Area of the circle. Leave your answer in terms of pi.

The area of the region enclosed by the curves y = 7sin x and y = sin(7x) , 0 < x < π is 13.7 square units.

Given the equation of the curves:

y = 7sin x and y = sin(7x)

Now, we have to find the area between the curves .

Area between y = 7sin x and y = sin(7x) ,

   A = ∫[7sin(x) - sin(7x)]dx

⇒ A = [-7cos(x) + 1/7 cos(7x)]

⇒ A = [-7cos + 1/7 cos(7)] - [-7cos(0) + 1/7 cos(0)]

Since cos(π) = -1  ;  cos(7) = -1  ; cos(0) = 1

⇒A = [-7(-1) + 1/7 * (-1)] - [-7 * 1 + 1/7 * 1]

⇒A = 7- 1/7 + 7 - 1/7

⇒A = 14 - 2/7

⇒A = 96/7

⇒A = 13.7 units

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Answer:

(g ￮ f)(x) = x² + 8x + 15

Step-by-step explanation:

to find (g ￮ f)(x) substitute x = f(x) into g(x)

(g ￮ f)(x)

= g(f(x))

= g(x + 4)

= (x + 4)² - 1 ← expand factor using FOIL

= x² + 8x + 16 - 1 ← collect like terms

= x² + 8x + 15

The solution of the given equation is x = 0 and the graph is shown in the given figure.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Here we have a equation |x| + 3 > 3 graph

Solve the given equation given below

=>  |x| + 3 > 3  

Subtract 3 from both sides

=>  |x| + 3 - 3 > 3 - 3

=>  |x| > 0  

Therefore,

The solution of the given equation is x = 0 and the graph is shown in the given figure.

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Step-by-step explanation:

This both answer can be

NO, the interior of x is not necessarily connected.

A connected subset is one that cannot be expressed as the union of two non-empty separated sets.

The interior of x may not have this property. For example, consider the subset of the real line given by the closed interval [0,1]. This set is connected, but its interior, (0,1), is not. It can be expressed as the union of the two separated sets (0,1/2) and (1/2,1). Therefore, the interior of a connected subset may not be connected.
1. A connected subset X of a metric space M means that there is no separation of X into two disjoint non-empty open sets.
2. The interior of X refers to the set of all interior points of X, which are points where every neighborhood of the point lies entirely within X.
3. However, the interior of X may have a different connectivity structure than X itself. It is possible for the interior of X to be disconnected, meaning it can be separated into two disjoint non-empty open sets.
4. As a result, the interior of a connected subset X is not guaranteed to be connected.

Hence, The main answer is: No, the interior of a connected subset X of a matrix space M is not necessarily connected.

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The probability that exactly 6 are white and 2 are red is equals to 7/15 and the probability that at least 6 of the balls are white is equals to the 8/15.

The probability of a series of dependent of events may be found by finding the probability of each event and combining all the probabilities together. We have a urn which contains total 10 balls.

Number of white balls in urn, W = 7

Number of red balls in urn, R = 3

Now, a sample of 8 balls is selected randomly without replacement. We have to determine the probability that exactly 6 are white and 2 are red.

The number of ways selecting 8 balls among 10 = ¹⁰C₈ = 10!/8!2! = 45

The number of ways selecting 6 white balls among 7 = ⁷C₆ = 7!/6! = 7

The number of ways selecting 2 red balls among 3 = ³C₂ = 3!/2! = 3

Total number of ways selecting exactly 6 white and 2 red balls = 7×3 = 21

So, probability that exactly 6 are white and 2 are red,

= favorable outcomes/total outcomes

= 21/45

= 7/15

b) ‘At least 6 white balls’ selected in 8 balls means 6 white balls and 2 red, or, 7 white balls and 1 red.

Total number of ways selecting at least 6 of the balls are white,

= ⁷C₆ × ³C₂ + ⁷C₇ ³C₁

= 21 + 7!/7! × 3!/2! = 21 + 3 = 24

Probability that at least 6 of the balls are white = 24/45 = 8/15

Hence, required probability is 8/15.

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Answer:

17

Step-by-step explanation:

I used a caculator...

Give Brillianst Please!!!

Answer:

2 11/12

Step-by-step explanation:

This is what I got for the answer in the test.

The value of m in the given equation would be; m = 2.91

An equation is an expression that shows the relationship between two or more numbers and variables.

We need to find the value of m.

This equation could also be given by;

−2.4(m−5/6)=−5

Distribute the negative;

−2.4(m−5/6)=−5

- 2.4m + 2.4 x 5/6 = -5

Now we get;

- 2.4m = -5 - 2

- 2.4m = -7

m = 2.91

Hence, the value of m in the given equation would be; m = 2.91

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The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

Answer:

False

Step-by-step explanation:

The coefficients (numbers in front) don't matter, but the exponents do.

Like terms have exactly the same exponents on the same variables.

\(54x^2y^3\text{ and }-12x^3y^2\) are not like terms.

Example: \(6x^3y^2\text{ and }-14x^3y^2\) are like terms--same exponents on the x's, same exponents on the y's.

Answer:

False

Step-by-step explanation:

two like therms have the same literal part. This is not the case because

x^3 is different from x^2 (for example if x = 2 ; 8 is not 4)

y^3 is different from y^2

Answer:

178

Step-by-step explanation:

235-113=122

122+56=178

Answer:

178 books

Step-by-step explanation:

235 minus 113 books that werr checked out and plus 56 books that came back in total it's 178, if nobody stole anything :)

The equation of the plane passing through the points \((0, 6, 6), (6, 0, 6), and (6, 6, 0)\) is \(36x + 36y + 36z = 432\).

To find the equation of the plane passing through the points \((0, 6, 6), (6, 0, 6), and (6, 6, 0)\), we can use the point-normal form of the equation of a plane.

Step 1: Find two vectors in the plane.

Let's find two vectors by taking the differences between the given points:

Vector v₁ = \((6, 0, 6) - (0, 6, 6) = (6, -6, 0)\)

Vector v₂ = \((6, 6, 0) - (0, 6, 6) = (6, 0, -6)\)

Step 2: Find the normal vector.

The normal vector is perpendicular to both v₁ and v₂. We can find it by taking their cross product:

Normal vector n = v₁ \(\times\) v₂ = \((6, -6, 0) \times (6, 0, -6) = (36, 36, 36)\)

Step 3: Write the equation of the plane.

Using the point-normal form, we can choose any point on the plane (let's use the first given point, \((0, 6, 6)\)), and write the equation as:

n · (x, y, z) = n · (0, 6, 6)

Step 4: Simplify the equation.

Substituting the values of n and the chosen point, we have:

(36, 36, 36) · (x, y, z) = (36, 36, 36) · (0, 6, 6)

Simplifying further:

\(36x + 36y + 36z = 0 + 216 + 216\\36x + 36y + 36z = 432\)

Therefore, the equation of the plane passing through the given points is:

\(36x + 36y + 36z = 432\)

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The predicted income for working 22 hours on an assembly job  is $450.6 which is determined using the given regression model with intercept and slope values.

The intercept (-242.3) represents the predicted income when the number of working hours is zero, and the slope (31.45) represents the increase in income for each additional hour worked. To find the predicted income for 22 hours of work, we substitute 22 for the number of working hours in the regression model and solve for the predicted income.

Therefore, the predicted income for working 22 hours on an assembly job can be calculated as follows:

Predicted income = Intercept + (Slope x Number of working hours)

Predicted income = -242.3 + (31.45 x 22)

Predicted income = -242.3 + 692.9

Predicted income = 450.6

Thus, the predicted income for working 22 hours on an assembly job is $450.6.

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Answer:

the answer should be D hope you pass

Answer:

D

Step-by-step explanation:

-10 + u = 14

u = 14+10=24.0

Answer:

To find the total length of the two sides, we simply add them together:

Total length = Side 1 + Side 2

Total length = (8x^2 - 5x - 2) + (7x - x^2 + 3)

Total length = -x^2 + 8x^2 - 5x + 7x - 2 + 3

Total length = 7x^2 + 2x + 1

Therefore, the total length of the two sides of the triangle is 7x^2 + 2x + 1.

Step-by-step explanation:

To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle:

Perimeter = Side 1 + Side 2 + Side 3

We are given the perimeter of the triangle as 4x^3 - 3x^2 + 2x - 6 and we know the lengths of Side 1 and Side 2. Therefore, we can rewrite the formula as:

4x^3 - 3x^2 + 2x - 6 = (8x^2 - 5x - 2) + (7x - x^2 + 3) + Side 3

Simplifying the right-hand side:

4x^3 - 3x^2 + 2x - 6 = 7x^2 + 2x + 1 + Side 3

Side 3 = 4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1

Simplifying further:

Side 3 = 4x^3 - 7x^2 - x - 7

Therefore, the length of the third side of the triangle is 4x^3 - 7x^2 - x - 7.

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction.

Closure under addition means that when two polynomials are added, the result is also a polynomial. In Part A, we added the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 to get the total length of the two sides of the triangle, which is 7x^2 + 2x + 1. Since the total length is also a polynomial, this shows that the polynomials are closed under addition.

Closure under subtraction means that when one polynomial is subtracted from another polynomial, the result is also a polynomial. In Part B, we subtracted the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 from the given perimeter of the triangle, 4x^3 - 3x^2 + 2x - 6, to get the length of the third side of the triangle, which is 4x^3 - 7x^2 - x - 7. Since the length of the third side is also a polynomial, this shows that the polynomials are closed under subtraction.

Therefore, the answers for Part A and Part B demonstrate that the polynomials are closed under addition and subtraction.

The difference between the 2 in the tens place and 2 to its left column in the given number 2,222.222 is 180.

According to the number system, a number can be written in its expanded form according to their pace value in the chart.

2,222.222 can be written as 2×1000+2×100+2×10+2X1+2×1/10+2×1/100+2×1/1000

The place value of 2 in the tens place in given number 2,222.222 = 20

The place value of 2 in its left column in the given number 2,222.22  = 200

Difference between the place of 2 in tens place and 2 in its left column

= 200 - 20

= 180

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To solve this problem, we can set up an equation based on the principle of concentration. Let's assume that x represents the number of gallons of the 5% salt solution that needs to be mixed.

The amount of salt in the 5% solution is 0.05x (since 5% is equivalent to 0.05) and the amount of salt in the 9% solution is 0.09 * 30 = 2.7 gallons.

When these two solutions are mixed, the total volume of the mixture is 30 + x gallons, and the amount of salt in the mixture is 0.07 * (30 + x) gallons.

Now we can set up the equation:

0.05x + 2.7 = 0.07 * (30 + x)

Simplifying the equation:

0.05x + 2.7 = 2.1 + 0.07x

0.05x - 0.07x = 2.1 - 2.7

-0.02x = -0.6

Dividing both sides by -0.02:

x = 30

Therefore, 30 gallons of the 5% salt solution must be mixed with 30 gallons of the 9% solution to obtain a 7% solution.

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How many gallons of a 5% salt solution must be mixed with 30 gallons of a 9% solution to obtain a 7% solution ??

Answer:

24 slices

Step-by-step explanation:

There are 3 whole pizzas. He cuts each of them into eighths. That means eight slices. 3 times 8 is 24. There are a total of 24 slices. This can also look like this: 24/8   or 24 over 8.  Which also equals to 3.

Answer:

c. (1,-1)

Step-by-step explanation:

5x + 2y = 3  4x – 8y = 12  Solve for (x, y)

4x-8y=12

+8y          +8y

4x=12+8y

Divide both sides by 4

4x/4=(12+8y)/4

x=3+2y

Then take x equation and input into 5x + 2y = 3

5(3+2y)+2y=3

15+10y+2y=3

Add 10y and 2y

15+12y=3

Subtract 15 on both sides

15-15+12y=3-15

12y=-12

Divide 12 both sides

12y÷12=-12÷12

Y = -1

Insert the Y equation into 4x – 8y = 12  

4x-8(-1)=12

4x+8=12

Subtract 8 on both sides

4x-8-8=12-8

4x=4

Divide 4 both sides

4x÷4=4÷4

X = 1

Answer: C. (1, -1)

Answer:

the correct answer is f(x)=(x-2)^2 + 1

Step-by-step explanation:

lets loof for f(2) :

f(2)=(2-2)^2 + 1

f(2)=(0)^2 + 1

f(2)= 1 ---> (2,1)

Answer:

1/3^4

1/81

Step-by-step explanation:

(3^2)^-2

We know that a^b^c = a^(b*c)

3 ^(2*-2)

3^-4

We know that a^-b = 1/a^b

1/3^4

1/81

The facts which are true for the graph of the function given f(x)= log 0.725 x are;

We say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'. This is another approach to indicate the power of numbers.

\(a^b\) = c

and, b log a =c

As a function's range is the set of all feasible values of f(x), its domain is the set of all possible values of x.

On that note, any number in the range x=0 causes the function to be undefined, hence the function's range is x> 0.

Also f(x) can be any real number, the set of all real numbers comprises the function's range.

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Таким образом, (X-2)(3x-1) = 0 можно переписать в виде двух уравнений:

X-2=0 или 3x-1=0

Решение для

X=2

Solving for x in the second equation, we get:

3x=1

x=1/3

Therefore, the possible values of X are X=2 and x=1/3.

Answer:

\(-\frac{6}{x^{2} } -6x-2\)

Step-by-step explanation:

\(x^{-2}\)  is equivalent  \(\frac{1}{x^{2} }\)

Then, that is multiplied by the coefficient of -6

Thus \(-6x^{-2}\) becomes \(-\frac{6}{x^{2} }\)

Answer:

1/5 is biggest fraction

Step-by-step explanation:

1/5 = 0.2

1/10 =0.1

⅕ > ⅒

The biggest fraction in between 1/5 and 1/10 is 1/5.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

We have the fractions:

1/5 and 1/10.

To find the biggest fraction:

Here, 1 is the numerator in both of the fractions.

So, 10 and 5 are the denominators.

And 5 < 10

That means, 1 is separated in 5 parts and 10 parts.

1/5 = 0.2

And 1/10 = 0.1

0.2 > 0.1

Therefore, the fraction 1/5 is bigger than 1/10.

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The solution to the given simultaneous equations using Cramer's Rule is:

x = 4/17

y = 0

z = 20/17

To solve the simultaneous equations using Cramer's Rule, we need to set up the matrix equation and calculate determinants. Let's denote the variables as x, y, and z.

The given system of equations can be represented in matrix form as:

| 1  5  2 |   | x |   | x |

|          | * |   | = |   |

| 2  4 20 |   | y |   | x |

|          |     |   | = |   |

| 4  2 10 |   | z |   | x |

To solve for the variables x, y, and z, we will use Cramer's Rule, which states that the solution is obtained by dividing the determinant of the coefficient matrix with the determinant of the main matrix.

Step 1: Calculate the determinant of the coefficient matrix (D):

D = | 1  5  2 |

| 2  4 20 |

| 4  2 10 |

D = (1*(410 - 220)) - (5*(210 - 44)) + (2*(22 - 44))

D = (-16) - (40) + (-12)

D = -68

Step 2: Calculate the determinant of the matrix replacing the x-column with the constant terms (Dx):

Dx = | x  5  2 |

| x  4 20 |

| x  2 10 |

Dx = (x*(410 - 220)) - (5*(x10 - 220)) + (2*(x2 - 410))

Dx = (-28x) + (100x) - (76x)

Dx = -4x

Step 3: Calculate the determinant of the matrix replacing the y-column with the constant terms (Dy):

Dy = | 1  x  2 |

| 2  x 20 |

| 4  x 10 |

Dy = (1*(x10 - 220)) - (x*(210 - 44)) + (4*(2x - 410))

Dy = (-40x) + (56x) - (16x)

Dy = 0

Step 4: Calculate the determinant of the matrix replacing the z-column with the constant terms (Dz):

Dz = | 1  5  x |

| 2  4  x |

| 4  2  x |

Dz = (1*(4x - 2x)) - (5*(2x - 4x)) + (x*(22 - 44))

Dz = (2x) - (10x) - (12x)

Dz = -20x

Step 5: Solve for the variables:

x = Dx / D = (-4x) / (-68) = 4/17

y = Dy / D = 0 / (-68) = 0

z = Dz / D = (-20x) / (-68) = 20/17

Therefore, the solution to the given simultaneous equations using Cramer's Rule is:

x = 4/17

y = 0

z = 20/17

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