Solve The Projection Of U Onto V And Show All Your Steps And Make Sure It Is Legible To Read.
Given u = 5i – j – 5k and v=-i+j – 2k, compute the projection proj,u.solve the projection of U onto V and show all your steps and make sure it is legible to read.

(a) The trigonometric equation for your height above the ground at t seconds after the ride starts is:

y(t) = 1 + 98*cos((π/15)*t)

(b) t = (15/π) * cos⁻¹(89/98). This will give us two values of t within one cycle when you are exactly at 90 feet off the ground.

(a) To draw a graph modeling one period of your movement on the Ferris wheel, we can use a sine or cosine function. Since your height starts at 1 foot off the ground, reaches a maximum of 99 feet, and then returns to 1 foot, a cosine function is appropriate.

Let's use the equation y(t) = a + b*cos(c(t-d)) to represent your height above the ground at t seconds after the ride starts.

Given:

- The lowest point is 1 foot off the ground, so a = 1.

- The highest point is 99 feet above the ground, so the amplitude is |a - 99| = 99 - 1 = 98, so b = 98.

- It takes 30 seconds for one full revolution, so the period is T = 30. Therefore, c = 2π/T = 2π/30 = π/15.

- The phase shift is d, which represents the horizontal displacement of the graph. Since your height starts at the lowest point, there is no horizontal displacement, so d = 0.

The trigonometric equation for your height above the ground at t seconds after the ride starts is:

y(t) = 1 + 98*cos((π/15)*t)

(b) To find the times within one cycle when you are exactly at 90 feet off the ground, we can set the equation y(t) = 90 and solve for t.

1 + 98*cos((π/15)*t) = 90

98*cos((π/15)*t) = 89

cos((π/15)*t) = 89/98

To find the solutions, we can take the inverse cosine (cos⁻¹) of both sides:

(π/15)*t = cos⁻¹(89/98)

Now we can solve for t by dividing both sides by π/15:

t = (15/π) * cos⁻¹(89/98)

This will give us two values of t within one cycle when you are exactly at 90 feet off the ground.

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Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

The capacitance of the capacitor is 0 F.

Part A:

Given that the discharge current decreases to 27% of its initial value in 1.40 ms, we can use the equation of discharge current:

I = I₀e^(-t/RC)

Here,

I₀ = initial current

R = resistance

C = capacitance

t = time

We are given that the current is 27% of the initial value, so the equation becomes:

0.27 = \(1e^(-1.40*10^-3/RC)\)

Simplifying the equation, we find:

RC =\(3.28* 10^-3 s\)   ----(1)

Part B:

The time taken to discharge a capacitor through a resistance R is given by:

t = RC ln (Vc/V₀)

where Vc = voltage across the capacitor at time t and V₀ = initial voltage across the capacitor.

Substituting the values, we have:

\(1.40*10^-3\) = C*90 ln (0/100)

Since a fully discharged capacitor has a voltage of 0, we set Vc = 0. Thus, the equation becomes:

\(1.40*10^-3\)= C*90 ln (0)

The natural logarithm of 0 is negative infinity. Therefore, the equation becomes:

\(1.40*10^-3\)= C*90*(-infinity)

Simplifying further, we find:

C = 0

Thus, the value of capacitance is 0 F.

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Answer:

A Hexagon has 6 sides so 6 Vertices

I got 9 7/9 by using a calculator

Answer:

Mean- 582.5

Median- 595

Mode- 310, 540, 820, 700, 650, 490, 770, 380

Step-by-step explanation:

Answer:

1

by looking only 1 is missing

Answer:

implicit array sizing

Step-by-step explanation:

The statement "int grades[] = { 100, 90, 99, 80 };" initializes an integer array called "grades" with the values 100, 90, 99, and 80. The given statement is an example of initializing an integer array in C++.

The array is named "grades" and has an unspecified size denoted by the empty square brackets []. The values inside the curly braces { } represent the initial values of the array elements.

In this case, the array "grades" is initialized with four elements: 100, 90, 99, and 80. The first element of the array, grades[0], is assigned the value 100, the second element, grades[1], is assigned 90, the third element, grades[2], is assigned 99, and the fourth element, grades[3], is assigned 80.

The array can be accessed and manipulated using its index values. This type of initialization allows you to assign initial values to an exhibition during its declaration conveniently.

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Answer:

2:29:32

Step-by-step explanation:

time = distance/speed= 162mi/65

=162/65 =2.49231

=2 hours 29 minutes 32 seconds

=02:29:32 (hh:mm:ss)

Hope this helps!

The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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Answer: 75

Step-by-step explanation:

Based on the information, we can determine convergence or divergence of series.The given options do not provide a clear representation of potential outcomes.It is not possible to select correct option.

The given series is "nvž enn |||-) En=12 100 1-) Σπίο 3* 2"-1 ||-) En=2 n". In the series, we have the characters "nvž enn |||-)" which indicate the series notation. The characters "En=12 100 1-" suggest that there is a summation of terms starting from n = 12, with 100 as the first term and a common difference of 1. The characters "Σπίο 3* 2"-1 ||-) En=2 n" indicate another summation, starting from n = 2, with a pattern involving the operation of multiplying the previous term by 3 and subtracting 1.

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To find the net displacement of the particle from time t=2 to time t=5, we need to integrate the velocity function over that time interval. Therefore, the net displacement of the particle from time t=2 to time t=5 is -2/π - 21 meters.

Given the velocity function of the particle, we can find the net displacement of the particle by integrating the velocity function over the time interval from t=2 to t=5. The integral of the velocity function gives us the change in position of the particle over that time interval.

To find the net displacement of the particle from time t=2 to time t=5, we need to integrate the velocity function over that time interval.

\(\int\limits^5_2 \, [-2sin(\pi t) - 2t] dt\)

Integrating, we get:

\([2/\pi cos(\pi t) - t^2]\)evaluated from t=2 to t=5

=\([2/\pi cos(\pi (5)) - 5^2] - [2/\pi cos(\pi (2)) - 2^2]\)

=\([2/\pi cos(\pi ) - 25] - [2/\pi cos(2\pi ) - 4]\)

=\([-2/\pi - 21]\)

Simplifying this expression, we get [-2/π - 21], which represents the net displacement of the particle from time t=2 to time t=5.

Therefore, the net displacement of the particle from time t=2 to time t=5 is\(-2/\pi - 21\)meters.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

BALALALALALAL

Step-by-step explanation:

7+5373)393()3

Answer:

2-5p

1-p

Step-by-step explanation:

put the whole equation into one one fraction. then you simplify. first do the bottom

1. first do 3-2=1

2. then the variable numbers i forget the fancy term

p-2p = -p

3. add together 1 - p

then do the top

its the same thing so then you put the new fraction together

4. 2-5p

1-p

I forget if there's anymore steps but I hope this helps

The time when the food price is most and cheapest is obtained from the extremum value of the function.

The extremum of a function is a maximum or minimum value of the function.

The function that models the food-price is I(t) = 0.00009045·t⁵ + 0.001438·t⁴ - 0.0656·t³ + 0.4598·t² - 0.6270·t + 99.33

Where;

t = The number of years since 1984

I(3) = 100

The time when the food is cheapest or most expensive can be obtained by differentiating the function for food-price and equating the result to 0 as follows;

I'(t) = 0.00009045×5·t⁴ + 0.001438×4·t³ - 0.0656×3·t² + 0.4598×2·t - 0.6270 = 0

Factoring the result, using a graphing calculator, we get;

(t - 0.823)·(t - 5.131)·(t - 11.05)·(t + 29.72) = 0

The values of the minimum and maximum values are therefore';

I(0.823) = 0.00009045×0.823⁵ + 0.001438×0.823⁴ - 0.0656×0.823³ + 0.4598×0.823² - 0.6270×0.823 + 99.33 ≈ 99.08

I(5.131) = 0.00009045×5.131⁵ + 0.001438×5.131⁴ - 0.0656×5.131³ + 0.4598×5.131² - 0.6270×5.131 + 99.33 ≈ 100.67

I(11.05) = 0.00009045×11.05⁵ + 0.001438×11.05⁴ - 0.0656×11.05³ + 0.4598×11.05² - 0.6270×11.05 + 99.33 ≈ 96.38

I(-29.72) = 0.00009045×(-29.72)⁵ + 0.001438×(-29.72)⁴ - 0.0656×(-29.72)³ + 0.4598×(-29.72)² - 0.6270×(-29.72) + 99.33 = 1270.8

Therefore, the food price when the food was cheapest is $99.08

The time when the food is most cheapest where 0 ≤ t ≤ 10 is t = 0.823 years ≈ 1 years

Similarly, the food price when the food was most expensive in a 10 year time frame is $100.67

The time when the food is most expensive is t ≈ 5.131 years ≈ 5 years

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The problem provides a table showing the probability of a salesperson making a certain number of sales per day. We are asked to find the expected sales per day, the variance, and the standard deviation of the number of sales.

The expected sales per day is the sum of the products of the number of sales and their corresponding probabilities. The variance is a measure of how much the number of sales varies from the expected value, and it is calculated as the sum of the squared differences between each value and the expected value, multiplied by their corresponding probabilities.

Finally, the standard deviation is the square root of the variance.

In summary, the problem involves using probability to find the expected value, variance, and standard deviation of a random variable representing the number of sales made by a salesperson in a day.

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Main Answer:The approximate probability is 0.033

Supporting Question and Answer:

How do we calculate the expected average and standard deviation for a sample?

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

Body of the Solution:

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Final Answer:Therefore, the approximate probability is 0.033, accurate to three decimal places.

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The approximate probability is 0.033

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Therefore, the approximate probability is 0.033, accurate to three decimal places.

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The answer choice that BEST describes the reaction of people in Japan to Hayabusa2's capsule landing would be A: "They were impressed, and they took pride in the mission's success."

Hayabusa2 was a Japanese space mission conducted by the Japan Aerospace Exploration Agency (JAXA), with the goal of collecting samples from the asteroid Ryugu and returning them to Earth. The mission was considered a significant achievement for Japan's space exploration efforts.

Given this context, it is reasonable to assume that the people in Japan would have been impressed and proud of the mission's success. The successful landing of the capsule would have been a cause for celebration and a source of national pride. The mission demonstrated Japan's technological capabilities and advancements in space exploration.

While it is important to note that individual reactions can vary, the option A aligns with the general sentiment expected from the people of Japan regarding the successful landing of Hayabusa2's capsule.

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Alan can conclude that the medicine given out to the treatment group does indeed work and reduces the amount of coughing and the control group with no treatment never got any better so the medicine is far better than no treatment at all.

Answer:

-6(a+8) simplified using distributive property would equal -6a+-120

Step-by-step explanation:

Answer:

In the triangle shown, AB = 11, BC = 61. Find AC. Right Triangle ABC v2. 3,600; 3,842; 60; 62. 4. Using the following measurements, find the length of the leg of the right triangle. leg = 5

Step-by-step explanation:

Not sure if that's helpful, but hope it is.

Answer:

1: x^2+y^2-6x-4y-3=0

2: x^2+y^2-10x+4y=0

3: x^2+y^2-10x+2y+1=0

Answer:

the answer is D

Step-by-step explanation:

i hope this helps and have a brilliant day :D

Answer:

Step-by-step explanation:

How to Solve for l: s=l+w

if s = l + w

l = s - w

Answer:

The correct answer is "66"

Step-by-step explanation:

P(-2) = 3*16 + 4*4 + 2

P(-2) = 48 + 16 + 2

P(-2) = 66

If the credit card did not have a promotional offer, Lori would have had to pay approximately $110.58 more in interest.

a. To determine how long it will take Lori to pay off the balance, we need to calculate the number of months it will take for the total balance to reach zero.

Let's assume it takes n months for Lori to pay off the balance. Each month, Lori pays $75 towards the balance. Since there is no interest during the promotional period, the balance decreases by $75 each month.

The initial balance is $562, so the remaining balance after n months can be represented as:

Remaining balance = Initial balance - (Monthly payment * Number of months)

0 = 562 - (75 * n)

Solving this equation for n:

75n = 562

n = 562 / 75

n ≈ 7.49

Therefore, it will take Lori approximately 7.49 months (or rounded up to 8 months) to pay off the balance.

b. To calculate the total interest paid, we need to subtract the initial balance from the total amount paid over the repayment period. The total amount paid is the monthly payment multiplied by the number of months.

Total interest paid = Total amount paid - Initial balance

Total amount paid = Monthly payment * Number of months

Total interest paid = (Monthly payment * Number of months) - Initial balance

Total interest paid = (75 * 8) - 562

Total interest paid = 600 - 562

Total interest paid = $38

Therefore, Lori will pay a total of $38 in interest.

c. If the credit card did not have a promotional offer, the interest would have been charged at a rate of 19.7% compounded daily after the promotional period.

To calculate the additional interest, we can use the formula for compound interest:

Additional interest = Initial balance * (1 + interest rate)^Number of months - Initial balance

Additional interest = 562 * (1 + 0.197/365)^(30 * 4) - 562

Calculating this value:

Additional interest ≈ $110.58

Therefore, if the credit card did not have a promotional offer, Lori would have had to pay approximately $110.58 more in interest.

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The mechanistic basis for linear polystyrene having phenyl groups attached to alternate carbons of the polymer chain is due to the nature of the polymerization reaction, specifically free-radical polymerization.

1. Free-radical polymerization of styrene starts with the initiation step, where a free radical initiator generates a reactive radical site.
2. The reactive radical site reacts with the double bond of the styrene monomer, forming a new radical site on the styrene molecule.
3. This new radical site on the styrene molecule can now react with another styrene monomer, effectively joining them together.
4. As the radical site is always at the end of the growing polymer chain, the phenyl groups of each added styrene monomer will be attached to alternate carbons. This occurs because the reactive site is situated between the phenyl group and the double bond in the monomer, creating a zigzag pattern as the chain grows.

Conclusion:
The attachment of phenyl groups to alternate carbons of the polymer chain in linear polystyrene can be attributed to the free-radical polymerization mechanism. The reactive radical site, created during the polymerization, allows the phenyl groups to be connected in an alternating pattern along the chain.

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Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet