Lisandra was the center a towel bar on her door that is 29 inches wide she determines that the better distance from each of the towel bar to the end of the door is 7. 75 inches write and solve an equation to find the length of the towel bar.

The statements regarding the median and the quartiles are given as follows:

a. True.

b. True.

c. False.

The ordered data-set in this problem is given as follows:

7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.

Hence:

More can be learned about median and quartiles at https://brainly.com/question/3514929

#SPJ1

A dot plot that represent this data set is shown in the image attached below.

In Mathematics and Statistics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of crosses or dots.

Based on the information provided about this data points, we can reasonably infer and logically deduce that the number with the highest frequency is 1.

In this scenario, we would use an online graphing calculator to construct a dot plot with respect to a number line that accurately fit the data set.

Read more on dot plots here: brainly.com/question/30486649

#SPJ1

V = ∫2πx f(y) dy volume of the solid

a. The integral of dz is simply z + C, where C is the constant of integration. So the result of integrating dz is:

∫ dz = z + C

b. To find the integral of (C^2 + I∫sin(x))/(1+cos(x)) dx, we can use the substitution u = 1 + cos(x), du/dx = -sin(x), and dx = du/(-sin(x)). Then we have:

∫(C^2 + I∫sin(x))/(1+cos(x)) dx = ∫(C^2 + I∫sin(x))/u (-du/sin(x))
= -I∫(C^2 + I∫sin(x))/u du
= -I(C^2ln|u| + I∫ln|u| sin(x) dx) + C'
= -I(C^2ln|1+cos(x)| - I∫ln|1+cos(x)| sin(x) dx) + C'

where C' is the constant of integration.

c. To find the volume of the solid obtained by rotating the shaded region about the x-axis or the y-axis, we need to use the method of cylindrical shells or disks, respectively.

If we rotate the region about the x-axis, we can use the formula:

V = ∫2πy f(x) dx

where f(x) is the distance from the x-axis to the function y(x) that defines the region. If we have a function y(x) = g(x) - h(x) that defines the region between two curves, then f(x) = g(x) - h(x) and the limits of integration are the x-values where the two curves intersect.

If we rotate the region about the y-axis, we can use the formula:

V = ∫2πx f(y) dy

where f(y) is the distance from the y-axis to the function x(y) that defines the region. If we have a function x(y) = g(y) - h(y) that defines the region between two curves, then f(y) = g(y) - h(y) and the limits of integration are the y-values where the two curves intersect.

To learn more about function click here

brainly.com/question/12431044

#SPJ11

The equation of the line with given coordinates in slope intercept form is given by y = 6x.

Use the slope-intercept form of the equation of a line,

y = mx + b,

where m is the slope of the line

And b is the y-intercept.

The slope of the line is equals to,

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points on the line.

Using the coordinates (-3, -18) and (3, 18), we get,

⇒m = (18 - (-18)) / (3 - (-3))

⇒m = 36 / 6

⇒m = 6

So the slope of the line is 6.

Now we can use the slope-intercept form of the equation of a line .

Substitute in the slope and one of the points, say (-3, -18) to get the y-intercept,

y = mx + b

⇒ -18 = 6(-3) + b

⇒ -18 = -18 + b

⇒ b = 0

So the y-intercept is 0.

Putting it all together, the equation of the line in slope-intercept form is,

y = 6x + 0

⇒ y = 6x

Therefore, the slope intercept form of the line is equal to y = 6x.

Learn more about slope intercept form here

brainly.com/question/19241768

#SPJ4

The limit of Ln as n approaches infinity is -1/2, and it can be expressed as the definite integral ∫0¹ (x - 1) dx over the interval [0, 1].

To express the limit of Ln as n approaches infinity as a definite integral, we can use the definition of the definite integral as the limit of a Riemann sum. We can divide the interval [0, 1] into n subintervals of equal width Δx = 1/n, and evaluate Ln as the limit of the Riemann sum:

Ln = 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

where f(x) = x - 1 is the function being integrated.

Taking the limit as n approaches infinity, we have:

lim(n→∞) Ln = lim(n→∞) 1/n * [f(0) + f(Δx) + f(2Δx) + ... + f((n-1)Δx)]

= ∫0¹ (x - 1) dx

where we have used the fact that the limit of the Riemann sum is equal to the definite integral of the function being integrated.

Therefore, the limit of Ln as n approaches infinity is equal to the definite integral of (x - 1) over the interval [0, 1].

So,

lim(n→∞) Ln = ∫0¹ (x - 1) dx = [x¹ - x] from 0 to 1

= [1/2 - 1] - [0 - 0]

= -1/2

Know more about limit here:

https://brainly.com/question/12211820

#SPJ11

Joey forgot to record approximately 9,412 views after the second month.

Using a regression calculator, we find that the equation that best models the data is:

y = 4298.76x + 809.72

The coefficient of determination (R-squared value) for this regression is 0.994, indicating a strong linear relationship between the number of months and the total number of views.

We need to find the value of y for x = 2, using the regression equation we found in part a:

y = 4298.76(2) + 809.72

y ≈ 9412.24

Learn more about regression on

https://brainly.com/question/25987747

#SPJ1

To evaluate the integral ∫sin(5x^2)dx using the Maclaurin series, we first need to find the Maclaurin series for sin(5x^2).

The Maclaurin series for sin(x) is given by:

sin(x) = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

Now, replace x with 5x^2:

sin(5x^2) = (5x^2) - (5x^2)^3/3! + (5x^2)^5/5! - (5x^2)^7/7! + ...

Now we have the Maclaurin series for sin(5x^2). To evaluate the integral ∫sin(5x^2)dx, we integrate term-by-term:

∫sin(5x^2)dx = ∫[(5x^2) - (5x^2)^3/3! + (5x^2)^5/5! - (5x^2)^7/7! + ...]dx

= (5/3)x^3 - (5^3/3!7)x^7 + (5^5/5!11)x^11 - (5^7/7!15)x^15 + ... + C

This is the integral of sin(5x^2) using the Maclaurin series, where C is the constant of integration.

To evaluate the integral ∫ sin (5x)^2 dx, we can use the identity sin^2(x) = (1-cos(2x))/2.

First, we need to find the Maclaurin series for sin (5x^2). Using the formula for the Maclaurin series of sin(x), we have:

sin (5x^2) = ∑ ((-1)^n / (2n+1)!) (5x^2)^(2n+1)

= ∑ ((-1)^n / (2n+1)!) 5^(2n+1) x^(4n+2)

Next, we substitute this series into the integral:

∫ sin (5x)^2 dx = ∫ sin^2 (5x) dx

= ∫ (1-cos(10x)) / 2 dx

= (1/2) ∫ 1 dx - (1/2) ∫ cos(10x) dx

= (1/2) x - (1/20) sin(10x) + C

where C is the constant of integration.

Therefore, using the Maclaurin series for sin (5x^2), the integral of sin (5x)^2 is (1/2) x - (1/20) sin(10x) + C.
learn more about Maclaurin series here: brainly.com/question/28455274

#SPJ11

Answer:

Supplementary angles are angles that have a sum of 180°. When two angles are supplementary, we say that one angle is the supplement of the other.

Complementary angles are angles that add up to 90°. When two angles are complementary, we can say that one angle is the complement of the other

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

To convert a percentage to a fraction, we divide the percentage by 100 and simplify the resulting fraction. For example, to convert 40% to a fraction, we divide 40 by 100 to get 0.4 and then simplify the fraction 2/5. Therefore, 40% is equal to 2/5.

The weight of the water in the tank is approximately 3,809 pounds.

A. To find the width and length of the tank that will use the smallest amount of glass, we need to consider the surface area of the tank. Let's use "x" to represent the length and "y" to represent the width. The formula for the surface area of a rectangular tank is:

Surface Area = 2xy + 2xz + 2yz

Since the top of the tank will be open, we can ignore the surface area of the top. We know that the tank needs to hold 500 gallons and be 2 feet deep, so we can use the formula for the volume of a rectangular tank to solve for one of the variables:

Volume = Length x Width x Depth

500 = xy x 2

xy = 250

Now we can substitute this into the surface area formula and simplify:

Surface Area = 2(250) + 2xz + 2yz
Surface Area = 500 + 2xz + 2yz

To minimize the surface area, we need to differentiate this formula with respect to one of the variables and set it equal to zero. Let's differentiate with respect to x:

d(Surface Area)/dx = 2z

Setting this equal to zero, we get:

2z = 0

z = 0

This doesn't make sense, so let's try differentiating with respect to y:

d(Surface Area)/dy = 2z

Setting this equal to zero, we get:

2z = 0

z = 0

Again, this doesn't make sense. We can conclude that the surface area is minimized when x = y, so the tank should be square. Since xy = 250, we can solve for the side length of the square:

x^2 = 250

x ≈ 15.81 feet

So the tank should be approximately 15.81 feet by 15.81 feet to use the smallest amount of glass.

B. The volume of the water in the tank will be:

Volume = Length x Width x Depth

Volume = 15.81 x 15.81 x 1.67

Volume = 397.25 gallons

Since the tank needs to hold 500 gallons with 2 inches of head space, we can find the weight of the water using the formula:

Weight = Volume x Density

The density of water is approximately 8.34 pounds per gallon, so:

Weight = 397.25 x 8.34

Weight ≈ 3,313.69 pounds

So the weight of the water in the tank will be approximately 3,313.69 pounds.
A. To minimize the amount of glass used for the rectangular fish tank, you'll need to create a tank with equal width and length (a square base). Since the tank needs to hold 500 gallons and is 2 feet deep, you can use the formula: Volume = Length × Width × Depth. Convert 500 gallons to cubic feet (1 gallon ≈ 0.1337 cubic feet), so 500 gallons ≈ 66.85 cubic feet.

66.85 = Length × Width × 2
33.425 = Length × Width

Since the length and width are equal, you can solve for one of the dimensions:

Length = Width = √33.425 ≈ 5.78 feet

So, the tank dimensions will be approximately 5.78 feet by 5.78 feet by 2 feet.

B. To find the weight of the water in the tank, first determine the volume of the water. There will be 2 inches of headspace (2 inches ≈ 0.167 feet), so the water depth is 2 - 0.167 = 1.833 feet. The volume of the water is:

Volume = Length × Width × Depth = 5.78 × 5.78 × 1.833 ≈ 61.05 cubic feet

To find the weight of the water, multiply the volume by the weight of water per cubic foot (62.43 lbs/cubic foot):

Weight = 61.05 × 62.43 ≈ 3,809 lbs
learn more about volume of a rectangle here: brainly.com/question/30759574

#SPJ11

We know that by solving for t, you can find the amount of time Roger spent answering phone calls

You can use the equation t + 40 = 90, where t represents the amount of time Roger answers phone calls at the information desk.

This equation takes into account that Roger spends 40 minutes delivering flowers and the total time he volunteers at the hospital is 90 minutes.

By solving for t, you can find the amount of time Roger spent answering phone calls.

To know more about amount refer here

https://brainly.com/question/13024617#

#SPJ11

The number of ways to arrange the letters in the word "probability" is 11 factorial (11!).

In this problem, we need to arrange the letters in the word "probability." Since the order of the letters matters, we are dealing with permutations of objects.

The value we are trying to solve is the number of ways to arrange the letters. The given value is the word "probability," which has a total of 11 letters. To solve for the unknown, we will use the formula for permutations.

The formula for permutations of objects is n! / (n - r)!, where n is the total number of objects and r is the number of objects being arranged. In this case, we have 11 letters to arrange, so the formula becomes 11! / (11 - 11)!.

Learn more about "probability."

brainly.com/question/11234923

#SPJ11

Given that 25% of students solved at least two tasks and there were 32 students who wrote the test, we can prove that there was at least one task that no more than 12 students solved.

There was at least one task that no more than 12 students solved, we can use a proof by contradiction.

Assume that all five tasks were solved by more than 12 students. This means that for each task, there were at least 13 students who solved it. Since there are five tasks in total, this implies that there were at least 5 * 13 = 65 students who solved the tasks.

However, we are given that only 25% of students solved at least two tasks. If we let the number of students who solved at least two tasks be S, then we can write the equation:

S = 0.25 * 32

Simplifying, we find that S = 8.

Now, let's consider the remaining students who did not solve at least two tasks. The maximum number of students who did not solve at least two tasks is 32 - S = 32 - 8 = 24.

If all five tasks were solved by more than 12 students, then the total number of students who solved the tasks would be at least 65. However, the maximum number of students who could have solved the tasks is 8 (those who solved at least two tasks) + 24 (those who did not solve at least two tasks) = 32.

This contradiction shows that our initial assumption is false. Therefore, there must be at least one task that no more than 12 students solved.

Hence, we have proven that there was at least one task that no more than 12 students solved if 32 students wrote the test.

To know more about contradiction , refer here :

https://brainly.com/question/30459584#

#SPJ11

Answer:

Pens=13

Pencils=27

Step-by-step explanation:

1. Pens = x, Pencils = y

x+y=40

2. y+5 & x-5 --> y=4x

3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.

4. Solve. 4x=40-x, 5x=40, x=8

5. Plug in x=8 to y=4x -> y=32.

6. Reverse the y+5 & x-5. y=27, x=13.

The value of x is calculated as x = 3, while the length of segment JL is calculated as 18 units.

Create an equation based on the fact that the diagonals of the shape shown bisects each other to form equal segments such as:

JN = LN

Plug in the values to find x:

15 - 2x = 4x - 3

Combine like terms:

15 + 3 = 4x + 2x

18 = 6x

18/6 = x

x = 3

Length of JL = 15 - 2x + 4x - 3 = 12 + 2x

Plug in the value of x:

Length of JL = 12 + 2(3) = 18 units

Learn more about the length on:

https://brainly.com/question/29123104

#SPJ1

The result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

To find the positive solution, to the nearest tenth, of f(x)=g(x) using Cora's process, the steps are as follows:

Input the initial value of x,if x=0.

Calculate f(x) and g(x):

f(x) = x² - 8 = 0 - 8 = -8

g(x) = 2x - 4 = 0 - 4 = -4

If f(x) is less than g(x), then x should be increased and vice versa.

Increase or decrease x accordingly and calculate the new values of f(x) and g(x).

Keep repeating steps 3 and 4 until the difference between the values of f(x) and g(x) is less than 0.1.

Hence, the result will be the x value when the difference between the values of f(x) and g(x) is less than 0.1, which will be the positive solution to the nearest tenth of f(x)=g(x).

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ1

Cora is using successive approximations to estimate a positive solution to f(x) = g(x), where f(x)=x2 - 8 and g(x)=2x - 4. The table shows her results for different input values of x. Use Cora's process to find the positive solution, to the nearest tenth, of f(x) = g(x)

So the equivalent expression that matches one of the answer choices is option C, 100c/3d.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.

Here,

To simplify the given expression, we need to multiply the two binomials using the distributive property:

(10c6d - 5)(2c - 5d/4)

= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)

= 20c² - 25cd + 10c + 25/4 d

None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:

20c² - 25cd + 10c + 25/4 d

= 5(4c² - 5cd + 2c + 5/4

20c/3 * 5d/4

= 100c/3d

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

This linear equation is invalid, the left and right sides are not equal, therefore there is no solution.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.

2x + -7 = -1(3 + -2x)

Reorder the terms:

-7 + 2x = -1(3 + -2x)

-7 + 2x = (3 * -1 + -2x * -1)

-7 + 2x = (-3 + 2x)

Add '-2x' to each side of the equation.

-7 + 2x + -2x = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0

-7 + 0 = -3 + 2x + -2x

-7 = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0

-7 = -3 + 0

-7 = -3

Solving

-7 = -3

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

The solution to the equation is w = 285.

To solve the equation 3⋅50 + 2w = 720, we first simplify the left side by multiplying 3 and 50, which gives us 150.

Therefore, the equation becomes 150 + 2w = 720. Next, we isolate the variable term by subtracting 150 from both sides of the equation, resulting in 2w = 570.

To solve for w, we divide both sides of the equation by 2, giving us w = 285.

Therefore, the solution to the equation is w = 285.

Learn more about multiplication and variables.

brainly.com/question/30076028

#SPJ11

The minimal value of the given parabola is y = 5/2, which occurs at x = 0.

To discover the minimum value of the given parabola & that's why we need to determine the vertex of the parabola.

The vertex of a parabola in the form of y = ax^2 + bx + c is given by means of (-b/2a, f(-b/2a)).

in the given parabola, a = 1, b = 0, and c = 5/2. consequently, the x-coordinate of the vertex is -b/2a = 0/(2*1) = 0.

To discover the y-coordinate of the vertex & we substitute x = 0 within the given equation:

y = 0^2 + 5/2 = 5/2

Therefore, the minimal value of the given parabola is y = 5/2.

Learn more about parabola:-

https://brainly.com/question/29635857

#SPJ1

Answer:

  (c)  12.5

Step-by-step explanation:

You want the unknown leg of a right triangle with one leg 10 and hypotenuse 16.

The triangle inequality tells you the unknown leg of the triangle will have a length between the difference of the two known legs, and the longest leg of the triangle.

Since this is a right triangle, its longest leg is the hypotenuse. The unknown side cannot be longer than that, so must be less than 16.

The difference of the given lengths is ...

  16 -10 = 6

so the missing leg must be longer than 6.

Only one answer choice is between 6 and 16: 12.5.

The missing leg length is 12.5 units.

__

Additional comment

If you want to figure the length, you can use the Pythagorean theorem:

  c² = a² +b²

  16² = 10² +b²

  b² = 256 -100 = 156

  b = √156 ≈ 12.49 ≈ 12.5

The length of the unknown leg is 12.5 units.

The vertical distance the Mars Rover Curiosity has traveled is approximately 84.954 meters.

An absolute value equation is an equation that contains an absolute value expression, which is defined as the distance of a number from zero on the number line. The equation |x-b|=c represents the distance between x and b is c units. To write the absolute value equations in the form |x-b|=c, we need to determine the values of b and c based on the given solution sets.

For the solution set "All numbers such that x ≤ -14", we know that the distance between x and -14 is always a non-negative value. Therefore, the absolute value of (x-(-14)) or (x+14) is equal to the distance between x and -14. Since we want x to be less than or equal to -14, we can set the absolute value expression to be equal to -c, where c is a positive number. Hence, the absolute value equation is |x+14|=-c.

Similarly, for the solution set "All numbers such that x ≥ -1.3", the distance between x and -1.3 is always a non-negative value. Therefore, the absolute value of (x-(-1.3)) or (x+1.3) is equal to the distance between x and -1.3. Since we want x to be greater than or equal to -1.3, we can set the absolute value expression to be equal to c, where c is a positive number. Hence, the absolute value equation is |x+1.3|=c.

Learn more about absolute value

brainly.com/question/1301718

#SPJ11

Answer:

Step-by-step explanation:

The English language is an art that I am using to convey this message to you. Without this form of communication, we would be unable to talk or write without using another language. We think everyday with this awesome language, and don't think much about the language we think in. English is an amazing language, and I am proud to be able to verbalize it to you today.

Step-by-step explanation:

To simplify the expression, we can factor out the common factor -6x²y² from each term in the numerator:

-6x²y²(3y² - 6xy + 4x²) / 6xy

We can cancel out the common factor of 6 in both the numerator and denominator:

- x²y(3y² - 6xy + 4x²) / xy

Now we can simplify the expression further by canceling out the common factor of xy in the numerator:

- x(3y² - 6xy + 4x²)

Thus, the quotient of the numerator and denominator is:

- x(3y² - 6xy + 4x²) / 6xy.

The perimeter of the rectangle that is inscribed in a circle of radius 5 cm is 28cm

Let x and y be the side of the rectangle

Diameter of circle = radius × 2

Diameter = 5×2

Diameter = 10

According to the Pythagorean theorem

(Diameter)² = X² + Y²

10² = X² + Y²

X² + Y² = 100

By this equation, possible value of x and y is 6 and 8 respectively only 6 and 8 will satisfy the equation

So, X = 6 and Y = 8

Perimeter = 2(X+Y)

Perimeter = 2(6+8)

Perimeter = 2(14)

Perimeter = 28 cm

perimeter of the rectangle is 28cm

To know more about perimeter click here :

https://brainly.com/question/6465134

#SPJ4

Answer: arithmetic. Common difference is -4

Step-by-step explanation:

 constantly subtract four to get to the next

a) To express ∂z/∂u and ∂z/∂v as functions of u and v, we first need to express z directly in terms of u and v. We are given that:

z = tan^-1(x/y)

And that:

x = ucosv
y = usinv

Substituting these expressions for x and y into the equation for z, we get:

z = tan^-1((ucosv)/(usinv))
z = tan^-1(cotv)

Now we can use the chain rule to find ∂z/∂u and ∂z/∂v:

∂z/∂u = ∂z/∂cotv * ∂cotv/∂u
∂z/∂v = ∂z/∂cotv * ∂cotv/∂v

To find ∂cotv/∂u and ∂cotv/∂v, we use the quotient rule:

∂cotv/∂u = -cosv/u^2
∂cotv/∂v = -csc^2v

Substituting these into the chain rule expressions, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+cot^2v))
∂z/∂v = (-csc^2v) * (1/(1+cot^2v))

Simplifying these expressions using trig identities, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+(cosv/usinv)^2))
∂z/∂v = (-1/sinv^2) * (1/(1+(cosv/usinv)^2))

b) To evaluate ∂z/∂u and ∂z/∂v at (u,v) = (1.3, pi/6), we simply plug in these values into the expressions we derived in part (a):

∂z/∂u = (-cos(pi/6)/(1.3)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))
∂z/∂v = (-1/sin(pi/6)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))

Simplifying these expressions using trig functions, we get:

∂z/∂u = (-sqrt(3)/1.69^2) * (1/(1+(sqrt(3)/1.3)^2))
∂z/∂v = (-4) * (1/(1+(sqrt(3)/1.3)^2))

Plugging in the values and evaluating, we get:

∂z/∂u ≈ -0.5167
∂z/∂v ≈ -1.5045
To answer this question, we'll first express z directly in terms of u and v, and then apply the chain rule to find the partial derivatives ∂z/∂u and ∂z/∂v.

Given:
z = tan^(-1)(x/y)
x = u*cos(v)
y = u*sin(v)

First, let's express z in terms of u and v:
z = tan^(-1)((u*cos(v))/(u*sin(v)))

Now, we can simplify the expression:
z = tan^(-1)(cot(v))

Next, we'll find the partial derivatives using the chain rule:

a) ∂z/∂u:
Since z doesn't have a direct dependence on u, we have:
∂z/∂u = 0

b) ∂z/∂v:
∂z/∂v = -csc^2(v)

Now let's evaluate the partial derivatives at the given point (u,v) = (1.3, π/6):

∂z/∂u(1.3, π/6) = 0
∂z/∂v(1.3, π/6) = -csc^2(π/6) = -4

So, the partial derivatives at the given point are:
∂z/∂u = 0 and ∂z/∂v = -4.

To learn more about derivatives visit;

/brainly.com/question/30365299

#SPJ11

The arc length XW in terms of pi is (10pi)/3.

To find the length of arc XW, we need to know the measure of the angle XDW in radians.

Since XV is the diameter of the circle, we know that angle XDV is a right angle, and angle VDW is half of angle XDW. We also know that XV is 20 inches, so its radius, XD, is half of that, or 10 inches.

Using trigonometry, we can find the measure of angle VDW:

sin(VDW) = VD/VDW
sin(VDW) = 10/20
sin(VDW) = 1/2

Since sin(30°) = 1/2, we know that angle VDW is 30 degrees (or π/6 radians). Therefore, angle XDW is twice that, or 60 degrees (or π/3 radians).

Now we can use the formula for arc length:

arc length = radius * angle in radians

So the length of arc XW is:

arc XW = 10 * (π/3)
arc XW = (10π)/3

Therefore, the arc length XW in terms of pi is (10π)/3.

Know more about arc length here:

https://brainly.com/question/31762064

#SPJ11

Answer: C. 1/24 and that's is your answer to your question