annual interest rate, and the time is the number of years the money is deposited.

In this case, the principal is $1,272, the rate is 3%, and the time is 20 years.

Plugging in these values into the formula, we get:

Simple Interest = (1272) x (0.03) x (20)

Simple Interest = $764.40

Therefore, the simple interest earned on $1,272 deposited in a bank for 20 years at 3% annual interest rate is $764.40.

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This means that the two lines are perpendicular to each other.

What is co-ordinate geometry ?

Coordinate geometry is a branch of mathematics that deals with the study of geometry using algebraic principles and techniques, specifically using the Cartesian coordinate system to determine geometric figures' properties, such as distance, midpoint, slope, and equations of lines and curves.

Lines FG and HJ are parallel because they have the same slope. To find the slope of a line, we use the formula:

slope = (change in y) / (change in x)

For line HJ, the slope is:

slope = (4 - (-2)) / (0 - (-4)) = 6 / 4 = 3/2

For line FG, the slope is:

slope = (-2 - 1) / (0 - (-4)) = -3 / 4

Since the slopes of both lines are different, they cannot be the same line. However, we can see that the slopes are negative reciprocals of each other:

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

Therefore, this means that the two lines are perpendicular to each other.

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The answer is 4 > n.

24 >6n

4 > n

Answer:

4>n

Step-by-step explanation:

11+13>6n

24>6n

4>n

Answer:

SP = (100-d%)/100 × MP

ans.12.36

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

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

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

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

Yes they can it would be a isosceles triangle.

Step-by-step explanation:

An isosceles triangle can have 1 side that is different from the other 2.

Answer:

yes

Step-by-step explanation:

an isosceles triangle can have those sides

Answer:

Step-by-step explanation:

\(24.\frac{3}{4}\\ = 6.3 \\= 18\)

Answer:

12a - 48

Step-by-step explanation:

12(a - 4) ← multiply each term in the parenthesis by 12

= 12a - 48

Answer:

12a-48

Step-by-step explanation:

12(a-4)

12*a-12*4

12a-48

The angle between the vector (3 - √2)i + 3j and the positive x-axis can be determined using trigonometry.

To find the angle between the vector and the positive x-axis, we can use the arctan function. The angle can be calculated by taking the arctan of the y-component divided by the x-component of the vector.

In this case, the vector is given as (3 - √2)i + 3j. The x-component is 3 - √2, and the y-component is 3. Using the arctan function, we can calculate the angle as arctan(3 / (3 - √2)).

By substituting the values into a calculator or using trigonometric identities, we can find the angle. It is important to note that the arctan function returns an angle in radians. If we want the result in degrees, we can convert it by multiplying the result by 180/π.

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Answer:

D. 16          i took the quiz trust me ok? ily stay safe queen

Step-by-step explanation:

Answer:

45x + 180 = 900

x being number of weeks

Step-by-step explanation:

The equation that can be used to find the number of weeks is 180+45x = 900 and the number of weeks she must save the money is 16 weeks.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have:

The amount of money Jenny saved each week = $45

The amount her brother gives = $180

Total amount Jenny wants to save = $900

Let's suppose the number of weeks is x

180+45x = 900    (as she has already $180 and each week she saves is                                    

                              $45)                

So from the above equation, we can find the number of weeks.

After solving the equation:

45x = 900 - 180

x = 16 weeks

Thus, the equation that can be used to find the number of weeks is 180+45x = 900 and the number of weeks she must save the money is 16 weeks.

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Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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club

club

club

club

club

Answer:

Step-by-step explanation: is the answer got the stuff while going up. On Tuesday. I am not sure if  this good but i thinkk so...

Answer:

4

Step-by-step explanation:

By the triangle midsegment theorem, 2(YW)=VZ.

This means 2(7s)=s+52, and thus s=4.

The amount of shirts and pants the clothier makes is an illustration of a linear equation

The equation that represents the number of shirts, and the number of pants is 4s + 6p = 40

The rates are given as:

Shirts = 4 hours

Pants = 6 hours

In time t, the shirts and pants made is represented with:

t = 4s + 6p

Given that the time is 40 hours, the equation becomes

4s + 6p = 40

Hence, the equation that represents the number of shirts, and the number of pants is 4s + 6p = 40

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The probability of getting doubles or a sum of 6, given that at least one die shows 2, is 1/6.

To solve this problem, we need to consider two events: Event A, which represents getting doubles (both dice showing the same number), and Event B, which represents getting a sum of 6.

Getting doubles: There are 6 possible outcomes for doubles (1-1, 2-2, 3-3, 4-4, 5-5, and 6-6) out of the total 36 possible outcomes when rolling two dice (6 outcomes for the first die multiplied by 6 outcomes for the second die). Therefore, the probability of getting doubles is 6/36, which simplifies it to 1/6.

Getting a sum of 6: There are five possible outcomes that give a sum of 6: (1-5, 2-4, 3-3, 4-2, and 5-1). Again, considering the total of 36 possible outcomes, the probability of getting a sum of 6 is 5/36.

Now, we need to find the probability of getting doubles or a sum of 6, given that at least one die shows 2. This means we have three favorable outcomes: (2-2 for doubles, 1-5, and 2-4 for a sum of 6), out of a total of 11 possible outcomes where at least one die shows 2.

To calculate the probability, we divide the number of favorable outcomes (3) by the total number of possible outcomes (11), resulting in a probability of 3/11.

Therefore, the final probability of getting doubles or a sum of 6, given that at least one die shows 2, is 3/11, which simplifies to approximately 0.273 or 27.3%.

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The new x-coordinate must be 2-2 = 0.

acc to our question-

Finding the distance between the known endpoint and the midpoint, then applying the same transformation to the midpoint, is the quickest technique to locate the missing endpoint. The x-coordinate changes in this situation from 4 to 2, or down by 2, hence the new x-coordinate is 2-2 = 0.

Hence,The new x-coordinate must be  = 0.

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