An object is taken from an oven at 300°F and left to cool in a room at 70°F. After 11 / hour, the temperature fell to 200°F. 2 (a) Find a formula for the temperature of the object at any time t. (b) What will be the temperature of the object after 3 hours?

The average speed of the plane is 240 km/h

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Let S represent the average speed of the plane.

S = 1200/t

When driving 40 km/h less, the total time = t + 1 hour, hence:

S - 40 = 1200 / (t + 1)

1200/t - 40 = 1200/(t+ 1)

1200 - 40t + 1200/t - 40 = 1200

- 40t + 1200/t - 40 = 0

Multiply through by t:

- 40t² + 1200 - 40t = 0

This gives t = 5 and t = -6

Since the time cannot be negative, hence the total time is 5 hours. Hence:

S = 1200/t = 1200 / 5 = 240 km/h

Hence the average speed of the plane is 240 km/h.

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Speed is a scalar quantity, we will ignore the negative sign.

The average speed of the plane is 240 km/h

The Parameters to work with in this question are :

Speed, Time and distance. Where

distance S = 1200 km and the formula for speed is

Speed V = distance S / Time T

The assumed equation for this assumption will be:

(V - 40) = 1200/ (T + 1 )

Cross multiply and open the bracket

(V - 40)(T + 1) = 1200 ............. Equation 1

The real equation for the real scenario will be

V = 1200/ t

Where V is the average speed of the plane.

Make t the subject of the formula

t = 1200/V

Substitute the above t in equation 1 since we are looking for V

(V - 40)(1200/V + 1) = 1200

Open the bracket

1200 + V - 48000/V - 40 = 1200

Rearrange

V - 48000/V + 1160 = 1200

V - 48000/V = 1200 - 1160

\(V^{2}\) - 48000 = 40V

\(V^{2}\) - 40V - 48000

The two numbers to multiply together to give -48000 and add together to give -40 are -240 and 200

\(V^{2}\) - 240V + 200V - 48000

V - 240 = 0 or V + 200 = 0

V = 240 or - 200

Since the speed is a scalar quantity, we will ignore the negative sign.

Therefore, the average speed of the plane is 240 km/h

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Answer:

No.

Step-by-step explanation:

It does not pass the vertical line test, so the relation is not a function. This is because there are x-values that have several y-values. To be a function, a relation must have x-values that only have one y-value each.

Hope this helps!

Answer:

No

Step-by-step explanation:

Because for any given point along the x-axis it has 2 values along y-axis.

For a relation to be a function it must have only one value at y-axis along any given point along the x-axis

The area of the figure can be obtained by splitting the figure into smaller components

The area of the irregular figure = Area of A + Area of B + Area of C

Area of A = L X B = 12 x 7 = 84 sq meters

Area of B = L X B = 5 X 8 = 40 sq meters

Area of C = L X B = 5 x 8 = 40 sq meters

Total area = 84 + 40 + 40 = 164 sq meters

Answer:

D.

Step-by-step explanation:

Answer:

Step

Y-0=-3/4(x-8)

Y=-3/4x+6

Answer:

b

Step-by-step explanation:

the 2 legs of the triangle are congruent, thus the triangle is isosceles with the 2 base angles congruent , then

3x = 60 ( divide both sides by 3 )

x = 20

Answer: b

Step-by-step explanation: the 2 legs of the triangle are congruent, thus the triangle is isosceles with the 2 base angles congruent , then

3x = 60 ( divide both sides by 3 )

x = 20

We know that there are 850 more red marbles left than blue marbles by solving equations.

The equals sign is used in mathematical equations to indicate that two expressions are equal.

An equation is a claim that demonstrates the equality of two mathematical expressions, according to algebra.

For instance, the word "equal" separates the formulas 3x + 5 and 14, which together form the equation 3x + 5 = 14.

So, a number of red marbles more than blue marbles is:

Mackenzie has 3200 more red than yellow marbles.
y + 3200 = r

Additionally, she has 3840 more blue than yellow marbles.

y + 3840 = b

Assume Mackenzie has one yellow marble, then.

1 + 3200 = 3201 red marbles

1 +3840 = 3841 blue marbles

She will have left over 2351 blue marbles after giving away 1490

3841 - 1490 = 2351

She now has 3201 red marbles and 2351 blue marbles.

r - b =?

3201 - 2351 = 850

Therefore, we know that there are 850 more red marbles left than blue marbles by solving equations.

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The correct population should she answered is  is A) 7th graders in the school

To find out the favorite after-school activity of 7th grade students, Ms. Smith should sample the population directly related to the question. In this case, the most appropriate population to sample would be:

A) 7th graders in the school

By sampling the 7th graders in the school, Ms. Smith can directly gather information about their favorite after-school activities. This population consists of the students themselves who engage in the activities, and they would have first-hand knowledge and experience of their preferences.

B) Parents of 7th graders in the school might provide some insights, but they may not accurately represent the activities chosen by the students themselves.

C) Other 7th-grade teachers in the school may have some observations, but it may not reflect the preferences of the entire 7th-grade student population.

D) Sampling all students in the school would be broader than necessary and may not specifically address the favorite after-school activities of 7th-grade students.

Therefore, option A) 7th graders in the school is the most suitable population for Ms. Smith to sample in order to answer her question about the favorite after-school activity of 7th-grade students.

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The expressions that can be used to describe how many milligrams of vitamin C are in the salad are:

(Choice A) 200b + (300s + 42d)

(Choice E) 300s + 200b + 42d

So, the correct answers are A and E.

The milligrams of vitamin C in the salad can be determined by considering the quantities of spinach, berries, and dressing used in the salad, along with their respective vitamin C content.

In the given scenario, the salad includes 300 milliliters (mL) of spinach, 200 mL of berries, and 42 mL of dressing. The vitamin C content is measured in milligrams per milliliter (mg/mL), with values denoted as s for spinach, b for berries, and d for dressing.

To calculate the milligrams of vitamin C in the salad, we can use the expressions provided:

(Choice A) 200b + (300s + 42d)

(Choice E) 300s + 200b + 42d

In Choice A, the expression 200b represents the milligrams of vitamin C in the berries, while (300s + 42d) represents the combined vitamin C content of spinach and dressing.

In Choice E, the expression 300s represents the milligrams of vitamin C in the spinach, 200b represents the milligrams of vitamin C in the berries, and 42d represents the milligrams of vitamin C in the dressing.

By substituting the respective values of s, b, and d into either expression, we can calculate the total milligrams of vitamin C in the salad.

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Answer:

U' (- 1, 3 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (- 1, - 3 ) → U' (- 1, 3 )

The rate of change of N is inversely proportional to N(x), where N > 0. If N (0) = 6, and N (2) = 9, find N (5). The answer is 12.186.

The rate of change of N is inversely proportional to N(x), which means that the rate of change of N is equal to some constant k divided by N(x). This can be written as dN/dt = k/N(x).

If we integrate both sides of this equation, we get ln(N(x)) = kt + C. If we then take the exponential of both sides, we get N(x) = Ae^(kt), where A is some constant.

We know that N(0) = 6, so we can plug in t = 0 and N(x) = 6 to get A = 6. We also know that N(2) = 9, so we can plug in t = 2 and N(x) = 9 to get k = ln(3)/2.

Now that we know A and k, we can plug them into the equation N(x) = Ae^(kt) to get N(x) = 6e^(ln(3)/2 t).

To find N(5), we plug in t = 5 to get N(5) = 6e^(ln(3)/2 * 5) = 12.186.

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Answer:

Step-by-step explanation:

4 x 10= 40 so true

The answer is true

Step by Step: None

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its Denominator, or to eliminate denominators from a radical expression.

To rationalize the denominator 1/7 + 3√2,

A rational number is a number that can be expressed as a ratio of two integers, with the denominator not equal to zero. The fraction 4/5, for example, is a rational number since it can be expressed as 4 divided by 5.

Step-by-Step SolutionTo rationalizes the denominator 1/7 + 3√2, we'll need to follow these steps.

Step 1: First, we need to create a common denominator for the two terms. The common denominator is 7. Thus, we can convert the expression to the following form:(1/7) + (3√2 × 7)/(7 × 3√2).

Step 2: Simplify the denominator to 7. (1/7) + (21√2)/(21 × 3√2).

Step 3: The numerator and denominator can now be simplified. (1 + 21√2)/(7 × 3√2).Step 4: Simplify further. (1 + 21√2)/(21√2).We have successfully rationalized the denominator!

The final answer is (1 + 21√2)/(21√2).

The final answer is (1 + 21√2)/(21√2). The process of rationalization involves changing the form of an expression to eliminate radicals from its denominator, or to eliminate denominators from a radical expression.

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Answer:

Step-by-step explanation:

Area of rectangle= 250 sq.units

Width = (250-10)÷3

          = 240÷3

          = 80 units

Answer:

Jenny es la más alejada de su novela, con 6.66/100 por delante de Gabriel, y 8.33/100 por delante de Jessica.

English Translation: "Jenny is furthest through her novel, at 6.66/100 ahead of Gabriel, and 8.33/100 ahead of Jessica."

Step-by-step explanation:

Translation to English: "Jenny is on page 250 of her 375-page novel, Gabriel is on page 243 of the 405 pages of hers, and Jessica is reading page 448 of the 768 pages of hers. Who has done the furthest reading of their novel and what fraction of the novel separates them from the others?"

For the first part of question, where is asks who is farther through their book, calculate percentage, which is calculated from division:

250/375 = 0.66..., or 66.66%

243/405 = 0.6, or 60%

448/768 = 0.5833..., or 58.33%

We can already see that Jenny is furthest through her book, as she is around 6.66% farther than Gabriel and 8.33% farther than Jessica.

But, to answer the second part of the question, we must convert this information to fractions, which can be done by putting the values over 100:

66.66/100, 60/100, 58.33/100.  Now, since they are already in the same denominators, we can easily tell how far they are from one another in fractions: Jenny is 6.66/100 ahead of Gabriel, and 8.33/100 ahead of Jessica.

If I helped, please make this answer brainliest! ;)

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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Answer:

1, 3, 5

Step-by-step explanation:

:)

Answer:

3 x 3 x 5

Step-by-step explanation:

Prime numbers are numbers that cannot factor any lower then itself and one (which includes, but is not limited too: 1, 3, 5, 7, 11, 13, 17, etc.

5 x 1 = 5

3 x 1 = 3

Factor:

45 = 15 x 3

15 = 5 x 3

3 x 3 x 5 is your answer.

In an RCL circuit with given parameters, the subsequent charge on the capacitor is zero, and the current follows an exponential decay pattern.

By plotting the charge and current on separate axes, their behavior over time can be visualized.

The subsequent charge on the capacitor and the current in the RCL circuit can be determined using the principles of circuit analysis. The charge on the capacitor and the current in the circuit can be found as a function of time. The charge on the capacitor is given by the equation Q(t) = Q(0)e^(-t/(RC)), and the current in the circuit is given by the equation I(t) = (E/R)e^(-t/(RC)). By substituting the given values of R, C, and E into these equations, we can calculate the charge and current at any time t. Plotting the charge and current on separate axes provides a visual representation of their variation over time.

Given parameters:

R = 6 Ω (resistance)

C = 0.02 F (capacitance)

L = 0.1 H (inductance)

E = 6 V (applied voltage)

To find the subsequent charge on the capacitor, we use the equation Q(t) = Q(0)e^(-t/(RC)). Since there is no initial charge when the voltage is first applied, Q(0) = 0. Thus, the equation simplifies to Q(t) = 0.

To find the current in the circuit, we use the equation I(t) = (E/R)e^(-t/(RC)). Substituting the given values, we have I(t) = (6/6)e^(-t/(6 * 0.02)) = e^(-t/0.12).

To plot the charge and current, we choose a time range, such as t = 0 to t = 1 second, with a suitable step size. For each time value in the range, we calculate the corresponding charge and current using the derived equations.

By plotting the charge on the y-axis and time on the x-axis, we can visualize that the charge on the capacitor remains zero throughout the entire time range.

By plotting the current on the y-axis and time on the x-axis, we can observe an exponential decay pattern. Initially, the current is at its maximum value of 1A (since E/R = 6/6 = 1). As time progresses, the current decreases exponentially.

Labeling each plot appropriately allows for clear identification of the charge and current curves.

In summary, for the given RCL circuit, the subsequent charge on the capacitor is zero, and the current in the circuit follows an exponential decay pattern. By plotting the charge and current on separate axes, we can visualize their behavior over time.

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Here are a few reasons why researchers exercise caution when interpreting statistical significance: Avoiding Type I and Type II errors, Generalizability, Replicability, Methodological limitations.

Researchers are careful about drawing conclusions regarding statistical significance because statistical significance is a measure of the likelihood that the observed results are not due to random chance. When conducting research, researchers aim to make inferences and draw conclusions based on evidence that is reliable and valid.

Here are a few reasons why researchers exercise caution when interpreting statistical significance: Avoiding Type I and Type II errors, Generalizability, Replicability, Methodological limitations.

Avoiding Type I and Type II errors: When testing hypotheses, there is always a possibility of making errors. Type I error occurs when a researcher mistakenly rejects a true null hypothesis (false positive), and Type II error occurs when a researcher fails to reject a false null hypothesis (false negative). By being cautious, researchers strive to minimize these errors and ensure that their conclusions are accurate.

Generalizability: Researchers often want to generalize their findings from a sample to a larger population. Statistical significance provides an indication of how likely the findings can be applied to the broader population. Drawing conclusions without considering statistical significance may lead to misleading or unreliable generalizations.

Replicability: Scientific research should be replicable, meaning that other researchers should be able to obtain similar results when conducting the same study. Statistical significance helps assess whether the observed effects are consistent and reproducible across different studies. Without proper consideration of statistical significance, it becomes difficult to determine if the results can be replicated reliably.

Methodological limitations: Research studies can have various limitations such as small sample sizes, confounding factors, measurement errors, or biases. By carefully assessing statistical significance, researchers can better understand the limitations of their study and make more informed conclusions.

In summary, researchers are cautious about drawing conclusions regarding statistical significance to ensure the validity, reliability, generalizability, and replicability of their findings. By exercising care in interpreting statistical significance, researchers aim to make robust and trustworthy conclusions based on the available evidence.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

I believe it would be 4,3 not sure though

Step-by-step explanation:

Answer:

The answer would be 4,3

Step-by-step explanation:

Graph the points on a graphing calculator, that should help when you need to find diagonals

Answer:

$8.19

Step-by-step explanation:

Divide both numbers together.

Don't forget to make 18% in a decimal format like this -> 0.18

45.50 / 0.18

let $p$ and $q$ be the two distinct solutions to the equation$$\frac{4x-12}{x^2 2x-15}=x 2.$$if $p > q$. The value of $p - q$ is 4.

To find the value of $p - q$, we first need to solve the given equation and determine the values of $p$ and $q$.

The equation is:

$$\frac{4x-12}{x^2 - 2x - 15} = x^2.$$

Step 1: Factorize the denominator:

The denominator can be factored as $(x - 5)(x + 3)$.

Step 2: Simplify the equation:

$$\frac{4x-12}{(x - 5)(x + 3)} = x^2.$$

Step 3: Multiply both sides of the equation by $(x - 5)(x + 3)$ to eliminate the denominator:

$$(4x - 12) = x^2(x - 5)(x + 3).$$

Step 4: Expand and rearrange the equation:

$$4x - 12 = x^4 - 2x^3 - 15x^2 + 25x.$$

Step 5: Rearrange the equation and combine like terms:

$$x^4 - 2x^3 - 15x^2 + 21x - 12 = 0.$$

Step 6: Factorize the equation:

$$(x - 3)(x + 1)(x - 2)(x + 2) = 0.$$

From this, we get four possible solutions: $x = 3$, $x = -1$, $x = 2$, and $x = -2$.

However, we are interested in the two distinct solutions $p$ and $q$, where $p > q$. Therefore, the values of $p$ and $q$ are $p = 3$ and $q = -1$.

Finally, we can find the value of $p - q$:

$$p - q = 3 - (-1) = 3 + 1 = 4.$$

Hence, the value of $p - q$ is 4.

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:

Step-by-step explanation:

here you go mate'

step 1

(60 + 10)130  equation

step 2

(60 + 10)130  simplify with the brackets

step 3

130(70)  multiply the numbers

answer

9100

Your answer: g(x) = 2(x + 2) ^2 + 6 (standard form) Minimum value of g(x) = 6. (a) To express the given quadratic function g(x) = 2x^2 + 8x + 14 in standard form, we need to complete the square:

g(x) = 2(x^2 + 4x) + 14

To complete the square, we take half of the coefficient of the x term (which is 4) and square it. Half of 4 is 2, and 2^2 = 4. Now, we add and subtract 4 inside the parentheses:

g(x) = 2(x^2 + 4x + 4 - 4) + 14

Factor the trinomial inside the parentheses and simplify:

g(x) = 2((x + 2)^2 - 4) + 14

Now distribute the 2:

g(x) = 2(x + 2)^2 - 8 + 14

Combine the constants:

g(x) = 2(x + 2)^2 + 6

Now, g(x) is in standard form: g(x) = 2(x + 2)^2 + 6.

The quadratic function has a minimum value since the leading coefficient (2) is positive. The minimum value occurs at the vertex of the parabola, which can be found using the formula: (-b/2a, f(-b/2a)).

For g(x), a = 2 and b = 8. So, -b/2a = -8/(2*2) = -2. Now, we can find the minimum value by plugging -2 back into the function:

g(-2) = 2(-2 + 2)^2 + 6 = 2(0)^2 + 6 = 6

The minimum value of g(x) is 6.

Your answer:
g(x) = 2(x + 2) ^2 + 6 (standard form)
Minimum value of g(x) = 6

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Given:

The scale factor of the actual sports utility vehicle to the toy model is 50:1.

Actual length = 7 feet

Actual width = 5 feet

To find:

The length and width of the toy model.

Solution:

a. Let l be the length of the toy model, then

\(\dfrac{\text{Actual length}}{\text{Length of the toy model}}=\dfrac{50}{1}\)

\(\dfrac{7}{l}=\dfrac{50}{1}\)

\(7=50l\)

\(\dfrac{7}{50}=l\)

\(0.14=l\)

Therefore, the length of the toy model is 0.14 feet.

b. Let w be the width of the toy model, then

\(\dfrac{\text{Actual width}}{\text{Width of the toy model}}=\dfrac{50}{1}\)

\(\dfrac{5}{w}=\dfrac{50}{1}\)

\(5=50w\)

\(\dfrac{5}{50}=w\)

\(0.10=w\)

Therefore, the width of the toy model is 0.10 feet.

The solution of each of the equations for the variable indicated in each case are as follows;

It follows from the task content that the equations given are to be solved for the variables indicated.

The equations can therefore be solved as follows;

11. u = vw + z

Isolate vw so that we have;

vw = u -z; Divide both sides by w;

v = (u - z)/w.

12. x = b - cd

Isolate cd so that we have;

cd = b -x; Divide both sides by d;

c = (b - x)/d.

13. fg - 9h = 10j

Isolate fg so that we have;

fg = 10j + 9h; Divide both sides by f;

g = (10j + 9h)/f.

14. m - p = -n

Isolate m; so that we have;

m = p - n.

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For the parameterizations r(t) = (t, 3 cos t, 3 sin t) and r(r) = (t^2, sin t - t cos t, cos t + t sin t), the unit tangent vectors are T(t) = (1/√10, -3 sin t / √10, 3 cos t / √10) and T(t) = (2t / √(4t^2 + 2), (cos t + t sin t) / √(4t^2 + 2), (-sin t + t cos t) / √(4t^2 + 2)) respectively, and the curvature is κ(t) = 3 / 10 and κ(t) = (2 - 4t^2) / (4t^2 + 2)^(3/2) respectively.

To find the unit tangent vector T(t) and unit normal vector N(t) for the given parameterizations, and subsequently calculate the curvature using Formula 9, we'll evaluate them for both cases:

(b) For r(t) = (t, 3 cos t, 3 sin t):

Calculate the first derivative r'(t) = (1, -3 sin t, 3 cos t).

Compute the magnitude of r'(t): ||r'(t)|| = √(1^2 + (-3 sin t)^2 + (3 cos t)^2) = √(1 + 9 sin^2 t + 9 cos^2 t) = √(10).

Obtain the unit tangent vector: T(t) = r'(t) / ||r'(t)|| = (1/√10, -3 sin t / √10, 3 cos t / √10).

Calculate the derivative of T(t): T'(t) = (0, -3 cos t / √10, -3 sin t / √10).

Calculate the magnitude of T'(t): ||T'(t)|| = √((-3 cos t / √10)^2 + (-3 sin t / √10)^2) = 3 / √10.

Compute the curvature using Formula 9: κ(t) = ||T'(t)|| / ||r'(t)|| = (3 / √10) / √10 = 3 / 10.

Therefore, for r(t) = (t, 3 cos t, 3 sin t), the unit tangent vector T(t) is (1/√10, -3 sin t / √10, 3 cos t / √10), and the curvature κ(t) is 3 / 10.

For r(r) = (t^2, sin t - t cos t, cos t + t sin t), t > 0:

Calculate the first derivative r'(t) = (2t, cos t + t sin t, -sin t + t cos t).

Compute the magnitude of r'(t): ||r'(t)|| = √((2t)^2 + (cos t + t sin t)^2 + (-sin t + t cos t)^2) = √(4t^2 + cos^2 t + 2t cos t sin t + sin^2 t + sin^2 t - 2t cos t sin t + t^2 cos^2 t) = √(4t^2 + 2).

Obtain the unit tangent vector: T(t) = r'(t) / ||r'(t)|| = (2t / √(4t^2 + 2), (cos t + t sin t) / √(4t^2 + 2), (-sin t + t cos t) / √(4t^2 + 2)).

Calculate the derivative of T(t): T'(t) = ((2 - 4t^2) / (4t^2 + 2)^(3/2), (-sin t + t cos t + t cos t + t^2 sin t) / √(4t^2 + 2), (-cos t + t sin t - t sin t + t^2 cos t) / √(4t^2 + 2)).

Calculate the magnitude of T'(t): ||T'(t)|| = √(((2 - 4t^2) / (4t^2 + 2)^3

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