To attend a Baseball game, a family of 2 adults and 4 kids pays $70. 90. Another group 7 adults and 3 kids attend the same game and pay


$139. 80.


Write a system of equations that can model this situation.


Let a = cost of one adult ticket and k = the cost of one kid ticket.

Let's start by defining our variables:

I = initial amount of ice cream = 6,200 gallons

r = rate of decrease per week = 8% = 0.08

We can use the formula for exponential decay to model the amount of ice cream left after x weeks:

f(x) = I(1 - r)^x

Substituting the values we get:

f(x) = 6,200(1 - 0.08)^x

Simplifying:

f(x) = 6,200(0.92)^x

Therefore, the function that models the number of gallons of ice cream left x weeks after the company first stocked their storage facility is f(x) = 6,200(0.92)^x.

To learn more about exponential decay click here : brainly.com/question/2193799

#SPJ11

The x-coordinate of the center of mass of the given lamina is 0.8.

The center of mass of a lamina is given by the equations:

[tex]Xc[/tex] = (1/M) ∬(D) x[tex]p(x,y) dA[/tex] and [tex]Yc[/tex] = (1/M) ∬(D) y [tex]p(x,y) dA[/tex]

where M is the total mass of the lamina and D is the region occupied by the lamina. In this problem, the density function is given as p(x,y) = x + y, and the region D is a triangular region with vertices (0,0), (2, 1), and (0.3).

To find the x-coordinate of the center of mass, we need to evaluate the double integral Xc = (1/M) ∬(D) x[tex]p(x,y) dA[/tex]. First, we need to find the mass of the lamina. This can be done by integrating the density function over the region D:

M = ∬(D) [tex]p(x,y) dA[/tex] = ∫(0,1) ∫(0,2-0.5y) (x+y) dx dy = 1.45

Now we can evaluate the double integral for [tex]Xc[/tex]:

[tex]Xc[/tex] = (1/M) ∬(D) x p(x,y) dA = ∫(0,1) ∫(0,2-0.5y) [tex]x(x+y)dydx =[/tex] 0.8

Therefore, the x-coordinate of the center of mass of the given lamina is 0.8.

Learn more about vertices here:

https://brainly.com/question/29154919

#SPJ11

The total cost of the dinner for you and your friend, including the 20% tip, is $30.98.

The cost of the meal for your friend is given as $25. To calculate the total cost, including the tip, you need to determine 20% of $25, which is the tip amount. To find 20% of a value, you can multiply the value by 0.2. In this case, 0.2 multiplied by $25 equals $5. Adding the tip amount to the cost of the meal gives you $25 + $5 = $30.

Therefore, the total cost of the dinner, including the tip, is $30. However, it's important to note that the initial tip amount of 20% is calculated based on the cost of the meal before tax. If there are additional taxes or fees, they would be added to the total cost of $30 to get the final amount.

Learn more about total cost here:

https://brainly.com/question/6506894

#SPJ11

The solution to the given initial value problem is:

w(t) = 1/2 - 1/4 e^{2(t-2)} + t^2/2 - t + 9/4 e^{2(t-4)} u(t-4)

To solve the given initial value problem using Laplace transform, we take the Laplace transform of both sides of the equation and use the properties of Laplace transform to simplify it. Let L{w(t)}=W(s) be the Laplace transform of w(t), then the Laplace transform of the right-hand side of the equation is:

L{u(t-2)-u(t-4)} = e^{-2s}/s - e^{-4s}/s

Using the properties of Laplace transform, we can find the Laplace transform of the left-hand side of the equation as:

L{w''(t)} = s^2W(s) - sw(0) - w'(0) = s^2W(s) - s

Substituting these results into the original equation and using the initial conditions, we get:

s^2W(s) - s = e^{-2s}/s - e^{-4s}/s

W(s) = (1/s^3)(e^{-2s}/2 - e^{-4s}/4 + s)

To find the solution w(t), we need to take the inverse Laplace transform of W(s). Using partial fraction decomposition and inverse Laplace transform, we get:

w(t) = 1/2 - 1/4 e^{2(t-2)} + t^2/2 - t + 9/4 e^{2(t-4)} u(t-4)

Therefore, the solution to the given initial value problem is:

w(t) = 1/2 - 1/4 e^{2(t-2)} + t^2/2 - t + 9/4 e^{2(t-4)} u(t-4)

Learn more about Laplace transform here:

https://brainly.com/question/31041670

#SPJ11

The average rate of growth of the rare 1823 stamp is 9.3% and its value increased from $250 to $1000 over a period of 10 years.

Given that ten years ago, Michael paid $250 for a rare 1823 stamp. Its current value is $1000. We have to find the average rate of growth.To find the average rate of growth, we use the formula of compounded interest rate as follows:
P = C (1 + r/n)^(nt)
Where
P = present value
C = initial value (or principal)
r = rate of interest
t = time taken to grown = number of times compounded in a year
t = 10 years
C = $250P = $1000So, $1000 = $250 (1 + r/1)^(1×10)r = 1.093-1r = 0.093
Average rate of growth is 9.3%

So, the average rate of growth of the rare 1823 stamp is 9.3% and its value increased from $250 to $1000 over a period of 10 years.

To know more about rate of growth, click here

https://brainly.com/question/18485107

#SPJ11

Thus, the sum of the series is 77. Answer: The sum of the series is 77. This answer contains a long answer that has 250 words.

To find the sum of the series (-2) + (-5) + (-8) + ... + (-20), we need to determine the number of terms in the series, and then use the formula for the sum of an arithmetic series,

which is S_n = (n/2)(a_1 + a_n), where S_n is the sum of the first n terms of the series, a_1 is the first term, a_n is the nth term, and n is the number of terms in the series. Here, a_1 = -2, and the common difference, d = -5 - (-2) = -3, so a_n = a_1 + (n-1)d = -2 + (n-1)(-3) = -2 - 3n + 3 = 1 - 3n.

We need to find n such that a_n = -20, which gives 1 - 3n = -20, or 3n = 21, or n = 7.

Therefore, there are 7 terms in the series. Using the formula, S_7 = (7/2)(-2 + (-20)) = (-7)(-22/2) = 77.

Thus, the sum of the series is 77. Answer: The sum of the series is 77.

This answer contains a long answer that has 250 words.

To know more about common difference visit:

https://brainly.com/question/28584885

#SPJ11

The asymptotes of the hyperbola with equation[tex](x - 2)^2/81 (y + 2)^2/4 = 1[/tex]are [tex]y = +(x - 2) + 2.[/tex]

The given hyperbola has a horizontal transverse axis and its center is at (2, -2). The standard form of a hyperbola with a horizontal transverse axis is[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex] , where (h, k) is the center of the hyperbola, a is the distance from the center to each vertex along the transverse axis, and b is the distance from the center to each vertex along the conjugate axis.

Comparing the given equation to the standard form, we can see that

[tex]a^2[/tex]= 81, so a = 9, and [tex]b^2[/tex] = 4, so b = 2. Therefore, the distance between the center and each vertex along the transverse axis is 9, and the distance between the center and each vertex along the conjugate axis is 2.

The asymptotes of a hyperbola with a horizontal transverse axis have equations y = +/- (b/a)(x - h) + k. Substituting the values of a, b, h, and k, we get:

y = +(2/9)(x - 2) - 2 and y = -(2/9)(x - 2) - 2

Therefore, the equations of the asymptotes for the given hyperbola are

y = +(x - 2)/9 - 2 and y = -(x - 2)/9 - 2.

Learn more about hyperbolas

brainly.com/question/28989785

#SPJ11

Step-by-step explanation:

Divided both side 2Z^2 -Y Then you will get J

(a) Zeetopia has an absolute advantage in producing coconuts since it can produce more coconuts than Freshland by using the same amount of resources.

(b) Zeetopia has a comparative advantage in producing coconuts because it has a lower opportunity cost of producing coconuts than Freshland.

The opportunity cost of producing one tonne of coconuts in Zeetopia is 3/5 tonne of mangoes, whereas, the opportunity cost of producing one tonne of coconuts in Freshland is 2 tonne of mangoes.

Therefore, Zeetopia has a comparative advantage in producing coconuts.

(c) According to the principle of comparative advantage, both islands should specialize in producing the good for which they have a lower opportunity cost. Thus, Zeetopia should specialize in producing coconuts and Freshland should specialize in producing mangoes. Both islands will gain from specialization and trade if they exchange one ton of coconuts for one ton of mangoes.

For Freshland, the opportunity cost of producing one tonne of mangoes is 2/3 tonnes of coconuts, whereas, for Zeetopia, the opportunity cost of producing one tonne of mangoes is 5/3 tonnes of coconuts.

Therefore, Freshland has a comparative advantage in producing mangoes. By specializing in producing mangoes, Freshland can produce 30 tonnes of mangoes, which can be exchanged for 30 tonnes of Zeetopia's coconuts. This exchange will benefit both countries as they will get a good that they are not efficient in producing.

(d) The production possibilities for Zeetopia and Freshland can be shown on the graph below. The horizontal axis represents the production of coconuts, while the vertical axis represents the production of mangoes. The slope of each production possibility curve (PPC) represents the opportunity cost of producing one good in terms of the other. The numerical values from the table above are plotted on the graph.

(e) The combination of coconuts and mangoes labeled X is unattainable for Freshland but feasible and inefficient for Zeetopia. Therefore, Freshland cannot produce at point X due to its limited resources, while Zeetopia is not using all of its resources efficiently if it produces at point X.

To know more about comparative advantage  please visit :

https://brainly.com/question/2827889

#SPJ11

The values, we get ; Percentage = (0.5/2.5) x 100= 20%.Therefore, the sugar required in the recipe is 20% of the quantity usually purchased by a household.

When given a recipe, it is essential to know how to convert the recipe from the metric to the US customary system and then to a percentage. For domestic purposes, sugar is usually purchased in 2.5kg. We can calculate the sugar required in the recipe as a percentage of the amount usually purchased by the household using the following steps:

Step 1: Convert the sugar required in the recipe from grams to kilograms.

Step 2: Calculate the percentage of the sugar required in the recipe to the quantity purchased by a household, usually 2.5 kg.  Let's say the recipe requires 500g of sugar.

Step 1: We need to convert 500g to kg. We know that 1000g = 1kg, so 500g = 0.5kg.

Step 2: We can now calculate the percentage of the sugar required in the recipe as a percentage of the amount usually purchased by a household, which is 2.5kg.

We can use the following formula: Percentage = (amount of sugar required/quantity purchased by household) x 100. Substituting the values, we get; Percentage = (0.5/2.5) x 100= 20%.Therefore, the sugar required in the recipe is 20% of the quantity usually purchased by a household.

To know more about Percentage visit :

https://brainly.com/question/3188366

#SPJ11

The measure of angle A in a right triangle with base 5 cm and hypotenuse 10 cm is approximately 38.21 degrees.

We can use the inverse cosine function (cos⁻¹) to find the measure of angle A, using the cosine rule for triangles.

According to the cosine rule, we have:

cos(A) = (b² + c² - a²) / (2bc)

where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively. In this case, we have b = 5 cm and c = 10 cm (the hypotenuse), and we need to find A.

Applying the cosine rule, we get:

cos(A) = (5² + 10² - a²) / (2 * 5 * 10)

cos(A) = (25 + 100 - a²) / 100

cos(A) = (125 - a²) / 100

To solve for A, we need to take the inverse cosine of both sides:

A = cos⁻¹((125 - a²) / 100)

Since this is a right triangle, we know that A must be acute, meaning it is less than 90 degrees. Therefore, we can conclude that A is the smaller of the two acute angles opposite the shorter leg of the triangle.

Using the Pythagorean theorem, we can find the length of the missing side at

a² = c² - b² = 10² - 5² = 75

a = √75 = 5√3

Substituting this into the formula for A, we get:

A = cos⁻¹((125 - (5√3)²) / 100) ≈ 38.21 degrees

Therefore, the measure of angle A is approximately 38.21 degrees.

Learn more about cosine rule here:

brainly.com/question/30918098

#SPJ1

The probability that a randomly chosen value is greater than 3 is 0.8413.

(a) Let X be a random variable with a normal distribution with mean μ = 10 and standard deviation σ = 7. We want to find the proportion of the population that is less than 21, or P(X < 21).

Using the standard normal distribution, we can find the z-score corresponding to 21:

z = (21 - μ) / σ = (21 - 10) / 7 = 1.57

Looking up the corresponding probability in the standard normal distribution table, we find that P(Z < 1.57) = 0.9418.

Therefore, P(X < 21) = P(Z < 1.57) = 0.9418.

(b) We want to find the probability that a randomly chosen value is greater than 3, or P(X > 3).

Again, we can use the standard normal distribution and find the z-score corresponding to 3:

z = (3 - μ) / σ = (3 - 10) / 7 = -1

Using the standard normal distribution table, we find that P(Z > -1) = P(Z < 1) = 0.8413.

Therefore, P(X > 3) = 1 - P(X < 3) = 1 - P(Z < -1) = 1 - 0.1587 = 0.8413.

So the probability that a randomly chosen value is greater than 3 is 0.8413.

To know more about probability refer here:

https://brainly.com/question/11234923

#SPJ11

Given data: A student takes an exam containing 11 multiple-choice questions. The probability of choosing a correct answer by knowledgeable guessing is 0.6. This problem is related to the concept of the binomial probability distribution, as there are two possible outcomes (right or wrong) and the number of trials (questions) is fixed.

Let p = the probability of getting a question right = 0.6

Let q = the probability of getting a question wrong = 0.4

Let n = the number of questions = 11

We need to find the probability of getting exactly 11 questions right, which is a binomial probability, and the formula for finding binomial probability is given by:

[tex]P(X=k) = (nCk) * p^k * q^(n-k)Where P(X=k) = probability of getting k questions rightn[/tex]

Ck = combination of n and k = n! / (k! * (n-k)!)p = probability of getting a question rightq = probability of getting a question wrongn = number of questions

k = number of questions right

We need to substitute the given values in the formula to get the required probability.

Solution:[tex]P(X = 11) = (nCk) * p^k * q^(n-k) = (11C11) * (0.6)^11 * (0.4)^(11-11)= (1) * (0.6)^11 * (0.4)^0= (0.6)^11 * (1)= 0.0282475248[/tex](Rounded to 4 decimal places)

Therefore, the required probability is 0.0282 (rounded to 4 decimal places).Answer: 0.0282

To know more about binomial probability, visit:

https://brainly.com/question/12474772

#SPJ11

To determine the size of carpets that will maximize the company's revenue, we need to find the dimensions that will generate the highest total sales. Let's analyze the situation step by step.

We know that the company can sell 200 carpets per week when the size is 3ft by 3ft. Beyond this size, for each additional foot of length and width, the number sold decreases by 4.

Let's denote the additional length and width beyond 3ft as x. Therefore, the dimensions of the carpets will be (3 + x) ft by (3 + x) ft.

Now, we need to determine the relationship between the number of carpets sold and the dimensions. We can observe that for each additional foot of length and width, the number sold decreases by 4. So, the number of carpets sold can be expressed as:

Number of Carpets Sold = 200 - 4x

Next, we need to calculate the revenue generated from selling these carpets. The price per square foot is $5, and the area of the carpet is (3 + x) ft by (3 + x) ft, which gives us:

Revenue = Price per Square Foot * Area

= $5 * (3 + x) * (3 + x)

= $5 * (9 + 6x + [tex]x^2)[/tex]

= $45 + $30x + $5[tex]x^2[/tex]

Now, we can determine the dimensions that will maximize the revenue by finding the vertex of the quadratic function. The x-coordinate of the vertex gives us the optimal value of x.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a = $5 and b = $30.

x = -30 / (2 * 5)

x = -30 / 10

x = -3

Since we are dealing with dimensions, we take the absolute value of x, which gives us x = 3.

Therefore, the additional length and width beyond 3ft that will maximize the revenue is 3ft.

The dimensions of the carpets that the company should sell to maximize its revenue are 6ft by 6ft.

To calculate the maximum weekly revenue, we substitute x = 3 into the revenue function:

Revenue = $45 + $30x + $[tex]5x^2[/tex]

= $45 + $30(3) + $5([tex]3^2)[/tex]

= $45 + $90 + $45

= $180

Hence, the maximum weekly revenue for the company is $180.

Learn more about statistics here:

https://brainly.com/question/31527835

#SPJ11

Answer:

The relationship between x and y is a negative linear relationship

Step-by-step explanation:

To construct a scatterplot, we plot each (x,y) pair as a point in a coordinate plane. Using the given data, we get:

(x,y) = (3,34), (6,28), (10,20), (14,12), (18,5), (23,0)

We can then plot these points and connect them with a line to visualize the relationship:


  35|                      .
    |                .      
    |          .            
    |    .                  
    |.                      
  0 +------------------------
    0   5   10   15   20   25  
              x              


From the scatterplot, we can see that the relationship between x and y is a negative linear relationship. As x increases, y tends to decrease.

To Know more about scatterplot refer here
https://brainly.com/question/30017616#
#SPJ11

To find the number of children, students, and adults attending the movie theater, we can solve the system of equations based on the given information.

Let's assume the number of children attending the movie theater is C. Since there are half as many adults as children, the number of adults attending is A = C/2. Let's denote the number of students attending as S.

From the seating capacity of the theater, we have the equation C + S + A = 379. Since there are half as many adults as children, we can substitute A with C/2 in the equation, which becomes C + S + C/2 = 379.

To solve for C, S, and A, we need another equation. We know the ticket prices for each category, so the total ticket sales can be calculated as 5C + 7S + 12A. Given that the total ticket sales amount to $2746, we can substitute the variables and obtain the equation 5C + 7S + 12(C/2) = 2746.

Now we have a system of two equations with two variables. By solving this system, we can find the values of C, S, and A, which represent the number of children, students, and adults attending the movie theater, respectively.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ11

To estimate the sum of 192 and 91 by rounding both values to the nearest ten, we round 192 to 190 and 91 to 90.

190 + 90 = 280

Therefore, the best estimate of the sum is 280.

Learn more about estimate here:

https://brainly.com/question/30870295

#SPJ11

Simplifying the expression gives the equivalent expression as: [tex]\frac{b}{2a^{2} b^{3} } \sqrt[3]{15b}[/tex]

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

The expression we want to solve is given as:

[tex]\sqrt[3]{\frac{75a^{7}b^{4} }{40a^{13}b^{9} } }[/tex]

Using laws of exponents, the bracket is simplified to get:

[tex]\sqrt[3]{\frac{75a^{7 - 13}b^{4 - 9} }{40} } } = \sqrt[3]{\frac{75a^{-6}b^{-5} }{40} } }[/tex]

This simplifies to get:

[tex]\frac{b}{2a^{2} b^{3} } \sqrt[3]{15b}[/tex]

Read more about Laws of Exponents at: https://brainly.com/question/11761858

#SPJ4

The between-group degrees of freedom is (a) 2

From the question, we have the following parameters that can be used in our computation:

Groups  = 3

Respondents = 15

The between-group degrees of freedom is calculated as

df = n - 1

Where

n = groups

So, we have

df = 3 - 1

Evaluate

df = 2

Hence, the between-group degrees of freedom is (a) 2

Read more about degrees of freedom at

https://brainly.com/question/12743198

#SPJ1

Given that a student takes 6 classes before Test #3. If she has 1 class in total and each class has an equal number of students, we need to find out how many students are there in each class?

Let's assume that the number of students in each class is 'x'. Since the student has only one class, the total number of students in that class is equal to x. So, we can represent it as: Total students = x We can also represent the total number of classes as:

Total classes = 1 We are also given that a student takes 6 classes before Test #3.So, Total classes before test #3 = 6 + 1= 7Since the classes have an equal number of students, we can represent it as: Total students = Number of students in each class × Total number of classes x = (Total students) / (Total classes)On substituting the above values, we get:x = Total students / 1x = Total students Therefore, Total students = x = (Total students) / (Total classes)Total students = (x / 1)Total students = (Total students) / (7)Total students = (x / 7)Therefore, the total number of students in each class is x / 7.Round off the answer to the nearest whole number (i.e., one student), we get: Number of students in each class ≈ x / 7

Know  more about find out how many students here:

https://brainly.com/question/21295513

#SPJ11

The surface area of the given object is 20 square yards

The question asks for the surface area of an object, but it does not provide any specific information about the object itself. Without knowing the shape or dimensions of the object, it is not possible to determine its surface area.

In order to calculate the surface area of a shape, we need to know its specific measurements, such as length, width, and height. Additionally, different shapes have different formulas to calculate their surface areas. For example, the surface area of a cube is given by the formula 6s^2, where s represents the length of a side. The surface area of a rectangular prism is calculated using the formula 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height, respectively.

Therefore, without further information about the shape or measurements of the object, it is not possible to determine its surface area. The given answer options of 20, 16, 20, 24, and 23 square yards are unrelated to the question and cannot be used to determine the correct surface area.

Learn more about area here:

https://brainly.com/question/27776258

#SPJ11

The statement "f(7) = 5" represents a function, where the input value is 7 and the output value is 5. In coordinate notation, this can be written as (7, 5).

In this case, the x-coordinate represents the input value (7) and the y-coordinate represents the output value (5) of the function .

In mathematics, a function is a relationship between input values (usually denoted as x) and output values (usually denoted as y). The notation "f(7) = 5" indicates that when the input value of the function f is 7, the corresponding output value is 5.

To represent this relationship as a coordinate point, we use the (x, y) notation, where x represents the input value and y represents the output value. In this case, since f(7) = 5, we have the coordinate point (7, 5).

This means that when you input 7 into the function f, it produces an output of 5. The x-coordinate (7) indicates the input value, and the y-coordinate (5) represents the corresponding output value. So, the point (7, 5) represents this specific relationship between the input and output values of the function at x = 7.

Learn more about geometry here:

https://brainly.com/question/19241268

#SPJ11

The line integral is: ∫_c F · dr = ∬_D (curl F) · dA = -70/3.

To apply Green's theorem, we need to find the curl of the vector field:

curl F = (∂Q/∂x - ∂P/∂y) = (-16x^2 - 6, 0, 5)

where F = (P, Q) = (3cos(x) - 6y^2, sin(5y) + 16x^3).

Now, we can apply Green's theorem to evaluate the line integral over the boundary of the square:

∫_c F · dr = ∬_D (curl F) · dA

where D is the region enclosed by the square [0, 1] × [0, 1].

Since the curl of F has only an x and z component, we can simplify the double integral by integrating with respect to y first:

∬_D (curl F) · dA = ∫_0^1 ∫_0^1 (-16x^2 - 6) dy dx

= ∫_0^1 (-16x^2 - 6) dx

= (-16/3) - 6

= -70/3

Therefore, the line integral is:

∫_c F · dr = ∬_D (curl F) · dA = -70/3.

Learn more about line integral  here:

https://brainly.com/question/30640493

#SPJ11

The mean area for these states is approximately 157,971 square miles, and the median area is 104,400 square miles.

To get the mean and median area for these states, you'll need to follow these steps:
Organise the data in ascending order:
6,000; 52,300; 53,400; 104,400; 114,600; 159,000; 615,100
Calculate the mean area (sum of all areas divided by the number of states)
Mean = (6,000 + 52,300 + 53,400 + 104,400 + 114,600 + 159,000 + 615,100) / 7
Mean = 1,105,800 / 7
Mean ≈ 157,971 square miles (rounded to the nearest integer)
Calculate the median area (the middle value of the ordered data)
There are 7 states, so the median will be the area of the 4th state in the ordered list.
Median = 104,400 square miles
So, the mean area for these states is approximately 157,971 square miles, and the median area is 104,400 square miles.

Lean more about median here, https://brainly.com/question/26177250

#SPJ11

Yes, it is possible for the sum of two lower triangular matrices to be a non-lower triangular matrix.

To see why, consider the following example:

Suppose we have two lower triangular matrices A and B, where:

A =

[1 0 0]

[2 3 0]

[4 5 6]

B =

[1 0 0]

[1 1 0]

[1 1 1]

The sum of A and B is:

A + B =

[2 0 0]

[3 4 0]

[5 6 7]

This matrix is not lower triangular, as it has non-zero entries above the main diagonal.

Therefore, the sum of two lower triangular matrices can be a non-lower triangular matrix if their corresponding entries above the main diagonal do not cancel out.

To know more about triangular matrix , refer here :

https://brainly.com/question/13385357#

#SPJ11

The value of cos2u is [tex]\frac{-527}{625}[/tex].

Let's start by finding sin v, which we can do using the Pythagorean identity:

[tex]sin^{2} + cos^{2} = 1[/tex]

[tex]sin^{2}v+(\frac{-7}{25} )^{2} = 1[/tex]

[tex]sin^{2} = 1-(\frac{-7}{25} )^{2}[/tex]

[tex]sin^{2}= 1-\frac{49}{625}[/tex]

[tex]sin^{2} = \frac{576}{625}[/tex]

Taking the square root of both sides, we get: sin v = ±[tex]\frac{24}{25}[/tex]

Since cos v is negative and sin v is positive, we know that v is in the second quadrant, where sine is positive and cosine is negative. Therefore, we can conclude that: [tex]sin v = \frac{24}{25}[/tex]

Now, let's use the double angle formula for cosine to find cos 2u: cos 2u = cos²u - sin²u

We can substitute the values we know:

[tex]cos 2u = (\frac{7}{25}) ^{2}- (\frac{24}{25} )^{2}[/tex]

[tex]cos 2u = \frac{49}{625} - \frac{576}{625}[/tex]

[tex]cos 2u = \frac{-527}{625}[/tex]

Therefore, the exact value of cos 2u is [tex]\frac{-527}{625}[/tex].

To know more about  "Pythagorean identity" refer here:

https://brainly.com/question/15586213#

#SPJ11

The triple integral of f(e, 0, ¢) = sin o in spherical coordinates over the region 0 < 0 < 27, 0<¢<, 3 is 54π. Spherical coordinates are a system of coordinates used to locate a point in 3-dimensional space.

To evaluate the triple integral of f(e, 0, ¢) = sin o in spherical coordinates over the region 0 < 0 < 27, 0<¢<, 3, we need to express the integral in terms of spherical coordinates and then evaluate it.

The triple integral in spherical coordinates is given by:

∫∫∫ f(e, 0, ¢)ρ²sin(φ) dρ dφ dθ

where ρ is the radial distance, φ is the polar angle, and θ is the azimuthal angle.

Substituting the given function and limits, we get:

∫∫∫ sin(φ)ρ²sin(φ) dρ dφ dθ

Integrating with respect to ρ from 0 to 3, we get:

∫∫ 1/3 [ρ²sin(φ)]dφ dθ

Integrating with respect to φ from 0 to π/2, we get:

∫ 1/3 [(3³) - (0³)] dθ

Simplifying the integral, we get:

∫ 27 dθ

Integrating with respect to θ from 0 to 2π, we get:

54π

Therefore, the triple integral of f(e, 0, ¢) = sin o in spherical coordinates over the region 0 < 0 < 27, 0<¢<, 3 is 54π.

To learn more about spherical coordinates : https://brainly.com/question/29555384

#SPJ11

The area of the surface as a double integral is ∫∫(3z/√(9z^2 - z^4)) dA, where the limits of integration are 9≤z≤12 and 0≤θ≤2π.

To express the surface area of the cone frustrum, we need to first parameterize the surface in terms of cylindrical coordinates (r, θ, z). The equation of the cone frustrum can be written as z=3√(x^2+y^2), which, in cylindrical coordinates, becomes z=3r.

The limits of integration for z are 9≤z≤12, and the limits for θ are 0≤θ≤2π. To express the surface area in terms of a double integral, we use the formula dA=r dz dθ, and we can find the surface area by integrating ∫∫(3z/√(9z^2 - z^4)) dA over the limits of integration.

After carrying out the integration, we obtain the surface area of the cone frustrum between the planes z=9 and z=12.

For more questions like Integral click the link below:

https://brainly.com/question/22008756

#SPJ11

Answer:

[tex] \frac{135 \times {10}^{ - 9} }{.0005 \times {10}^{ - 5} } = \frac{135 \times {10}^{ - 9} }{5 \times {10}^{ - 9} } = 27 = \frac{27}{1} [/tex]

The ratio of the size of cell A to the size of cell B is 27, or 27/1.

The probability of choosing a jack and then an eight is (4/52) * (4/52) = 16/2704, which simplifies to 1/169.

Step 1: Probability of choosing a jack

In a standard deck of 52 cards, there are four jacks (one in each suit). So the probability of choosing a jack on the first draw is 4/52.

Step 2: Probability of choosing an eight

After replacing the first card, the deck is restored to its original state with 52 cards. Therefore, the probability of choosing an eight on the second draw is also 4/52.

Step 3: Probability of choosing a jack and then an eight

Since we want to find the probability of both events happening (choosing a jack and then an eight), we need to multiply the probabilities from steps 1 and 2.

The probability of choosing a jack (4/52) and then an eight (4/52) can be calculated as (4/52) * (4/52). This multiplication gives us 16/2704.

Simplifying the fraction, we get 1/169.

Therefore, the probability of choosing a jack and then an eight is 1/169.

Learn more about probability Visit : brainly.com/question/13604758

#SPJ11