Let f (x) = (2 . x^4 – 2)^8 . (-3.x^3 +8)^14. Find f'(x) =

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = \(\int_a^b \delta\left|r^{\prime}(t)\right| d t\)

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

\(\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}\)

Further simplifying;

\(\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}\)

Now, use integration to find the mass of the wire;

       \(\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}\)

Therefore, the mass of the wire is estimated as 40π√2 units.

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

The solution to the equation 513x + 241 = 113 (mod 11) is x = 4.

To solve this equation, we need to isolate the variable x. Let's break it down step by step.

Simplify the equation.

513x + 241 = 113 (mod 11)

Subtract 241 from both sides.

513x = 113 - 241 (mod 11)

513x = -128 (mod 11)

Reduce -128 (mod 11).

-128 ≡ 3 (mod 11)

So we have:

513x ≡ 3 (mod 11)

Now, we can find the value of x by multiplying both sides of the congruence by the modular inverse of 513 (mod 11).

Find the modular inverse of 513 (mod 11).

The modular inverse of 513 (mod 11) is 10 because 513 * 10 ≡ 1 (mod 11).

Multiply both sides of the congruence by 10.

513x * 10 ≡ 3 * 10 (mod 11)

5130x ≡ 30 (mod 11)

Reduce 5130 (mod 11).

5130 ≡ 3 (mod 11)

Reduce 30 (mod 11).

30 ≡ 8 (mod 11)

So we have:

3x ≡ 8 (mod 11)

Find the modular inverse of 3 (mod 11).

The modular inverse of 3 (mod 11) is 4 because 3 * 4 ≡ 1 (mod 11).

Multiply both sides of the congruence by 4.

3x * 4 ≡ 8 * 4 (mod 11)

12x ≡ 32 (mod 11)

Reduce 12 (mod 11).

12 ≡ 1 (mod 11)

Reduce 32 (mod 11).

32 ≡ 10 (mod 11)

So we have:

x ≡ 10 (mod 11)

Therefore, the solution to the equation 513x + 241 = 113 (mod 11) is x = 10.

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Answer:

54ft of fence for the PUPPY

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

my answer is A

Step-by-step explanation:

it is A-105

Part A. Lines are parrelel means that they never touch.They go in the same direction.

Answer:

students 150

adult 550

Step-by-step explanation:

x + y = 700

5x + 2y = 3050

x = 700 - y

5(700 - y) + 2y = 3050

3500 - 5y + 2y = 3050

-3y + 3500 = 3050

-3y = 3050 - 3500

-3y = -450

y = -450 / -3

y = 150

x = 700 - y

x = 700 - 150

x = 550

Answer:

X=60

Step-by-step explanation:

X fraction 2 - 5 = 25

X/2-5=25

X/2 =25+5

X/2=30

X=60

60 is the answer

There are 5 elements in 32 proper subsets.

What are subsets?

If every element of set A is also an element of set B, then set B is a superset of set A, and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Here, we have

Given:  32 proper subsets.

We have to find how many elements are in 32 proper subsets.

Subsets of a set having n elements = 2^n

2ⁿ = 32

n = 5

Hence, there are 5 elements in 32 proper subsets.

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Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.

To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29

This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05

This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.

By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.

One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:

304x + 247y = 176.51
-304x - 96y = -144.8

Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41

So the cost of one orange is $0.41 and the cost of one lemon is $0.21.

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Answer:

11. 3

12. 78.74

13. 30

14. 69.74

15. 48

16. 7

17. 36.9

18. 69.5125888

Step-by-step explanation:

Used a calculator.

The concept is Data Analysis,  which is the process of totally applying statistical tools to dissect data. The answer is options B, C, and D.

To help you consider data limitations, critically dissect correlations, examine the environment, and understand tool strengths and sins. Data analysis applies statistical and/ or logical ways to describe, illustrate, epitomize, and estimate data.

Data analysis helps individualities and associations make sense of data. Data analysts typically analyze raw data for insights and trends.

Limitations include:

Question

You're preparing a question-and-answer session that will follow your donation. Which styles help you to consider data limitations? elect everything that suits you.

A) exclude the outliers

B) Understand the strengths and sins of the tools

C) Critically dissect the correlations

D) Look at the environment

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We can represent both numbers as fractions with a common denominator of 1. Subtracting the numerators gives us 2, and the denominator remains 1. Therefore, the result is 2/1.

To evaluate 5 - 3 as a fraction, we can represent the numbers as fractions with a common denominator.

The fraction equivalent of 5 is 5/1, and the fraction equivalent of 3 is 3/1.

To subtract fractions, we need a common denominator. In this case, both fractions already have a denominator of 1, so we can subtract them directly.

5/1 - 3/1 = (5 - 3)/1 = 2/1

Therefore, the result of 5 - 3, expressed as a fraction, is 2/1.

When we evaluate 5 - 3, we are subtracting the number 3 from the number 5. In order to express this as a fraction, we can represent both numbers as fractions with a common denominator. Since both 5 and 3 have a denominator of 1, we can subtract them directly.

Subtracting the numerators (5 - 3) gives us 2, and the denominator remains 1. Therefore, the result of 5 - 3, expressed as a fraction, is 2/1.

The fraction 2/1 can also be simplified further, as it represents a whole number. Dividing both the numerator and denominator by the greatest common divisor, which is 1, we get 2/1 in its simplest form.

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The difference between the prices of both books is: $4,266.67.

Let's call the price of the cheapest book "x". According to the statement, the other book costs twice the price of the cheapest one, that is, "2x". Furthermore, we are told that this second book is worth $200 more than the other.

Therefore, we can establish the following equation:

x + 2x + $200 = $13,000

Add like terms:

3x + $200 = $13,000

We subtract $200 from both sides of the equation:

3x = $12,800

We divide both sides by 3 to solve for "x":

x = $4,266.67

The price of the most expensive book is 2 times the price of the cheapest, that is, 2 * $4,266.67 = $8,533.33.

The difference between the prices of both books is:

$8,533.33 - $4,266.67 = $4,266.67.

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Answer: 444

Step-by-step explanation:

2x2 - 11x - 40= 444

a) The missing frequency is 20

b) The modal number of people in a car is 1

c) The median is 3

d) The mean is 0.95

The sum of the frequencies must be 60.

The missing frequency by subtracting the sum of the other frequencies from 60

60 - (28 + 3 + 7 + 1 + 1) = 20

To find the median, we need to arrange the data in order from smallest to largest:

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6

There are 60 numbers in total, so the median is the average of the 30th and 31st numbers:

median = (3 + 3)/2 = 3

The mode is the value with the highest frequency, which is 1.

mean = (1 x 28 + 2 x 20 + 3 x 3 + 4 x 7 + 5 x 1 + 6 x 1) / 60

= (28 + 40 + 9 + 28 + 5 + 6) / 60

= 0.95

Therefore, the missing frequency, mode, median and mean has been found

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The given question is incomplete, the complete question is

Hassan recorded the number of people in 60 passing cars

people 1 2 3 4 5 6

frequency 28 ? 3 7 1 1

a)find the missing frequency

b)median

c)modal

d)mean

Answer:

86.6 feet

Step-by-step explanation:

this could be represent as a triangle (as shown in the image)

The red rectangle is the building

the green person is Amari

So we use the (soh cah toa) to solve this

and specifically the (toa) which mean tan=opposite/adjacent

the opposite is the side that been directly in the opposite of the angle and in this case is equal to the tall of the building

the adjacent is the side that near the angle (and not the hypotenuse) and in this case is equal 50 feet

tan60 = opposite/50

tan60 = opposite/50

√3 = opposite/50

opposite = 50√3

opposite = 86.6 feet

the tall of the building = 86.6 feet

The height of the building is 50√3 feet.

Given to us,

Distance between the building and Amar = 50 feet,

Angle between the top of the building and Amar = 60°

We know that the value of tan 60° is √3.

Thus,

\(tan\theta=\dfrac{Perpendicular}{Base} \\\\\rm tan\ 60^o =\dfrac{Height\ of\ the\ building}{Distance\ between\ building\ and\ Amar}\)

\(\sqrt{3} =\dfrac{Height\ of\ the\ building}{50\ feet} \\\)

\({Height\ of\ the\ building}= {50\ feet}\times\sqrt{3}\)

Therefore, the height of the building is 50√3 feet.

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Answer:

Intro: Yourself

Conflict: Hunger

Rising action: Find bread

Second Conflict: It's moldy

Climax: Go to the store

Falling action get bread

Step-by-step explanation:

Not enough points for me to write a whole story, so heres just a simple plotline.

Answer:

Given expression:

Parts of it are:

First rewrite the expression

\(\\ \rm\longmapsto 242c+125\)

By side side side congruence theorem if any two triangles have three pairs of congruent sides, then the triangles are congruent.

We know that side side side (S-S-S) congruence theorem is a theorem for triangle congruence.

It states that if any two triangles have three pairs of congruent sides, then the triangles are congruent.

We need to prove:  the SSS congruence theorem

Consider ΔABC and ΔPQR

here, AB = PQ, BC = QR and AC = PR

Construct a congruent copy of triangle ABC that shares a side with PQR.  

∠SQR ≅ ∠ABC and AB = QS

In ΔABC and ΔSQR,

AB = QS                     ..............(by construction)

∠SQR ≅ ∠ABC                 ..............(by construction)

BC = QR                 ..............(given)

ΔSQR ≅ ΔABC         ...............(SAS congruence theorem)

So, by corresponding angles of congruent theorem,

∠A ≅ ∠S and ∠ACB ≅ SRQ      

But the quadrilateral PQRS is a kite, since we have QP = QS and RP = RS

We know that the diagonal divides the kite into two congruent triangles. Here,  the diagonal QR  divides the kite into ΔSQR and ΔPQR.

But ΔSQR ≅ ΔABC

so we have ΔPQR ≅ ΔABC

Hence the side side side congruence theorem proved.

Therefore, if any two triangles have three pairs of congruent sides, then the triangles are congruent.

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The improper integral ∫[0,+∞] (sin(x) + cos²(x))/(sin²(0) + cos²(0) + |x| + 1) dx is divergent.

To determine the convergence or divergence of the given improper integral, we need to analyze the behavior of the integrand as x approaches infinity. First, let's simplify the expression within the integral:

(sin(x) + cos²(x))/(sin²(0) + cos²(0) + |x| + 1) = (sin(x) + cos²(x))/(1 + |x|) As x approaches infinity, the absolute value function |x| increases without bound. This means that the denominator (1 + |x|) also increases without bound.

Now, let's consider the numerator. The sine and cosine functions oscillate between -1 and 1 as x increases. This means that the numerator does not have a definite limit as x approaches infinity. Since the numerator does not approach a finite limit and the denominator increases without bound, the integrand does not tend to zero as x approaches infinity. Consequently, the given improper integral is divergent. Therefore, the improper integral ∫[0,+∞] (sin(x) + cos²(x))/(sin²(0) + cos²(0) + |x| + 1) dx is divergent.

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The probability of selecting a 2 on the first pick and a 5 on the second pick is 1/90.

It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

If the first ball was not replaced after it was selected, then the probability of selecting a 2 on the first pick is 1/10, since there is only one ball labeled 2 out of 10 balls in the bag. Since the first ball was not replaced, there are now only 9 balls remaining in the bag for the second pick. The probability of selecting a 5 on the second pick is 1/9, since there is only one ball labeled 5 remaining in the bag out of the 9 remaining balls.

To find the probability of both events happening, we need to multiply their probabilities:

P(2 on first pick and 5 on second pick) = P(2 on first pick) * P(5 on second pick | 2 on first pick)

P(2 on first pick and 5 on second pick) = (1/10) * (1/9)

P(2 on first pick and 5 on second pick) = 1/90

Therefore, the probability of selecting a 2 on the first pick and a 5 on the second pick is 1/90.

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The scalar projection is 42/13, and the vector projection is 42/169⟨-5,12⟩.

The scalar projection of b onto a can be calculated using the formula \(\frac{a.b}{|a|}\), and the vector projection of b onto a can be calculated using the formula \(\frac{a.b}{|a|^{2} } .a\). The formula for finding the magnitude of a is |a| = √c²+d² if a = ⟨c,d⟩.

a = ⟨−5, 12⟩, b = ⟨4, 6⟩

a⋅b = ⟨−5, 12⟩⟨4, 6⟩

= -20 + 72

= 42

|a| = √[(-5)² + (12)²]

= √25 + 144

= √169

= 13

The scalar projection is

\(\frac{a.b}{|a|}\) = [⟨−5, 12⟩⟨4, 6⟩]/√[(-5)² + (12)²]

= [-20 + 72]/√25 + 144

= 42/√169

= 42/13

The vector projection is

\(\frac{a.b}{|a|^{2} } .a\) = [42/(13)²] ⟨−5, 12⟩

= 42/169⟨−5, 12⟩

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the original number Juan started with was 6.

Let "x" represent the original number. Juan first adds 2 to the original number, which can be expressed as (x + 2). He then multiplies this by 2, resulting in 2(x + 2). Next, he subtracts 2 from this product: 2(x + 2) - 2. Finally, he divides the resulting number by 2, giving us the equation [(2(x + 2) - 2) / 2] = 7.
Now, let's solve for the original number, x:
1. Simplify the equation by distributing the 2: [2x + 4 - 2] / 2 = 7
2. Combine the constants: (2x + 2) / 2 = 7
3. Multiply both sides by 2 to remove the denominator: 2x + 2 = 14
4. Subtract 2 from both sides: 2x = 12
5. Divide both sides by 2: x = 6

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The given statement " MP=0 and M is idempotent" is proved.

To verify that MP = 0, we need to substitute the given expressions for M and P and simplify the expression:

MP = (Ix - P)P

= IxP - PP

= X(X x)(X x) - X(X x)(X x)(X x)

= X(X x)[(X x) - (X x)(X x)]

= X(X x)[Ix - (X x)]

= X(X x)Ix - X(X x)(X x)

= X(X x) - X(X x)

= 0

Therefore, MP = 0.

To show that M is idempotent, we need to prove that M^2 = M. First, we compute M^2:

M^2 = (Ix - P)(Ix - P)

= IxIx - IxP - PIx + PP

= Ix - Ix(X x)(X x) - X(X x)Ix + X(X x)P

= Ix - X(X x)(X x) - X(X x)X(X x) + X(X x)(X x)(X x)

= Ix - X(X x)(X x) - X(X x)(X x) + X(X x)(X x)(X x)

= Ix - X(X x)(X x)

= M

Therefore, M is idempotent since M^2 = M.

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