What are two motion that are illustrated as a horizontal line on a speed time graph?

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

area of rectangle= l*b

2and 2/3  * 7 and 3/4

8/3 * 31/4

62/3 sq . feet

20 and 2/3 feet

Answer:

10km/h

Step-by-step explanation:

speed = distance/time

s = 150/5

s = 30km/h

the total must be 30km/hr

less the 20km/hr that Jerry is going

is the speed Susan must go in the opposite direction

30 - 20 = 10

10km/h

Answer:

3562.6 m³

Step-by-step explanation:

In this question, we have to find the volume of a cylinder.

The formula to find the volume of a cylinder is V = πr²h

Plug in your values and solve.

Solve:

V = π(9)²(14)

V = π(81)(14)

V = π(1,134)

V = 3562.566069

Round to the nearest tenths place.

V = 3562.6

Don't forget that the units for volume is already cubed, or to the power of 3.

Your final answer would be 3562.6 m³

Answer:

Its the 3 one

Step-by-step explanation:

Answer:

x ≥ -2

Step-by-step explanation:

Answer:

Usha is correct

Step-by-step explanation:

See attachment

Given

Dimension of the development

\(Height = \frac{1}{2}\ mile\)

\(Base = \frac{1}{2}\ mile\)

Dimension of a football field

\(Length = 100m\)

\(Width = 50m\)

First, we calculate the area of the development.

Because it is triangular in shape, the area is:

\(Area = \frac{1}{2} * Height * Base\)

\(Area = \frac{1}{2} * \frac{1}{2}mile * \frac{1}{2}mile\)

Convert mile to meter

\(Area = \frac{1}{2} * \frac{1}{2}* 1600m * \frac{1}{2} * 1600m\)

\(Area = \frac{1}{2} * 800m * 800m\)

\(Area = 400m * 800m\)

\(Area = 320000m^2\)

The area of 50 football pitch is then calculated as:

\(Area = 50 * Length * Width\)

\(Area = 50 * 100m * 50m\)

\(Area = 250000m^2\)

By comparison:

\(320000 > 250000\)

Hence, Usha's thought is correct

Answer:

1) x+y=-2

x=-2-y

2) x-y=-8

substitude value of x

(-2-y)-y=-8

-2-2y=-8

-2y=-6

y=3

Substitute value of y in 1

x=-2-3

x=-5

Brainliest please~

Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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The scientific notation of 5 x 10−7 is 5 x 10 to the power of negative 7.

Notation is a set of symbols and instructions used to represent numbers, equations, and other mathematical expressions. Notation is used to explain rules and procedures, as well as make complex mathematical concepts easier to read and understand. Notations can range from simple abbreviations to complex mathematical symbols. In mathematics, notation can help to simplify complex problems and provide a way for mathematicians to communicate their ideas.


This means that it is 5 times as small as 1. The scientific notation of 8.5 x 10^−4 is 8.5 x 10 to the power of negative 4. This means that it is 8.5 times as small as 1. Therefore, 5 x 10−7 is 8.5 times smaller than 8.5 x 10^−4. By dividing the two numbers, we get 8.5/5 = 1.7. This means that 5 x 10−7 is 1.7 times smaller than 8.5 x 10^−4.

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The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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The expected value for the number of siblings of a randomly chosen student is 1.11.

"In a probability distribution, the weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value".

For the given situation,

The table shows the probability distribution of siblings of students in a high school with 1500 students.

For number of siblings = 0, Probability = 0.18.

For number of siblings = 1, Probability = 0.65.

For number of siblings = 2, Probability = 0.09.

For number of siblings = 3, Probability = 0.05.

For number of siblings = 4, Probability = 0.02.

For number of siblings = 5, Probability = 0.01.

The formula for expected value mean, E(x) = ΣxP(x)

\(E(x)=(0)(0.18)+(1)(0.65)+(2)(0.09)+(3)(0.05)+(4)(0.02)+(5)(0.01)\)

⇒ \(E(x)=1.11\)

Hence we can conclude that the expected value for the number of siblings of a randomly chosen student is 1.11.

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The linear function passing through points (1,7) and (2.5, 1) is given by:

y = -4x + 11.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

y = mx + b

In which the coefficients are described as follows:

For this problem, the two points that form the function are given as follows:

(1,7) and (2.5, 1).

The slope is given by change in y divided by change in x, hence it is given by:

m = (1 - 7)/(2.5 - 1) = -4.

Then:

y = -4x + b.

When x = 1, y = 7, hence we can find the intercept b of the function as follows:

7 = -4(1) + b

b = 7 + 4

b = 11.

Hence the equation is:

y = -4x + 11.

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Step-by-step explanation:

a= c-b pls let me know if it is correct or not

Answer:

C

Step-by-step explanation:

We are given the two functions:

\(\displaystyle f(x) \text{ and } g(x)=\sin^{-1}(f(x))\)

And we want to find the ratio that represents:

\(\displaystyle \frac{f^\prime(x)}{g^\prime(x)}\)

To do so, we will compute the derivatives of both functions.

For f,  we can simply write that:

\(f^\prime(x)=f^\prime(x)\)

For g, we will use the chain rule:

\(\displaystyle (u(v(x))^\prime=u^\prime(v(x))\cdot v'(x)\)

We can let:

\(u(x)=\sin^{-1}(x)\text{ and } v(x)=f(x)\)

We can double check this by doing the composition:

\(g(x)=u(v(x))=\sin^{-1}(f(x))\)

Therefore, by the chain rule, we acquire that:

\(\displaystyle g^\prime(x)=\frac{1}{\sqrt{1-(v(x))^2}}\cdot v'(x)\)

By substitution:

\(\displaystyle g^\prime(x)=\frac{f^\prime(x)}{\sqrt{1-(f(x))^2}}\)

Hence, our ratio is:

\(\displaystyle \frac{f^\prime(x)}{g^\prime(x)}=\frac{f^\prime(x)}{\dfrac{f^\prime(x)}{\sqrt{1-(f(x))^2}}}\)

Simplify:

\(\displaystyle \frac{f^\prime(x)}{g^\prime(x)}=\sqrt{1-(f(x))^2}\)

Hence, our answer is C

Answer:

This isn't the answer as you can see it above, but do you have the rest of the questions?

Step-by-step explanation:

Thank you in advance.

Answer:

It's too short. Write at least 20 characters to explain it well.

Answer: well solve what's in the parentheses first

Step-by-step explanation: that is the first step

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

6 days

Step-by-step explanation:

Ratio 4:12

Ratio 6:x

4*? = 6

6/4 =1.5

12*1.5 = 18

18-12 = 6

6:6

6 days

Answer:

i think 8 or 6

Step-by-step explanation:4 times 12 is 48 and 48 divided by 6 is 8

Step-by-step explanation (2):

Ratio 4:12

Ratio 6:x

4*? = 6

6/4 =1.5

12*1.5 = 18

18-12 = 6

6:6

6 days

I am probably wrong tho

Answer:

A=0.51

B=0.73

C=0.41

D=A student taking algebra II is dependent on whether they prefer it and a student being in 10th grade is dependent on their age

Step-by-step explanation:

These answers are all in fractions btw

A)5/255+20/245+65/225+90/725=0.514267 which rounds to 0.51

B)100+65=165

165/225=0.73

C)100/245=0.41

Hope it helps !

Answer:

x < 1939

Step-by-step explanation:

If we want years before 1939, then x must be less than 1939. From this we can make the inequality: x < 1939. It shows that x must be anything less than 1939.

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

Work Shown:

A = old value = 12 pounds

B = new value = 15 pounds

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (15-12)/12 ] * 100%

C = (3/12)*100%

C = 0.25*100%

C = 25%

The positive C value indicates a percent increase

So effectively, we find the difference or change in weight (B-A) and divide it over the original weight (A). That leads to 0.25 which converts to 25%

Note that,

25% of 12 = 0.25*12 = 3

This says that the puppy gained 3 pounds, which is the value of B-A

Since the puppy gained 3 pounds, the new weight is 12+3 = 15 pounds

-----------

As an alternative, we could divide the two values B over A to find that

B/A = 15/12 = 1.25

Then subtract 1 from this result: 1.25 - 1 = 0.25 = 25%

The girl which is correct between kate and her friend Margo is Margo.

The correct answer option is option B

If each friend gets the same number of pens;

Number of pens each friend get = Number of pens Kate has / Number of Kate's friends

= 63 / 9

= 7

Check:

Number of pens each friend get × Number of Kate's friends = Number of pens Kate has

7 × 9 = 63

Therefore, Kate's friend, Margo is correct.

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Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Let A be the first sequence, and denote by \(a_n\) the n-th term in A.

Consider the forward differences of A :

16 - 7 = 9

30 - 16 = 14

49 - 30 = 19

73 - 49 = 24

Call this sequence of first differences B, so that for n ≥ 1,

\(b_n=a_{n+1}-a_n\)

where \(b_n\) is the n-th term of B.

Now consider the forward differences of B, which is another sequence we'll call C :

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

Then if \(c_n\) is the n-th term of C, we have for all n ≥ 1,

\(c_n=b_{n+1}-b_n=5\)

which gives

\(b_{n+1} = b_n+5\)

This tells us B is an arithmetic sequence - the first term is 9 and the difference between consecutive terms is 5, so we have for n ≥ 1,

\(b_n = 9 + 5(n-1) = 5n + 4\)

Plug this into the recurrence for A :

\(a_{n+1} = a_n + b_n = a_n + 5n + 4\)

We don't need to solve for \(a_n\), fortunately; we just want the next term, which would be

\(a_6 = a_5 + 5^2 + 4 = 73 + 25 + 4 = \boxed{102}\)

Answer: 30.36

Step-by-step explanation:

92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.