Is this table a function or not a function
X Y
-3 1
0 -5
4 7
-3 0

Of the signals given, only signal (b) is periodic, with a fundamental period of t0 = 2π and a fundamental frequency of ω0 = 1/2π. The rest of the signals are not periodic because their frequencies are not rational multiples of each other.

The fundamental period of a periodic signal is the smallest positive value of t0 for which x(t) = x(t + t0) for all values of t. The fundamental frequency is the inverse of the fundamental period, ω0 = 1/t0.

(a) x(t) = cos3t + sin5t

(b) x(t) = cost + sinπt

(c) x(t) = cos(3t) + sin(9t)

(d) x(t) = cos(3πt) + sin(4πt) + cos(5t)

(e) x(t) = cos(4πt) + sin(6πt) + ej5πt

(f) x(t) = cos(3t+30∘) + ej2t + sin(3πt)

In conclusion, only signal (b) is periodic with a fundamental period of t0 = 2π and a fundamental frequency of ω0 = 1/2π. The rest of the signals are not periodic because their frequencies are not rational multiples of each other.

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There are 10,000 probability codes if the four digits can be repeated, as each digit has 10 possible options (0-9). This ensures that customers have a secure and safe way to access their storage containers.

In the event that the four numbers can be repeated, there are 10,000 potential codes. This is because there are 10 potential values for each digit (0-9). If you multiply all the possible options of each number you get 10x10x10x10 which equals 10,000. This means there are 10,000 possible combinations of four digits when the numbers can be repeated. For example, 0000, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999 and all their different combinations with the numbers 0-9 in between them. With this many choices, it can be hard to remember your specific code. However, it also means that there is a low risk of someone else guessing your code. The Store-It-All storage facility is ensuring that their customers have a secure and safe way to access their storage containers.

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A demand curve is a graph that shows the relationship between the price of a product or service and the quantity of that product or service that consumers are willing to buy at that price.

A graph is a visual representation of data that is used to show the relationship between two or more variables. Graphs are used in many fields, such as mathematics, science, economics, and social sciences, to display and analyze data in a way that is easy to interpret.

There are several types of graphs, each with its own unique features and uses. Some common types of graphs include:

Line graphs: A line graph is used to display data that changes over time. The data points are connected by lines to show the trend of the data.

Bar graphs: A bar graph is used to compare data across different categories. The height or length of the bars represents the quantity or value of the data.

Pie charts: A pie chart is used to display the proportion of data in different categories. The size of each slice of the pie represents the percentage of the total data.

Scatter plots: A scatter plot is used to display the relationship between two variables. Each data point is represented by a dot on the graph, and the position of the dot represents the value of the two variables.

A demand curve is a graph that shows the relationship between the price of a product or service and the quantity of that product or service that consumers are willing to buy at that price. The demand curve is downward sloping, meaning that as the price of the product or service increases, the quantity demanded decreases, and as the price decreases, the quantity demanded increases.

TRIBE is an acronym that stands for the five factors that can affect the demand for a product or service. These factors are:

An increase in demand, represented by the curve D1, could be caused by a shift in one or more of these factors. For example, if a new study finds that consuming the product has health benefits, the taste and preferences of consumers may shift, leading to an increase in demand for the product.

A decrease in demand, represented by the curve D2, could also be caused by a shift in one or more of these factors. For example, if the price of a related good or service decreases, consumers may switch to that alternative, leading to a decrease in demand for the original product.

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We can conclude that f(x) has exactly one critical point and that this point is a local minimizer but not a global minimizer.

To show that f(x) has exactly one critical point and that this point is a local minimizer but not a global minimizer, we need to find the first and second derivative of the function and analyze their behavior at the critical point.

First, let's find the first derivative of f(x):

f'(x) = (d/dx) f(x)

Next, let's find the critical point by setting f'(x) = 0 and solving for x:

0 = f'(x)

x = critical point

Now, let's find the second derivative of f(x):

f''(x) = (d/dx) f'(x)

Finally, let's analyze the behavior of f''(x) at the critical point. If f''(x) > 0 at the critical point, then the point is a local minimizer. However, if f''(x) < 0 at the critical point, then the point is not a global minimizer.

Therefore, we can conclude that f(x) has exactly one critical point and that this point is a local minimizer but not a global minimizer.

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The solution of the system of equation by converting them into matrix is equal to ( x  y ) = ( -3  2/19 ).

Convert the system of equations to a matrix equation,

( -3  5  2  3 ) (x y ) = ( 5  0 )

To solve for ( x y ) multiply both sides by the inverse of the coefficient matrix by ( -3  5  2  3 ),

find the inverse,

( a  b c d )^(-1) = ( 1/ ad -bc ) (d  -b  -c  a )

where ad - bc is the determinant of the matrix.

In this case, the determinant is,

(-3)(3) - (5)(2)

= -19

so the inverse is,

( -3 5 2 3 )^(-1)

= (1 /-19)( 3  -5  -2  -3 )

= ( -3/19  5/19  2/19  3/19  )

Multiplying both the sides of the matrix equation by the inverse we get,

(x y ) = ( -3/19  5/19  2/19  3/19  )(5  0)

⇒( x  y ) = ( -3  2/19 )

Therefore , the solution of the system of equation using matrix is equal to  ( x y ) = ( -3  2/19 ).

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To make the first element in row 2 equal to 0, we need to perform a row operation on the matrix.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Matrices are commonly used in mathematics, computer programming, and other fields to represent and manipulate data, equations, and transformations.

One way to do this is to add 2 times the first row to the second row:

4  -4   0  10

0  -6   2 -16

-1  -4   7  -6

The resulting matrix has a 0 in the first element of the second row. Note that we added 2 times the first row to the second row because we want to eliminate the first element of the second row by making it zero.

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Answer: add row 1 and row 2 and insert the result in row two.

Step-by-step explanation:

did it on edge

The effective interest rate in the fifth year for Sylvia's account will be 1.9216% The effective interest rate in the fifth year for Sylvia's account will be the same as the annual rate of 2%, since simple discount is calculated using the same rate each year.

Simple discount is a method of calculating interest where the interest is calculated based on the original principal amount, and the rate is the same each year. Therefore, the effective interest rate in the fifth year will be the same as the annual rate of 2%.

To calculate the effective interest rate in the fifth year, we can use the formula: Effective interest rate = [tex](1 - (1 - annual rate) ^ number of years) / number of years[/tex]

Plugging in the values for Sylvia's account: Effective interest rate = [tex](1 - (1 - 0.02) ^ 5) / 5[/tex], Effective interest rate = [tex](1 - 0.98 ^ 5) / 5[/tex], Effective interest rate = (1 - 0.90392) / 5, Effective interest rate = 0.09608 / 5 Effective interest rate = 0.019216

Therefore, the effective interest rate in the fifth year for Sylvia's account is 0.019216, or 1.9216%. This is the same as the annual rate of 2%, since simple discount is calculated using the same rate each year.

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The Future Value at the end of 14 years is $68,522.69.

What is Compound interest?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

For the first $10,000, we have:

Principal (P) = $10,000

Annual interest rate (r) = 12%

Compounding period (n) = 12 (since it's compounded monthly)

Time (t) = 14 years

Using the formula for compound interest, we get:

[tex]A = P(1 + r/n)^(nt)[/tex]

A = 10000(1 + 0.12/12)^(1214)

A = 10000(1 + 0.01)^168

A = 10000(1.01)^168

A = 10000(4.6934)

A = $46,934.07

Principal (P) = $10,000

Annual interest rate (r) = 12%

Compounding period (n) = 12 (since it's compounded monthly)

Time (t) = 7 years

Using the same formula, we get:

[tex]A = P(1 + r/n)^(nt)[/tex]

A = 10000(1 + 0.12/12)^(127)

A = 10000(1 + 0.01)^84

A = 10000(2.1589)

A = $21,588.62

Adding the two amounts together, we get:

$46,934.07 + $21,588.62 = $68,522.69

Therefore, the Future Value at the end of 14 years is $68,522.69.

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Polynomial function p(x) is continuous for all values of x, or on the interval (-∞, ∞).

A limit in calculus is a mathematical notion that defines how a function behaves when its input approaches a particular value. The value that f(x) approaches when x comes arbitrarily close to a value c—but not necessarily equals—is the limit of a function f(x) as x approaches that value. This idea is crucial to understanding calculus because it enables us to investigate the behaviour of functions that could be ill-defined or discontinuous at some points.

The given polynomial is p(x) = 6x⁵ + 7x⁴ + 5.

We know that, all polynomial functions are continuous on their entire domain.

Hence, p(x) is continuous for all values of x, or on the interval (-∞, ∞).

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Clyde needs an additional 1 cup of flour to make twice the recipe.

If the recipe requires 1} cups of flour, then double the recipe would require 2(1.5) = 3 cups of flour. Since Clyde already has 2 cups of flour, he still needs to get an additional amount of flour, which we can represent as "c".

The equation that represents the problem is:

2 + c = 3

where "2" represents the cups of flour that Clyde already has, "c" represents the additional amount of flour that he needs, and "3" represents the total amount of flour required for the doubled recipe.

Simplifying the equation, we get:

c = 3 - 2

c = 1

Therefore, Clyde needs an additional 1 cup of flour to make twice the recipe.

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The required surface area of the prism with area of the triangular base as 6 square centimeters and volume 18 cm³ is given by 12.5√12 square centimeters.

Let the triangular base of the prism be an equilateral triangle with side length s.

Then, the perimeter of the base is 12,

so we have

3s = 12,

⇒s = 4.

The area of the triangular base is

(√3/4)s²

= (√3/4)(4)²

= 4√12

The volume of the prism is equal to 18 cubic centimeters,

Set up the equation V = Bh,

where B is the area of the base

And h is the height of the prism.

Now,  solve for $h to get,

h

= V /B

= 18 /4√12

= 9/2√12

= 3√12/8

Lateral surface area of the prism is given by the formula

A = Ph,

where P is the perimeter of the base

And h is the height of the prism.

The perimeter of the base is 12,

height is 3√12/8,

so we have

A = 12 ( 3√12/8 )

   = 9√12/2

Total surface area of the prism is the sum of the area of the two triangular bases and the lateral surface area.

Each triangular base has area 4√12,

Total surface area is

= 2 (4√12 ) + 4.5√12

= 12.5√12

Therefore, the surface area of the prism is 12.5√12 square centimeters.

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Answer:

D.76

Step-by-step explanation:

First, go 2x4x2 for the bottom, and the top of it

Then, for both sides go 5x4x2

Then, for the other sides go 2x5x2

After that, add all of the numbers after you do the equation.

The y-intercept of the tangent line to the two circles at points in the first quadrant is 8/3. So, Option (c) is correct answer.

Let's first find the equation of the line tangent to both circles. Since the two circles have centers on the x-axis, the tangent line must also pass through the point (3, y) for some y > 0. Let (x1, y1) be the point of tangency on the circle of radius 2 and (x2, y2) be the point of tangency on the circle of radius 1. Then we have:

(x1 - 2)^2 + y1^2 = 2^2, (1)

(x2 - 5)^2 + y2^2 = 1^2, (2)

y - y1 = (x - 3)tanθ, (3)

y - y2 = (x - 3)tanθ, (4)

where θ is the angle between the positive x-axis and the line. Subtracting (2) from (1) and simplifying, we get:

2x1 - x2 = 9. (5)

Differentiating (1) and (2) with respect to x and setting them equal to (3) and (4), respectively, we get:

x1 - 2ytanθ = 3tanθ, (6)

x2 - 5ytanθ = 3tanθ. (7)

Substituting (5) into (6) and (7) and solving for y1 and y2, we get:

y1 = √7/3, (8)

y2 = (2√2 - 5√7)/3. (9)

Since y > 0, the tangent line must pass through the point (3, √7/3). Plugging this into (3), we get:

y - √7/3 = (x - 3)tanθ.

At the point of tangency (x1, y1), the slope of the tangent line is given by dx/dy = -dy/dx = -1/(4t+1), where t = (x1 - 2)/4. Therefore, at t = (3 - 2)/4 = 1/4, we have:

slope = -1/(4(1/4)+1) = -1/5.

So the slope of the tangent line at time t = 3 is also -1/5. Therefore, the equation of the tangent line is:

y - √7/3 = -(1/5)(x - 3),

or y = -(1/5)x + (8√7)/15.

Setting x = 0, we get the y-intercept:

y = (8√7)/15.

Therefore, the answer is (c) 8/3.

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The functions and their domains. (enter the domains in interval notation.) f(x) = x 1 x , g(x) = x 8 x 2 (a) f ∘ g is :

 f ∘ g is f(g(x)) = x9/x and its domain is (0,∞).

The function f(x) = x1/x has a domain of all real numbers greater than zero (0,∞). The function g(x) = x8/x2 has a domain of all real numbers greater than zero (0,∞).

The composition of f ∘ g is f(g(x)) = x9/x and its domain is (0,∞).

Interval notation is a way of expressing intervals or ranges of numbers in a concise and easy-to-understand format. It uses brackets, parentheses, and infinity symbols to indicate whether the endpoints of the interval are included or excluded.

The basic forms of interval notation are:

1.Open interval: (a, b) denotes all the numbers between a and b, excluding both endpoints.

Example: (2, 5) represents all the numbers between 2 and 5, but not including 2 and 5.

2.Closed interval: [a, b] denotes all the numbers between a and b, including both endpoints.

Example: [2, 5] represents all the numbers between 2 and 5, including 2 and 5.

3.Half-open interval: (a, b] or [a, b) denotes all the numbers between a and b, including one endpoint but not the other.

Example: (2, 5] represents all the numbers between 2 and 5, including 5 but not including 2.

4.Unbounded interval: (-∞, a) or (a, ∞) denotes all the numbers less than or greater than a, respectively.

Example: (-∞, 5) represents all the numbers less than 5, while (2, ∞) represents all the numbers greater than 2.

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2 is verified.

a) Solving the differential equation for x(t) with Laplace transforms and given u(t) = 1(t)We know that Laplace transforms of the derivative of x(t) is sX(s) − x(0).Thus, sX(s) − x(0) + 4X(s) = 2/s ...(1)On putting x(0) = −5 and u(t) = 1(t), we getX(s) = -5s+2/s(s+4)On partial fractions and inverse Laplace transforms, we get x(t) = (2/3)e-4t + (5/3) - (5/3)e-4tThe initial condition, x(0) = -5 is verified.b) Solving the differential equation for x(t) with Laplace transforms and given u(t) = 1(t)We know that Laplace transforms of the derivative of x(t) is sX(s) − x(0).Thus, s^2X(s) − sx(0) − x′(0) + 4X(s) + 13X(s) = 5/s ...(2)On putting x(0) = 2 and u(t) = 1(t), we getX(s) = 1/((s^2 + 4s + 13) × s) {2s + 5}On inverse Laplace transforms, we get x(t) = (3/13)e-t(2sin3t + 5cos3t) + 2cos2tThe initial condition, x(0) = 2 is verified.On putting x(0) = 0 and u(t) = 1(t), we getX(s) = 1/((s^2 + 4s + 13) × s)Thus, x(t) = (3/13)e-t(2sin3t + 5cos3t) + 2cos2tThe initial condition, x(0) = 0 is verified.c) Solving the differential equation for x(t) with Laplace transforms and given u(t) = 1(t)We know that Laplace transforms of the derivative of x(t) is sX(s) − x(0).Thus, s^2X(s) − sx(0) − x′(0) + 6X(s) + 9X(s) = 2/s ...(3)On putting x(0) = 0 and u(t) = 1(t), we getX(s) = 2/(s(s+3)^2)On inverse Laplace transforms, we get x(t) = (2/3)t - 2/3e-3t - 2te-3tThe initial condition, x(0) = 0 is verified.On putting x(0) = 2 and u(t) = 1(t), we getX(s) = 2/(s(s+3)^2) + 4/(s+3)^2On inverse Laplace transforms, we get x(t) = (2/3)t - 2/3e-3t - 2te-3t + 2te-3tThe initial condition, x(0) = 2 is verified.

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total number of tickets sold = x + y = 9 + 18 = 27. So, Darius sold 27 tickets altogether.

what is an algebraic expression?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division) that represent a quantity.

Let x be the number of children's tickets sold, and let y be the number of adult tickets sold.

From the problem statement, we know that:

The price of a children's ticket is $4.50

The price of an adult ticket is $6.50

The total amount collected is $157.50

The number of adult tickets sold is twice the number of children's tickets sold

Using this information, we can set up the following system of equations:

x + y = total number of tickets sold (equation 1)

4.5x + 6.5y = 157.5 (equation 2)

y = 2x (equation 3)

We can use equation 3 to substitute y in terms of x in equations 1 and 2:

x + 2x = total number of tickets sold (substitute y = 2x from equation 3 into equation 1)

4.5x + 6.5(2x) = 157.5 (substitute y = 2x from equation 3 into equation 2)

Simplifying these equations, we get:

3x = total number of tickets sold (simplifying the left side of the first equation)

17.5x = 157.5 (simplifying the second equation)

x = 9 (dividing both sides of the second equation by 17.5)

Therefore, the number of children's tickets sold is x = 9, and the number of adult tickets sold is y = 2x = 2(9) = 18.

To find the total number of tickets sold, we can add x and y:

therefore, total number of tickets sold = x + y = 9 + 18 = 27

So, Darius sold 27 tickets altogether.

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Solution of 12 divided by 912 is, 76

We have,

To calculate 12 divided by 912.

Now, By using long division method,

12 divided by 912.

12 ) 912 (76

    - 84

   ---------

         72

       - 72

      ------------

            0

Therefore, Solution of 12 divided by 912 is, 76

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Answer:

Step-by-step explanation:

using [tex]i=\sqrt{-1}[/tex],

[tex]\sqrt{-6} = \sqrt{6\times-1}[/tex]

        [tex]=\sqrt{6} \times \sqrt{-1}[/tex]

        =[tex]\sqrt{6} \times i\\[/tex]

Solution: [tex]a=0, b=\sqrt{6}[/tex]

In circle centered on (0,0) and a right triangle with one vertex at the origin of the circle  and the hypotenuse as a radius of the circle. By using Pythagorean theorem, the length of leg a is 4 units, and the length of leg b is 3 units. We can label corner A as (4,0) and corner C as (0,3).

Consider a circle centered at M (0,0) with a radius of 5 units. Let the hypotenuse of the right triangle be a radius of the circle. Let's say this hypotenuse is 5 units. Then, using the Pythagorean theorem, we can find the length of the other two sides:

a^2 + b^2 = c^2

where c is the hypotenuse (5 units), and a and b are the other two sides we want to find.

Let's say we want to label the corner of the triangle opposite to the hypotenuse as C, and the corners adjacent to the legs as A and B. Then we can set up the following:

Leg a runs from the origin (0,0) to corner A.

Leg b runs from corner A to corner C.

Hypotenuse c runs from the origin (0,0) to corner C.

Using the Pythagorean theorem, we can find the length of leg a as:

a^2 = c^2 - b^2

a^2 = 5^2 - b^2

a^2 = 25 - b^2

Assuming b = 3, we can find the length of leg a as:

a^2 = 25 - 3^2

a^2 = 16

a = 4

So, the length of leg a is 4 units, and the length of leg b is 3 units. We can label corner A as (4,0) and corner C as (0,3).

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Answer:

126cm².

Step-by-step explanation:

To use Heron's formula to find the area (A) of a triangle given the lengths of its sides, we need to first calculate the semiperimeter (s), which is half the perimeter of the triangle:

s = (21 + 20 + 13) / 2 = 27

Then, we can use the formula:

A = sqrt(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle. Substituting the values, we get:

A = sqrt(27(27-21)(27-20)(27-13))

A = sqrt(27 x 6 x 7 x 14)

A = sqrt(15876)guu

A=126 cm²

Therefore, the area of the triangle is approximately 126cm².

To find:-

Answer:-

The given sides of triangle are 21cm , 20cm and 13cm . For a traingle of sides [tex] a [/tex] , [tex] b [/tex] and [tex] c [/tex] , area of triangle by Heron's Formula is given by,

[tex]\implies A =\sqrt{ s(s-a)(s-b)(s-c)} \\[/tex]

where,

We can find semi perimeter as ,

[tex]\implies s =\dfrac{a+b+c}{2} \\[/tex]

[tex]\implies s =\dfrac{21cm + 20cm + 13cm}{2} \\[/tex]

[tex]\implies s =\dfrac{54}{2}=\boxed{27}[/tex]

Now on substituting the respective values, we have;

[tex]\implies A =\sqrt{ 27 ( 27 - 21) (27-20)(27-13)}cm^2 \\[/tex]

[tex]\implies A =\sqrt{ 27 \ . \ 6 \ . \ 7 \ . \ 14}cm^2\\[/tex]

[tex]\implies A =\sqrt{ 3^3 \ . \ 3 \ . \ 2 \ . \ 7 \ . \ 7 \ . \ 2} cm^2\\[/tex]

[tex]\implies A = 3^2 \ . \ 2 \ . \ 7 cm^2 \\[/tex]

[tex]\implies Area = 126 cm^2 \\[/tex]

Hence the area of the traingle is 126 cm² .

and we are done!

The implementation-level description of a Turing machine that decides the language {w|w contains twice as many 0s as 1s}

States: q0, q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12, q13, q14, q15, q16, q17, q18, q19, q20, q21, q22, q23, q24, q25, q26.

Input alphabet: {0, 1}.

Tape alphabet: {0, 1, X, Y, B}

The implementation-level description of a Turing machine that decides the language {w|w contains twice as many 0s as 1s}

States: q0, q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12, q13, q14, q15, q16, q17, q18, q19, q20, q21, q22, q23, q24, q25, q26.

Input alphabet: {0, 1}.

Tape alphabet: {0, 1, X, Y, B}.

a. (q0, 0) -> (q1, X, R) : If the input is 0, mark it with X and move the head to the right.

b. (q0, 1) -> (q10, Y, R) : If the input is 1, mark it with Y and move the head to the right.

c. (q0, B) -> (q26, B, R) : If the input is blank, halt and accept.

d. (q1, 0) -> (q2, 0, R) : If the input is 0, move to state q2 and move the head to the right.

e. (q1, 1) -> (q1, 1, R) : If the input is 1, stay in state q1 and move the head to the right.

f. (q1, Y) -> (q1, Y, R) : If the input is Y, stay in state q1 and move the head to the right.

g. (q2, 0) -> (q3, X, R) : If the input is 0, mark it with X and move the head to the right.

h. (q2, 1) -> (q2, 1, R) : If the input is 1, stay in state q2 and move the head to the right.

i. (q2, Y) -> (q2, Y, R) : If the input is Y, stay in state q2 and move the head to the right.

j. (q3, 0) -> (q4, 0, R) : If the input is 0, move to state q4 and move the head to the right.

k. (q3, 1) -> (q3, 1, R) : If the input is 1, stay in state q3 and move the head to the right.

l. (q3, Y) -> (q3, Y, R) : If the input is Y, stay in state q3 and move the head to the right.

m. (q4, 0) -> (q5, Y, L) : If the input is 0, mark the next available blank cell with Y, move the head to the left and go to state q5.

n. (q4, 1) -> (q4, 1, R) : If the input is 1, stay in state q4 and move the head to the right.

o. (q4, Y) -> (q4, Y, R) : If the input is Y, stay in state q

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The graph of the data has been plotted and attached below.

What is a graph?

A diagram or pictorial representation of facts or values that is ordered might be referred to as a graph in mathematics. The relationship between two or more items is commonly depicted by graph points.

In the question, we are given the data relating to the distance covered in the specific time duration.

Using this data, a graph has been obtained which has been attached below.

On the x - axis, time is shown and on the y - axis, distance has been shown.

Hence, the graph of the data has been plotted.

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According to the given information, tan A in simplest radical form is 7/25.

What are trigonometric ratios?

Trigonometric ratios are ratios of the sides of a right-angled triangle that are used to relate the angles of the triangle to the lengths of its sides. In a right-angled triangle, the three sides are the hypotenuse (the longest side), the opposite (the side opposite to the angle of interest), and the adjacent (the side adjacent to the angle of interest). The three main trigonometric ratios are:

Sine (sin) of an angle: the ratio of the length of the opposite side to the length of the hypotenuse.

Cosine (cos) of an angle: the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent (tan) of an angle: the ratio of the length of the opposite side to the length of the adjacent side.

In a right-angled triangle ABC with angle C = 90 degrees, we have the following trigonometric ratios:

sin A = opposite / hypotenuse = BC / AC

cos A = adjacent / hypotenuse = AB / AC

tan A = opposite / adjacent = BC / AB

Substituting the given values, we get:

sin A = BC / AC = 7 / 24

cos A = AB / AC = 25 / 24

tan A = BC / AB = 7 / 25

Therefore, tan A in simplest radical form is 7/25.

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Answer:

2n^(2)+5n-12

Step-by-step explanation:

i hope this help and have a good

Answer:

2n2 +5n -12

Step-by-step explanation:

Answer:

-2.5×10^1

Step-by-step explanation:

-25

-2.5×10^1

the area of the shaded area of the is 105.49 cm².

The formula A = [tex]r^{2}[/tex], where r is the circle's radius, determines the area of a circle.

The huge circle's diameter in this issue is 21 cm, meaning that its radius is 10.5 cm, or half of that measurement. The thickness between the big and tiny circles is subtracted to get the radius of the smaller circle, which is 10.5 cm - 1.75 cm = 8.75 cm.

The large circle's surface area is:

A big = π(10.5 cm) (10.5 cm)² = 346.36 cm²

The little circle's surface area is:

A small is equal to 8.75 x 2 = 240.87 [tex]cm^{2}[/tex].

the huge circle's area less the small circle's area equals:

A big - A small = [tex]346.36 cm^{2} - 240.87 cm^{2} = 105.49 cm^{2}[/tex] is what A diff stands for.

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To answer this question, we need to know how many of Grayson's friends are 91_2 and 10_2 years old. The numbers "91_2" and "10_2" likely mean "nine and a half" and "ten and a half", respectively.

Assuming that we are only considering whole numbers for ages, we can interpret "nine and a half" as "nine or ten", and "ten and a half" as "ten or eleven". Therefore, we need to determine how many of Grayson's friends are either nine or ten years old, and how many are either ten or eleven years old. If we assume that Grayson has a total of N friends, then we can represent the number of friends who are either nine or ten years old as X, and the number of friends who are either ten or eleven years old as Y. Then, we can write:

X + Y = N (equation 1)

We also know that the number of friends who are 10 years old is equal to:

X + Y - 1 (since we counted the overlap between X and Y twice)

So, we can write another equation:

X + Y - 1 = Z (equation 2)

where Z is the number of friends who are 10 years old.

We can solve this system of equations for X and Y by substituting equation 2 into equation 1:

2X + 2Y - 2 = N + Z

2X + 2Y = N + Z + 2

X + Y = (N + Z + 2)/2

Now we have an expression for X + Y in terms of N and Z. Since we know Z (the number of friends who are 10 years old), we can use this expression to solve for X + Y, and then subtract Z from it to get the total number of friends who are either nine or ten years old, or ten or eleven years old. However, since we don't have any specific information about N and Z, we cannot give a numerical answer to this question. We can only provide a general method for calculating the answer.

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Answer:

by the question,

area of particle 1 bigger than 2

=area of particle 1/area of particle

=2.5mm/ 0.5mm= 5 times

Step-by-step explanation:

The area of the figure is 108

After answering the presented question, we can conclude that As a inequality result, the total of the next two numbers in the pattern is roughly 4.793 1011 + 9841.5 = 4.793 1011.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.  

Each succeeding number appears to be the cube of the previous number divided by 2. The next two numbers in the pattern, using this pattern, are:

[tex](27^3)/2 = 19683/2 = 9841.5[/tex]

and

[tex](9841.5^3)/2 = 4.793 × 10^11[/tex]

As a result, the total of the next two numbers in the pattern is roughly 4.793 1011 + 9841.5 = 4.793 1011.

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