Consider a circle of radius 2 centered at the origin. Find parametfizations of this curve under the following assumptions. Clearly state any restriction on the variable of parametrization. (a) A single, complete traversal of the circle in a counter-clockwise direction.x=2cos(t)y=2sin(t)
(b) A single, complete traversal of the circle in a clockwise direction.=2sin(t)y=2cos(t)
(c) A clockwise traversal of the front half of the circle (i.e.x>0)

If f(x) is integral from 0 to x of (1/√(t³+2))dt, then the FALSE, statement is (e) f(-1) is greater than or equal to 0.

Option (a) is True, because the integral from 0 to 0 is zero, So, f(0) = 0.

Option (b) is True. The integrand is continuous for all x greater than or equal to 0, So, f(x) is differentiable and continuous for all x greater than or equal to 0.

Option (c) is True. The integrand is positive for all x, so the integral is positive for all x, including x = 1.

Option (d) is True. By using the Fundamental Theorem of Calculus and the Chain-Rule,

We have f'(x) = 1/√(x³+2).

So, f'(1) = 1/√3.

Option (e) is False, We see that integrand is undefined for negative values of t,

So, the integral from 0 to "x" is possible for non-negative values of x.

Therefore, f(x) is defined only for x greater than or equal to 0. In particular, f(-1) is undefined,

Therefore, option (e) is false.

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The given question is incomplete, the complete question is

If f(x) = the integral from 0 to x of (1/√(t³+2))dt, which of the following is FALSE?

(a) f(0) = 0,

(b) f is continuous at x for all x greater than or equal to 0,

(c) f(1) is greater than 0,

(d) f '(1) = 1/√3,

(e) f(-1) is greater than or equal to 0.

Step-by-step explanation:

Statement                                                        Reason                              

∠5 and ∠7 are vertical angles                        Vertical angles theorem

m∠5 = m∠7                                                      Definition of vertical angles

m∠5 = -2(3x - 4), m∠7 = 3(x - 3) - 1                  Given

-2(3x - 4) = 3(x - 3) - 1                                       Substitution property of equality

-6x + 8 = 3x - 9 - 1                                            Distributive property

3x + 6x = 8 + 10                                               Addition property

9x = 18                                                              Addition property

x = 18/9                                                             Division property

x = 2                                                                  Proved

Step-by-step explanation:

hope this helpsssssssss

Answer:

SSS (Or Side-Side-Side) is a theorem uses to proove congruency in triangles. In the following picture, we can tell that line AB = CD. We can also tell that line BC = AD. And because both triangles share the line BD, we can use the reflexive property and define line BD = BD. That is how we know that ΔABD + ΔCDB

(PLEASE MARK ME AS BRAINLIEST!)

Answer:x=1,-9

Step-by-step explanation:

Answer:

1/ $ 4.08

2/ $675.92

Step-by-step explanation:

Take 68 times 0.06% = $4.08

680 - 4.08= 675.92

Answer:

Step-by-step explanation:

40.80 it told me the answer

Answer:

It's B. (2x+5) (x+4)

Answer:

b

Step-by-step explanation:

2x²+13x+20

You can just try all the answers if you'd like and see which one equals 2x²+13x+20.

Using FOIL for all of them:

a. (2x-5)(x-4) = 2x²-8x-5x+20 = 2x²-13x+20

b. (2x+5)(x+4) = 2x²+8x+5x+20 = 2x²+13x+20

c. (2x+2)(x+10) = 2x²+20x+2x+20 = 2x²+22x+20

d. is obviously not correct since we already have an answer.

Our answer is b. (2x+5)(x+4)

Answer: it's a linear equation

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

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Answer: 3:5

Step-by-step explanation: heres the answer

A random number x from fx(x) using a uniform distribution on [0, 1], we calculate x = sqrt(U), where U is a random number generated from a uniform distribution on [0, 1].

To generate random numbers from the given density function fx(x), which has the piecewise defined density function, we can use the inverse transform method.

The steps to generate random numbers from fx(x) using a uniform distribution on [0, 1] are as follows:

Generate a random number U from a uniform distribution on [0, 1].

Solve the equation U = Fx(x) for x, where Fx(x) is the cumulative distribution function (CDF) of fx(x).

Evaluate the inverse CDF, Fx^(-1)(x), to obtain the value of x.

Let's apply these steps to generate a random number from fx(x):

Generate a random number U from a uniform distribution on [0, 1].

Solve the equation U = Fx(x) for x:

U = ∫[0, x] fx(t) dt

U = ∫[0, x] 2t dt

U = [t^2] evaluated from 0 to x

U = x^2

Evaluate the inverse CDF, Fx^(-1)(x), to obtain the value of x:

Fx^(-1)(x) = sqrt(x)

Therefore, to generate a random number x from fx(x) using a uniform distribution on [0, 1], we calculate x = sqrt(U), where U is a random number generated from a uniform distribution on [0, 1].

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The growth factor b can be determined from the growth rate; r by the formula; b = ( 1 + r/100).

Often time, when the growth rate, r in an exponential growth situation. The growth rate is expressed as a percentage, r%.

Hence, to determine the growth factor given the growth rate, r; we must use the formula;

b = ( 1 + r/100).

Ultimately, the correct formula is; b = ( 1 + r/100).

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Answer:

It's 6 to the left and 8 down

All possible outcomes are shown as distinct paths from the beginning of the diagram to the end of each last branch option D, Counting the number of final branches gives the total number of outcomes option B.

A probability space can be represented by a tree diagram in probability theory. A succession of independent occurrences or conditional probabilities may be represented using a tree diagram. The diagram's nodes each represent an occurrence and their respective probabilities.

With the help of a tree diagram, you may see every possible combination in visual form and make predictions about the outcomes.

About the sequence of events:

a) A tree diagram may be used to list all potential outcomes; each one is represented by a separate route that extends from the diagram's start to its last branch.

b) You may use a tree diagram to calculate the overall number of outcomes of a sequence of events by counting the number of final branches.

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Answer:

By the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Step-by-step explanation:

Since a woman deposits 100 EUR in her daughter's bank account on her first birthday, and on every subsequent birthday, she deposits 10 EUR more than she deposited the previous year, so on her second birthday, she deposits 110 EUR, and on her third birthday she deposits 120 EUR, to determine, by the time her daughter is 21 years old, how much money has been deposited in her account, the following calculation must be performed:

100 + (20 x 10) = X

100 + 200 = X

300 = X

Therefore, by the time her daughter is 21 years old 300 EUR will have been deposited into the account.

Answer:

2/15

Step-by-step explanation:

Step one:

given data

sample space

1 elephant,

4 bears,

3 cats, and

2 dogs.

sample size= 1+4+3+2= 10

Required:

By selecting without replacement, the probability that she chooses a bear both times

Step two:

the first event= Pr(bear)= 4/10= 2/5

the second event, the sample size is now 9 and the number of bears is now 3

Pr(bear)= 3/9= 1/3

Hence, the probability that she chooses a bear both times

= 2/5*1/3

=2/15

Determine how the ABC contingency can be altered to promote more positive behavior. (Option (a) is correct one )

The method that intervention development will be influenced by the ABC data that are gathered on the function of the target behavior is through the determination of how the ABC contingency can be changed to encourage more positive behavior.

By identifying the functional reinforcers that sustain problem behavior, practitioners can create therapies that are more effective (i.e., from a smaller pool of potential interventions to choose from) and efficient.

Linking therapies to the outcomes of functional assessments has become accepted clinical practice and is now covered by both federal and state laws. This represents a significant and advantageous change in the method of behavioral intervention.

Therefore,

Determine how the ABC contingency can be altered to promote more positive behavior. (Option (a) is correct one )

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Answer:

a) X + X + 1 = 11

Step-by-step explanation:

Em matemática, a soma de consecutivos é expressa matematicamente como:

X + (X + 1) + (X + 2) + (X + 3) .............

Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11

Portanto, esta expressão algébrica é dada como:

X + (X + 1) = 11

X + X + 1 = 11

Portanto, a opção a) X + X + 1 = 11 é a opção correta

The volume of water in the container is approximately 383.098 liters.

we first need to convert the dimensions of the container from feet to inches, so we have:

Length: 4.500 ft * 12 in/ft = 54.000 in

Width: 7.20 ft * 12 in/ft = 86.4 in

Depth: 5.00 in

The volume of water can be calculated by multiplying the length, width, and depth of the container, which gives:

Volume = 54.000 in * 86.4 in * 5.00 in = 23,364 cubic inches

To convert cubic inches to liters, we need to multiply by the conversion factor, which is 0.0163871 liters/cubic inch. This gives us:

Volume in liters = 23,364 cubic inches * 0.0163871 liters/cubic inch = 383.098 liters

Therefore, the volume of water in the container is approximately 383.098 liters.

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The condition should be satisfied are as np>=5 and n(1-p)>=5.

When both requirements are satisfied, we can utilise the normal distribution to provide probabilistic responses to binomial distribution-related problems.

For instance, let's say we want to know the likelihood that during 100 flips, a coin will land on heads less than or equal to 45 times. In other words, we seek P (X <= 45). Instead, we would discover P (X <= 45.5) in order to approximate the binomial distribution using the normal distribution.

So, the main condition is np>=5 and n(1-p)>=5.

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Answer:

b

Step-by-step explanation:

The SSS Similarity Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are similar. This theorem is also known as the Side-Side-Side Similarity Theorem or the SSS Similarity Postulate.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SSS or Side-Side-Side Similarity.
If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
From this result, we can conclude that-
∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
Hence, we have described the SSS similarity theorem.

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Answer:

C. 36

Step-by-step explanation:

3x12=36 :]

Answer:

3. x=4   4. x= 2

Step-by-step explanation:

just trust me

Answer:

\(\frac{x-3}{x+2}\)

Step-by-step explanation:

\(\frac{3x^2+6x-45}{3x^2+21x+30}\)                   Rewrite

\(\frac{x^2+2x-15}{x^2+7x+10}\)                      Factor out GCF (3)

\(\frac{x^2+5x-3x-15}{x^2+5x+2x+10}\)                 Replace b with factors

\(\frac{(x-3)(x+5)}{(x+5)(x+2)}\)                     Factor by grouping

\(\frac{x-3}{x+2}\)                               Final answer

For a more detailed explanation, please look at the help image attached. It shows each step on how to factor polynomials.

I hope this helps!

Answer:

y = -2x + 4

Step-by-step explanation:

y = -2x + b

-8 = -2(6) + b

-8 = -12 + b

4 = b

Answer: \(Y=-3\)

Step-by-step explanation:

\(Y=5x-3\)

\(Y=5 * (x) -3\)

Then replace x by 0

\(Y=5 * (0) -3\) or \(Y= 5(0) -3\)

\(Y=0 -3\)

\(Y=-3\)

The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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