Help!!! I need to turn in in 10 minutes

(a) The unit tangent and unit normal vectors T(t) and N(t) is ⟨-sin t, 0, -cos t⟩.

(b) The curvature is 3/(9 cos² t + 4 + 9 sin² t)

To find T(t), we first take the derivative of r(t) with respect to t, which gives us the velocity vector v(t) = ⟨3 cos t, 2, -3 sin t⟩. Then, we divide this vector by its magnitude to get the unit tangent vector T(t) = v(t)/||v(t)||, where ||v(t)|| is the magnitude of v(t). This gives us:

T(t) = ⟨(3/√(9 cos² t + 4 + 9 sin² t)), 2/√(9 cos² t + 4 + 9 sin² t), (-3/√(9 cos² t + 4 + 9 sin² t)))⟩

To find N(t), we take the derivative of T(t) with respect to t, and divide by the magnitude of this derivative:

N(t) = T'(t)/||T'(t)||, where T'(t) is the derivative of T(t) with respect to t.

After some algebraic simplification, we find that T'(t) = ⟨-3 sin t, 0, -3 cos t⟩, so

||T'(t)|| = 3, and

N(t) = ⟨-sin t, 0, -cos t⟩.

Now that we have the unit tangent and unit normal vectors, we can move on to finding the curvature, denoted k(t).  Specifically, the curvature is given by the formula:

k(t) = ||T'(t)||/||v(t)||²

where ||T'(t)|| is the magnitude of the derivative of the unit tangent vector, and ||v(t)||² is the square of the magnitude of the velocity vector.

We already found ||T'(t)|| and ||v(t)|| in the previous steps, so we can plug these values into the formula to get:

k(t) = 3/(9 cos² t + 4 + 9 sin² t)

This gives us the curvature for every value of t.

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Complete Question:

Consider the vector function given below. r ( t ) = ⟨ 3 sin t , 2 t , 3 cos t ⟩ Do the following:

(a) Find the unit tangent and unit normal vectors, T(t) and N(t).

(b) Find the curvature, k(t).

Answer:

I think it is D

Step-by-step explanation:

sorry if I am wrong

Answer:

41.5

Step-by-step explanation:

you use the trigonometric equations. in this case, we will use SOH:

sin 49=opposite/adjacent

sin 49=x/55

55 sin 49=x

41.50=x

Therefore, x is equals to 41.50. And it is already to it's nearest hundredth.

The value of x is  41.25.

There are three commonly used trigonometric identities.

Sin x = Perpendicular / Hypotenuse

Cosec = Hypotenuse / Perpendicular

Cos x = Base / Hypotenuse

Sec x = Hypotenuse / Base

Tan x = Perpendicular / Base

Cot x = Base / Perpendicular

We have,

We use the sin function.

Sin 49 = DE/DF

Sin 49 = x / 55

0.75 = x / 55

x = 0.75 x 55

x = 41.25

Thus,

The value of x is  41.25.

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The correct statement regarding the relative frequencies in the table is given as follows:

D. More students prefer Model 55 calculators than Model 77

For each model, the relative frequencies are given by the Total row, as follows:

Hence Model 55 is the favorite of the students, and thus option D is the correct option for this problem.

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Answer:

144

Step-by-step explanation:

(ab)²

(4*-3)²

(-12)²

144

Best of Luck!

Answer:

yes or no?...

Step-by-step explanation:

thank u?

Np!...

Hello,

\(0\leq a\leq 1 \Longrightarrow 0*a\leq a*a\leq 1*a \Longrightarrow 0 \leq a^2 \leq a\\\\0\leq a^2\leq a \Longrightarrow \sqrt{0} \leq \sqrt{a^2} \leq \sqrt{a} \\\\The\ function\ y=x^2\ is\ increasing\\\\Answer A\\\\ex: a=0.5 \\\\a^2=0.25\\\\\sqrt{a}=\dfrac{\sqrt{2}}{2}\approx{0.7071...}\\\\and\ 0.25\leq 0.5 \leq 0.7071...\)

Answer:

16/22, 24/33, and 40/55

or

72.7272...% = Percentage form

0.7272... = Decimal form

Hope this helps :)

Pls brainliest...

========================================================

Explanation:

For the x value x = 3, the observed y value is y = 6 which is from the point (3,6).

The predicted y value is found by plugging x = 3 into the line of best fit equation

y = 5x-2.5

y = 5(3)-2.5

y = 12.5

The residual is the difference between the two y values

e = residual

e = (observed y value) - (predicted y value)

e = 6 - 12.5

e = -6.5

The negative residual tells us the observed y value is smaller than the predicted y value for this given x value.

We can find the percentage of increase in the number of Magikarps that Jose captured in the lake by taking the initial number of them and subtracting it from the number that he had by the end of the day, like this:

16 - 8 = 8

Now, we just have to divide 8 by 16 and then multiply by 100, like this:

Then, his number of Magikarps increased a 50%

The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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The positions of the keys in a hash table of size n = 7 has been determined and the collisions are resolved by linear probing.

To determine the positions of the keys in a hash table of size n=7 and insert them into the hash table while resolving collisions by linear probing, we need to first apply a hash function that maps the keys to a specific position in the table. Let's assume that we use the simple mod function as the hash function: h(key) = key % 7.
Using this hash function, the keys will be mapped to the following positions in the hash table:
- 34 -> h(34) = 6
- 78 -> h(78) = 1
- 93 -> h(93) = 2
- 5 -> h(5) = 5
- 74 -> h(74) = 4
- 81 -> h(81) = 4
We can see that two keys, 74 and 81, are mapped to the same position in the table (position 4). This is called a collision. To resolve collisions using linear probing, we simply look for the next available position in the table and insert the key there.
Starting from the position of the collision (position 4), we check the next positions in the table sequentially until we find an empty position. The keys will be inserted into the following positions:
- 34 -> position 6
- 78 -> position 1
- 93 -> position 2
- 5 -> position 5
- 74 -> position 4 (original position)
- 81 -> position 5 (next available position after collision)
Therefore, the final hash table with the keys inserted using linear probing will look like this:
0 | |
1 |78|
2 |93|
3 | |
4 |74|
5 |5|
6 |34|

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4x−2y=14

Step-by-step explanation:

Answer:

The solution to the system of linear equations is x = 4, y = 1.

Step-by-step explanation:

Given system of linear equations:

\(\begin{cases}4x-2y=14\\y=\dfrac{1}{2}x-1\end{cases}\)

To solve the system of linear equations by the method of substitution, substitute the second equation into the first equation:

\(\implies 4x-2\left(\dfrac{1}{2}x-1\right)=14\)

Solve the equation for x:

\(\implies 4x-x+2=14\)

\(\implies 3x+2=14\)

\(\implies 3x=12\)

\(\implies x=4\)

Substitute the found value of x into the second equation and solve for y:

\(\implies y=\dfrac{1}{2}(4)-1\)

\(\implies y=2-1\)

\(\implies y=1\)

Therefore, the solution to the system of linear equations is:

Answer:

8

Step-by-step explanation:

8(2x+1) =136

16x+8=136

16x=136-8

16x=128

x=128÷16

x=8

✽ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ✽

➷ \(\boxed{x = 8}\)

✽ First, Simplify both sides of the equation.

\(8(2x + 1) = 136\)

\((8) (2x) + (8) (1) = 136\)

       ↑↑↑↑

(✽ Distribute✽)

_______________

\(16x + 8 = 136\)

✽ Then, Subtract 8 from both sides.

\(16x + 8 - 8 = 136 - 8\)

\(16x = 128\)

✽ Last, Divide both sides by 16.

\(\frac{16x}{16} = \frac{123}{16}\)

\(x = 8\)

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ May ♡

The average number of calls per day is approximately 5.298 calls.

To solve this problem, we'll first use the information given about the probability of receiving no calls (0.5%) and the Poisson distribution formula to find the average number of calls per day (λ).

Step 1: Convert the percentage of no calls into a decimal.
0.5% = 0.005

Step 2: Use the Poisson distribution formula for the probability of receiving no calls (k = 0).
P(X = 0) = (e^(-λ) * λ^0) / 0! = 0.005

Step 3: Simplify the equation.
(e^(-λ) * 1) / 1 = 0.005

Step 4: Solve for λ.
e^(-λ) = 0.005
-λ = ln(0.005)
λ = -ln(0.005)

Step 5: Calculate the average number of calls per day.
λ ≈ 5.298

So, the average number of calls per day is approximately 5.298 calls.

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Answer:

9.8 units

Step-by-step explanation:

distance = sqrt (x2 - x1)^2 + ( y2 - y1)^2

sqrt (-3 - (-6))^2 + (5 - 1)^2

sqrt (9)^2 + (4)^2

sqrt 81 + 16

sqrt 97

9.848857802

Answer:

1)I don't know

2)-2

Step-by-step explanation:

2)6-5(1/1/x)= 2

6-5(1/1)-x= 2

6-6-x=2

-x/-1=2/-1

x= -2

A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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Answer:

C. Supplementary Angles

One way to remember that is that C is the top half of S and Complementary Angles =90 and Supplementary angles =180. 90 is one half of 90

Answer:

you need to save $21

We need to determine the difference in earnings between Star Wars and The English Patient based on the given information. We can say that Star Wars earned $328,300,000 more than The English Patient in their first year.

To calculate the difference in earnings between Star Wars and The English Patient, we subtract the earnings of The English Patient from the earnings of Star Wars.

Star Wars earned $670,900,000 in its first year, while The English Patient earned $342,600,000. By subtracting the earnings of The English Patient from Star Wars, we find that Star Wars earned $328,300,000 more than The English Patient.

This means that Star Wars had a significantly higher earning compared to The English Patient, with a difference of $328,300,000. The difference in earnings highlights the disparity in popularity and financial success between the two movies in their respective first years of release.

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Answer:

C. 3((x+4) + (x-2))

Step-by-step explanation:

Area of a triangle: \(\frac{1}{2}bh\)

Area of the left triangle:

\(\frac{1}{2}(x+4)(6)\)

The 6 multiplied by the 1/2 equals 3, so:

\(A = 3(x+4)\)

Area of the right triangle:

\(\frac{1}{2}(x-2)(6)\\\)

Again, the 6 multiplied by the 1/2 equals 3, so:

\(A= 3(x-2)\)

Adding the two areas together equals:

\(3(x+4) + 3(x-2)\)

We can factor out the 3 from both, giving us the final answer:

\(A = 3((x-4)+(x-2))\)

Danielle knows that the point of intersection is also the y-intercept of 5x - 2y = 4 because when x=0, the equation simplifies to -2y = 4, which gives y = -2.

This means that the point of intersection is (0, -2), which is also the point where the line intersects the y-axis.

To find the point of intersection of the two rules given, we can substitute x=0 from the second equation into the first equation

which gives 5 - 2y = 4.

Solving for y we get y = 1/2.

Therefore, the point of intersection is (0, 1/2).

In summary, Danielle was able to determine that the point of intersection is the y-intercept of 5x - 2y = 4 by recognizing that the line x=0 is the y-axis. To find the actual point of intersection, we substituted x=0 into the first equation and solved for y, which gave us the coordinates (0, 1/2).

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Answer:

Step-by-step explanation:

C)   Sarah is trying to say that 72 and 64 are opposite, if 68 is used as the starting point.  So from the point 68,   72 is +4 and 64 is -4.   68 is the "baseline"   or starting point

Answer:9

Step-by-step explanation:draw a line threw the equal sign, add 36 instead of subtracting it, which then would be 9.

Answer:

down below

Step-by-step explanation:

In order for you to get a negative number, you need to put in the variables place, 9.

9 is your answer.

The amount of sleep that is exceeded by only 25% of students is 6.78 hours.

The amount of sleep that is exceeded by only 25% of students can be found using the z-score formula.

A z-score is a measure of the number of standard deviations that a value is above or below the mean. It is calculated using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Using this formula, we can find the z-score that corresponds to the 25th percentile, or the amount of sleep that is exceeded by only 25% of students:z = invNorm(0.25) = -0.6745 (rounded to 4 decimal places)Here, invNorm is the inverse normal cumulative distribution function, which gives the z-score for a given percentile. In this case, we use invNorm(0.25) because we want to find the z-score for the 25th percentile.

Next, we can use the z-score to find the amount of sleep that corresponds to it:x = μ + zσx = 7.2 hours + (-0.6745) * 40 minutes / 60 minutes/hours = 6.783 hours (rounded to 2 decimal places)Therefore, the amount of sleep that is exceeded by only 25% of students is 6.78 hours.

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(b) There are two Nash equilibria in this game:(S, S): Both A and B choose to Stop. Neither player has an incentive to deviate as they both receive a payoff of 0, and any deviation would result in a lower payoff.

(C, C): Both A and B choose to Continue. Similarly, neither player has an incentive to deviate since they both receive a payoff of -1, and any deviation would result in a lower payoff. (c) There is no dominant strategy in this game. A dominant strategy is a strategy that yields a higher payoff regardless of the actions taken by the other player. In this case, both players' payoffs depend on the actions of both players, so there is no dominant strategy. (d) The Subgame Perfect Nash equilibria (SPNE) can be found by considering the game as a sequential game and analyzing each subgame individually.

In this game, there is only one subgame, which is the entire game itself. Both players move simultaneously, so there are no further subgames to consider. Therefore, the Nash equilibria identified in part (b) [(S, S) and (C, C)] are also the Subgame Perfect Nash equilibria of this game.

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118,813,760 different combination license plates can the country produce

Permutations and combinations:

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number of all possible subsets for many games of chance in the 17th century, the French mathematicians Blaise Pascal and Pierre de Fermat gave impetus to the development of combinatorics and probability theory.

Given that

In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet

X = 10 × 26 × 26 × 26 × 26 × 26

  = 10 × 11881376

  = 118,813,760

118,813,760 different combinations license plates can the country produce

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