Find rand o complex numbers: (a) Z,= 1 (5) Z, - - 51 Zz = -5_5i 2-2i 2+2 i =

The scalar projection of b onto a is 5/9, and the vector projection of b onto a is (20/81, 35/81, -20/81).

To find the scalar and vector projections of vector b onto vector a, we can use the following formulas:

Scalar Projection:

The scalar projection of b onto a is given by the formula:

Scalar Projection = |b| * cos(θ)

Vector Projection:

The vector projection of b onto a is given by the formula:

Vector Projection = Scalar Projection * (a / |a|)

where |b| represents the magnitude of vector b, θ is the angle between vectors a and b, a is the vector being projected onto, and |a| represents the magnitude of vector a.

Let's calculate the scalar and vector projections of b onto a:

a = (4, 7, -4)

b = (4, -1, 1)

First, we calculate the magnitudes of vectors a and b:

|a| = √(4² + 7² + (-4)²) = √(16 + 49 + 16) = √81 = 9

|b| = √(4² + (-1)² + 1²) = √(16 + 1 + 1) = √18

Next, we calculate the dot product of vectors a and b:

a · b = (4 * 4) + (7 * -1) + (-4 * 1) = 16 - 7 - 4 = 5

Using the dot product, we can find the angle θ between vectors a and b:

cos(θ) = (a · b) / (|a| * |b|)

cos(θ) = 5 / (9 * √18)

Now, we can calculate the scalar projection:

Scalar Projection = |b| * cos(θ)

Scalar Projection = √18 * (5 / (9 * √18)) = 5 / 9

Finally, we calculate the vector projection:

Vector Projection = Scalar Projection * (a / |a|)

Vector Projection = (5 / 9) * (4, 7, -4) / 9 = (20/81, 35/81, -20/81)

Therefore, the scalar projection of b onto a is 5/9, and the vector projection of b onto a is (20/81, 35/81, -20/81).

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Answer:

42.09 cubic units

Step-by-step explanation:

[tex]\frac{4.11*5.12}{2} *4[/tex]

=42.0864, which rounds to 42.09

Note: The 6.57 is not needed to solve this problem

The vector that is parallel to the line of intersection of the planes 4x - 3y + 2z = 12 and x + 5y - z = 7 is option (c) -7i + 6j + 23k.

To find a vector that is parallel to the line of intersection of two planes, we need to determine the direction of the line. This can be achieved by finding the cross product of the normal vectors of the planes.

The normal vector of the first plane 4x - 3y + 2z = 12 is (4, -3, 2), obtained by taking the coefficients of x, y, and z. Similarly, the normal vector of the second plane x + 5y - z = 7 is (1, 5, -1).

To find the cross product of these two normal vectors, we take their determinant: (4i, -3j, 2k) x (1i, 5j, -1k). Evaluating the determinant, we get (-23i - 6j - 13k).

The resulting vector -23i - 6j - 13k is parallel to the line of intersection of the planes. However, the given options only include positive coefficients for i, j, and k. To match the given options, we can multiply the vector by -1 to obtain a parallel vector. Thus, -(-23i - 6j - 13k) simplifies to -7i + 6j + 23k, which matches option (c). Therefore, option (c) -7i + 6j + 23k is the vector parallel to the line of intersection of the planes.

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Answer:

80%

Step-by-step explanation:

You started of with 5/5 once one slice was eat it became 4/5

you must then convert 4/5 into a percent

To convert a fraction to a percent, divide the numerator by the denominator. Then multiply the decimal by 100.

so 4 divided by 5 =0.8

0.8 x 100= 80

80%

The average sum of differences of a series of numerical data from their mean is zero (option a).

This property holds true for any data set when calculating the mean deviation (also known as the average deviation) from the mean. The mean deviation is calculated by taking the absolute difference between each data point and the mean, summing them up, and dividing by the number of data points.

However, it's important to note that this property does not hold true when using squared differences, which is used in the calculation of variance and standard deviation. In those cases, the average sum of squared differences from the mean would give the variance (option c) or the squared standard deviation (option e).

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The density function fy(t) of the random variable Y, where Y = 2x - 2, can be determined by transforming the density function of the random variable X using the given relationship.

To find fy(t), we first need to find the inverse relationship between X and Y. From Y = 2x - 2, we can solve for x:

x = (Y + 2) / 2

Next, we substitute this expression for x in the density function of X, fX(x):

fX(x) = c(3x² + 4)

Substituting (Y + 2) / 2 for x, we have:

fX((Y + 2) / 2) = c[3((Y + 2) / 2)² + 4]

Simplifying the expression:

fX((Y + 2) / 2) = c(3/4)(Y² + 4Y + 4) + 4c

Expanding and simplifying further:

fX((Y + 2) / 2) = (3/4)cY² + 3cY + (3/4)c + 4c

Combining like terms:

fX((Y + 2) / 2) = (3/4)cY² + (12c + 3c)Y + (3/4)c + 4c

Now, we can see that fy(t), the density function of Y, is a quadratic function of Y. The specific coefficients and constants will depend on the values of c.

It is important to note that we need to specify the region where fy(t) is defined. Since fy(t) is derived from fX(x), we need to ensure that the transformation (Y = 2x - 2) is valid for the range of x values where fX(x) is defined.

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Answer:

I think it's B

Step-by-step explanation:

x = -2

2 + x > -8

2 + -2 > -8

0 > -8

Answer:

3x² – 5x + 2 is a polynomial because:

Exponents are whole numbers, and the expression has at least 1 term.

Exponents other than whole numbers can take the form of variables in denominators, and roots which we don't want.

The solution to the given initial-value problem is a power series given by y(x) = 1 - 2x^3 + 3x^4 + O(x^5).  As x increases, higher powers of x become significant, and the series must be truncated at an appropriate order to maintain accuracy .

y(x) = a_0 + a_1x + a_2x^2 + a_3x^3 + a_4x^4 + ..., where a_0, a_1, a_2, ... are constants to be determined. We then differentiate the series term-by-term to find the derivatives y' and y''. Differentiating y(x), we have

y' = a_1 + 2a_2x + 3a_3x^2 + 4a_4x^3 + ..., and differentiating once more, we find y'' = 2a_2 + 6a_3x + 12a_4x^2 + ...Substituting these expressions into the given differential equation, we have:

(x + 3)(2a_2 + 6a_3x + 12a_4x^2 + ...) + 2(a_0 + a_1x + a_2x^2 + a_3x^3 + a_4x^4 + ...) = 0

Given the initial conditions y(0) = 1 and y'(0) = 0, we can use these conditions to find the values of a_0 and a_1. Plugging in x = 0 into the power series, we have a_0 = 1. Differentiating y(x) and evaluating at x = 0, we get a_1 = 0.Therefore, the power series solution is y(x) = 1 + a_2x^2 + a_3x^3 + a_4x^4 + ..., where a_2, a_3, a_4, ... are yet to be determined.

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Answer:

2 friends have more than 5 cards

Step-by-step explanation:

Incomplete question;

I will answer this question with the attached dot plot

The horizontal axis represents the friends, the vertical represents the number of baseball trading cards and the dots represent the frequency

So, we have:

[tex]Friend\ 1 = 2[/tex]

[tex]Friend\ 2 = 3[/tex]

[tex]Friend\ 3 = 7[/tex]

[tex]Friend\ 4 = 4[/tex]

[tex]Friend\ 5 = 2[/tex]

[tex]Friend\ 6 = 6[/tex]

[tex]Friend\ 7 = 2[/tex]

[tex]Friend\ 8 = 5[/tex]

[tex]Friend\ 9 = 1[/tex]

[tex]Friend\ 0 = 0[/tex]

The friends that has more than 5 are:

[tex]Friend\ 3 = 7[/tex]

[tex]Friend\ 6 = 6[/tex]

Hence, 2 friends have more than 5 cards

Answer:

let's divide the figure into two parts.

radius of the semicircle is 3.5m. two semi-circles make a circle and

area of circle=pi×r²

area of circle=22/7×(3.5m)2².

area of circle=38.5m²

area of rectangle=length ×width

area of rectangle =18m×7m

area of rectangle =126m²

area pf figure =38.5m²+126m²

area of figure=164.5m²

Answer:

0.43496 miles

Step-by-step explanation:

To convert from km to miles you can divide the km by 1.609 and that should give you an aproximate value for miles.

Answer:

Inequality Form:

h > 6

Interval Notation:

( 6 , ∞ )

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

x= 114, y= 66

Step-by-step explanation:

Opposite angles of a parallelogram are equal

9514 1404 393

Answer:

  6 3/10 pounds

Step-by-step explanation:

The weight change will be found by multiplying the rate of change by the time.

  ∆w = (-1.8 lb/h)(3.5 h) = -6.3 lb

The total change in weight after 3 1/2 hours is 6 3/10 = 6.3 pounds.

Answer:

8x+3y-2x-4y-6x​ = -y

Step-by-step explanation:

8x+3y-2x-4y-6x​ = ?

combine like terms:

(8x - 2x - 6x) + (3y - 4y) = ?

The x total is 0 and the y total is -1y

Answer:

-1y

Step-by-step explanation:

8x-2x-6x=0

3y-4y=-1y

That means the solution I think is -1y.

I say this because the X gets completely cancelled, and then the only thing left is -1y. If the X still had a number in front of it, it would then be like (This Is An Example: 2x = -1y) That's what it would look like if the X wasn't completely cancelled out. Have a good day. And if you see any fault in my answer please let me know so I can get better with problems like these. Thanks.

Answer:

Step-by-step explanation:

As each step has the same depth and rise, they are respectively 1.2/4=0.3m and 1.8/4=0.45m.

Dividing the steps along the dotted lines, the total rise of the 4 concrete steps  = (1+2+3+4)*0.45

= 4.5m

Total concrete volume = total rise * depth * width

= 4.5*0.3*1.8

= 2.43m^3

Answer:30

Step-by-step explanation:

The approximation of the integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3 is approximately 1.01259.

The integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval.

The formula for composite Simpson's rule is

I ≈ (h/3) × [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f([tex]x_{n-2}[/tex]) + 4f([tex]x_{n-1}[/tex]) + f([tex]x_{n}[/tex])]

where h is the step size, n is the number of subintervals, and f([tex]x_{i}[/tex]) represents the function value at each subinterval.

In this case, n = 3, so we will have 4 equally-sized subintervals.

Let's assume the lower limit of integration is a and the upper limit is b. We can calculate the step size h as (b - a)/n.

Since the limits of integration are not provided, let's assume a = 0 and b = 1 for simplicity.

Using the formula for composite Simpson's rule, the approximation becomes:

I ≈ (h/3) [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + f(x₄)]

For n = 3, we have four equally spaced subintervals:

x₀ = 0, x₁ = h, x₂ = 2h, x₃ = 3h, x₄ = 4h

Using these values, the approximation becomes:

I ≈ (h/3) × [f(0) + 4f(h) + 2f(2h) + 4f(3h) + f(4h)]

Substituting the function f(x) = cos(x³ - 5):

I ≈ (h/3)  [cos((0)³ - 5) + 4cos((h)³ - 5) + 2cos((2h)³ - 5) + 4cos((3h)³ - 5) + cos((4h)³ - 5)]

Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = 0 and b = 1, the interval width is 1.

h = (b - a)/n = (1 - 0)/3 = 1/3

Substituting h = 1/3 into the expression:

I ≈ (1/3)  [cos((-1)³ - 5) + 4cos((1/3)³ - 5) + 2cos((2/3)³ - 5) + 4cos((1)³ - 5) + cos((4/3)³ - 5)]

Evaluating the expression further:

I ≈ (1/3)  [cos(-6) + 4cos(-4.96296) + 2cos(-4.11111) + 4cos(-4) + cos(-3.7037)]

Approximating the values using a calculator, we get:

I ≈ 1.01259

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[tex]\sinh'(x) = \cosh(x)$.[/tex]

Hence, we have shown that [tex]\cosh'(x) = \sinh(x)$ and $\sinh'(x) = \cosh(x)$[/tex] using the rules for differentiating [tex]e^x$.[/tex]

What are Hyperbolic Functions?

Hyperbolic functions are a set of mathematical functions that are analogs of the trigonometric functions. While trigonometric functions are defined based on the unit circle, hyperbolic functions are defined using the hyperbola.

To show that [tex]\cosh'(x) = \sinh(x)$ and $\sinh'(x) = \cosh(x)$[/tex] using the rules for differentiating [tex]e^x$:[/tex]

[tex]\textbf{1. Derivative of $\cosh(x)$:}[/tex]

Starting with the definition of [tex]\cosh(x)$:[/tex]

[tex]\[\cosh(x) = \frac{1}{2}(e^x + e^{-x})\][/tex]

Taking the derivative with respect to x using the chain rule and the derivative of [tex]e^x$:[/tex]

[tex]\cosh'(x) &= \frac{1}{2}\left(\frac{d}{dx}(e^x) + \frac{d}{dx}(e^{-x})\right) \\\\&= \frac{1}{2}(e^x - e^{-x}) \\\\&= \sinh(x)[/tex]

Therefore, [tex]\cosh'(x) = \sinh(x)$.[/tex]

[tex]\textbf{2. Derivative of $\sinh(x)$:}[/tex]

Starting with the definition of [tex]\sinh(x)$:[/tex]

[tex]\[\sinh(x) = \frac{1}{2}(e^x - e^{-x})\][/tex]

Taking the derivative with respect to x using the chain rule and the derivative of [tex]$e^x$[/tex]:

[tex]\sinh'(x) &= \frac{1}{2}\left(\frac{d}{dx}(e^x) - \frac{d}{dx}(e^{-x})\right) \\\\&= \frac{1}{2}(e^x + e^{-x}) \\\\&= \cosh(x)[/tex]

Therefore, [tex]\sinh'(x) = \cosh(x)$.[/tex]

Hence, we have shown that [tex]\cosh'(x) = \sinh(x)$ and $\sinh'(x) = \cosh(x)$[/tex] using the rules for differentiating [tex]e^x$.[/tex]

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Answer:

reflection??.........

Answer:

they are congruent

Step-by-step explanation:

because they are the same size and have the smae area!

Answer:

The answer is B

Step-by-step explanation:

Divide 48 by 3 which gives you the total amount for one bracelet then you have to multiply the amount by 9 and 13 and then find your answer in the letters.

The proportion relationship is as follows;

number of bracelet         total cost($)

                3                           48

                9                            144

               13                           208

Proportional relationship is one in which two quantities vary directly with each other.

Therefore, we can establish a proportional relationship between the number of bracelets and it cost.

Hence,

let

x = number of bracelet

y = cost of the bracelets

Therefore,

y = kx

where

k = constant of proportionality

48 = 3k

k = 48 / 3

k = 16

Let's find the cost for 9 or 13 bracelet

y = 12x

y = 16(9) = 144

y = 16(13) = 208

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Answer: D

Step-by-step explanation:

The orange divisor(s) above are the prime factors of the number 7,776. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 = 7,776. It can also be written in exponential form as 25 x 35.

Answer:

8√2

Step-by-step explanation:

this one is a right triangle so both side are equal since the angle is 45 degrees