40 points: how do u calculate this and what is sin, cos and what is the formula

Answer:

not enough information to answer

Step-by-step explanation:

Writing linear equations given two points can be a useful skill when graphing linear equations.

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Answer:

38

Step-by-step explanation:

X+35=73

x=73-35

x=38

Answer:

X=38

Step-by-step explanation:

x+35=73

-35 -35

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

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For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Answer:

Step-by-step explanation:

The length of a curve can refer to the arc length of a function, or the distance along a curved path between two points.

Arc Length of a Function:

For a continuous and differentiable function y = f(x) defined over an interval [a, b], the arc length of the curve between x = a and x = b can be found using the following definite integral:

L = ∫_a^b √(1 + (dy/dx)^2) dx

Where L is the arc length, dy/dx is the derivative of the function with respect to x, and the integral is taken from x = a to x = b.

Length of a Curved Path:

For a curved path defined by a continuous and differentiable function y = f(x), the length of the path between two points (x1, y1) and (x2, y2) can be found using the same definite integral formula as the arc length of a function:

L = ∫_(x1)^(x2) √(1 + (dy/dx)^2) dx

Where L is the length of the path and the integral is taken from x = x1 to x = x2.

Note that finding the exact length of a curve can sometimes be difficult and may require numerical methods such as numerical integration or approximation techniques like Simpson's rule.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Classifying polynomials refers to categorizing polynomials based on the degree of the polynomial and the number of terms in the polynomial.

The degree of a polynomial is the highest exponent in the polynomial. Polynomials can be classified into several types, including constant polynomials (degree 0), linear polynomials (degree 1), quadratic polynomials (degree 2), and so on. Adding and subtracting polynomials is the process of combining two or more polynomials by combining like terms. Like terms are terms with the same variable and exponent. To add or subtract polynomials, simply line up the terms with the same variable and exponent and add or subtract the coefficients. The result will be a new polynomial with the combined terms.

For example, to add the polynomials \(2x^2 + 3x + 4\) and \(-x^2 + 5x - 6\), we line up the terms with the same variable and exponent and add the coefficients:

\((2x^2 + 3x + 4) + (-x^2 + 5x - 6) = (2x^2 - x^2) + (3x + 5x) + (4 - 6) \\\)

                                                   \(= x^2 + 8x - 2.\)

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Answer:

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the missing side that is 1/2 the side of the missing heptagon. You have to assume that the figure is a regular heptagon, something you should point out to your teacher. Math really requires well qualified diagrams.

c^2 = a^2 + b^2

c = 2.77

a = 2.5

b = 1/2 the side of the heptagon.

2.77^2 = 2.5^2 + b^2

7.6729 =6.25 + b^2

7.5629 - 6.25 = b^2

b^2 = 1.4229

b = sqrt(1.4229)

b = 1.1928

But the side is twice that long

s = 2.3857

Now draw another line from the side you just found. It will be the same length as 2.77. It's a radius of the circumcircle.

Area of the triangle so formed is

Area = 1/2 * b * h

b = 2.3857

h = 2.5

Area = 1/2 * 2.5 * 2.3857

Area = 2.982

There are 7 such triangles.

Answer: 7 * 2.982

Answer: 20.87

The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.

The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.

In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.

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To find an equation of the plane perpendicular to the line of intersection between the planes 4x - 3y + 27 = 5 and 3x + 2y + z + 11 = 0, passing through the point (6, 2, -1),

The normal vector of the first plane is (4, -3, 0), and the normal vector of the second plane is (3, 2, 1). Taking their cross product, we get the direction vector of the line as (3, -12, 17). This vector represents the direction in which the line extends. Next, using the point (6, 2, -1),

we can substitute its coordinates into the general equation of a plane, which is ax + by + cz = d, to determine the values of a, b, c, and d. Substituting the point coordinates, we obtain 3(x - 6) - 12(y - 2) + 17(z + 1) = 0. This equation represents the plane perpendicular to the line of intersection between the given planes, passing through the point (6, 2, -1).

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Answer: do 8 x 12

Step-by-step explanation:

Answer:

48cm^2

Step-by-step explanation:

(b*h)/2 -> (8*12)/2 -> 96/2 = 48 cm^2

Answer:

-5/6 ___ -0.1

Step-by-step explanation:

Answer:

59

Step-by-step explanation:   x=number of hours

150+7.50x=595

7.50x=595-150

7.50x/7.50=445/7.50

x=59

Answer:

\(60 \frac{152}{101} \)

Answer:

61 80/101

Step-by-step explanation:

Divide 6241 and 101 which equals 61 R80

(i) The pdf of random variable X is:

\(fx(x) = {2bx e^{(-bx^2)}\), x > 0

0, x < 0

(ii) The pdf of Y is:

\(fy(y) = b\sqrt y / e^{(by)} , y > 0\)

0, y ≤ 0

(i) To find the probability density function (pdf) of X, we need to take the derivative of the cumulative distribution function (cdf) with respect to x.

For x > 0, we have:

\(Fx(x) = 1 - e^{(-bx^2)}\)

Differentiating both sides with respect to x gives:

fx(x) = d/dx Fx(x) = \(d/dx [1 - e^{(-bx^2)}] = 2bx e^{(-bx^2)}\)

For x < 0, we have:

Fx(x) = 0

Differentiating both sides with respect to x gives:

fx(x) = d/dx Fx(x) = d/dx [0] = 0

Therefore, the pdf of X is:

\(fx(x) = {2bx e^{(-bx^2)}\), x > 0

{0, x < 0

(ii) To find the pdf of \(Y = X^2\), we can use the transformation method. The transformation function is \(g(x) = x^2\).

We have:

Fy(y) = P(Y ≤ y) = P(\(X^2\) ≤ y) = P(-√y ≤ X ≤ √y) = Fx(√y) - Fx(-√y)

Differentiating both sides with respect to y gives:

fy(y) = d/dy Fy(y) = d/dy [Fx(√y) - Fx(-√y)]

= (1/2y) fx(√y) - (-1/2y) fx(-√y)

\(= (1/2y) 2b\sqrt y e^{(-by)}\)

= \(b\sqrt y / e^{(by)}\)

Therefore, the pdf of Y is:

\(fy(y) = b\sqrt y / e^{(by)} , y > 0\)

0, y ≤ 0

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Answer:

Step-by-step explanation:

The domain is the set of x values, and the range is the set of y values.

Answer:

$175

Step-by-step explanation:

you need to specify if harriet got the 7 portion or the 5 portion. I'll answer as if she got the 7 portion.

They split it into 12 portions because the ratio is 7:5 and 7+5=12. So do $300/12=25

Assuming Maya got the 5 portion, do $25 x 5 = $125, so Maya got $125.

Assuming Harriet got the 7 portion, do $25 x 7 = $175, so Harriet got $175.

The amount of monthly increase will be 8$

What is Quadratic Equation?

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. x is an unknown variable, whereas a, b, and c are numerical coefficients.

Solution:

Given Equation is x² - 16x + 64 = 0

Using the formula method we will first find the discriminant

D = b² - 4ac

D = 256 - 256 = 0

x = -b +- √D / 2a

x = 16/2 = 8

x = 8

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While you look behind to see how many people you beat, you are gathering information for your Competitive intelligence via the use of social comparison.

Competitive intelligence is a process of learning as much as possible outside oneself to increase one's competition level.

It tells us about our position in the competition or market .it helps in self-improvement and skill development.

Social comparison helps in determining our own worth in society.

You are gathering information for your Competitive intelligence via the use of social comparison.

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We have the equations :

To solve graphically, we should plot the graph of the equation on the same graph.

For y = x-2

We can obtain two points to plot the graph of y = x-2

At x= 0:

At y= 0:

We have the points : (0,-2) and (2,0)

For 2x + y =1

At x = 0:

At y = 0:

We have the points : (0, 1) and (1/2, 0)

Plotting these points gives the graph shown below:

From the graph, we have the point of intersection of the two lines as (1,-1)

Hence, the solution to the system of equation is (1, -1)

Answer:

1=27

2=65

3=115

4=

Step-by-step explanation:

I am still working on four i will put it in the comments

Answer

13.95

Step-by-step explanation:

31.7 is 31.70 then add 13.95 then it equals 45.65.

(a)  The probability of the with replacement is 3/80.

(b) The probability of the without replacement is 15/380.

Two cards are selected at random Of a deck of 20 cards ranging from 1 to 5 with monkeys, frogs, lions, and birds on them all numbered 1 through 5 .

a) with replacement.

5/20 * 3/20 = 3/80.

b) without replacement.

5/20 3/19 = 15/380.

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Answer:

See below

Step-by-step explanation:

Slope intercept form is   y = mx + b    so you need to manipulate this equation to look like this.....in other words, you need to solve for 'y'

4 = 5x - 4y        add 4y to both sides of the equation

4y + 4 = 5x        now subtract 4 from both sides

4y = 5x - 4         Now divide both sides by 4

y = 5/4 x - 1        <====and ..done !

The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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Answer:

12.5 cents per box

Step-by-step explanation:

First, find the price difference of the cases.

11.99 - 10.49 = $1.50

We want to find the money saved per box so divide $1.50 by 12.

1.50/12 = 12.5 cents

Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:

x1 + x2 + x3 + 2x4 + s1 = 4,

-x1 + x3 + x4 - s2 = -1,

2x1 + x2 + s3 = 2,

and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.

To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.

The standard form of a linear programming problem is as follows:

Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4

Subject to:

a11x1 + a12x2 + a13x3 + a14x4 = b1

a21x1 + a22x2 + a23x3 + a24x4 = b2

a31x1 + a32x2 + a33x3 + a34x4 = b3

an1x1 + an2x2 + an3x3 + an4x4 = bn

x1, x2, x3, x4 >= 0

Now let's reformulate the given problem:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 <= 4

-x1 + 0x2 + x3 + x4 >= -1

2x1 + x2 + 0x3 + 0x4 <= 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4 >= 0

The reformulated linear programming problem in standard form is as follows:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 + s1 = 4

-x1 + x3 + x4 - s2 = -1

2x1 + x2 + s3 = 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4, s1, s2, s3 >= 0

Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.

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