Cheyenne is playing a board game. Her score was −175 at the start of her turn, and at the end of her turn her score was −325. What was the change in Cheyenne’s score from the start of her turn to the end of her turn? How did you determine your answer?

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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TU is parallel to MN.

Given that the slope of a line MN is -3, we need to find a line which is parallel to the MN.
So we know that the parallel lines are having equal slope so the line which is parallel to the MN it must have slope of -3.

Therefore,

Considering the line TU, find the slope = y₂-y₁ / x₂-x₁

= 10-1 / 5-8 = -9/3 = -3

Since, the slope of the line TU is -3 therefore we can say the lines TU and MN are parallel liens.

Hence TU is parallel to MN.

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Answer:

The correct option is (c).

Step-by-step explanation:

The combined formula is given by :

\(h=\dfrac{V}{\pi r^2}\) ...(1)

h is height

V is volume

r is radius

It is clear from formula (1) that h varies directly with V and inverse;y with the square of r.

Hence, the correct option is (c).

Answer:

h varies directly with V and inversely with the square of r.

Step-by-step explanation:

(Since pie is a constant, it's not said in the "sentence")

I also just got it right on the quiz.

Answer:

2 dollars?

Step-by-step explanation:

8 divided by 4

Answer:

Well -7>-7.5

Step-by-step explanation:

Negative numbers are that the Humber that is closest to 0 is the greatest. Like in -7 and -7.5, the -7 is closer to 0 so its greater.

Answer:

the answer to your question is -7.5<-7

After considering all the given data we conclude that the total distance traveled by the car is 285m, under the condition that the given car starts from rest and moves with an acceleration of 1m/s2 for 15.

The distance traveled during this time can be evaluated using the formula

\(s = ut + (1/2)at^2\)

Here,

s = distance traveled,

u =  initial velocity (0),

a = acceleration (1m/s2)

t = time (15s).

Placing in these values we get

s = 0 + (1/2) × 1 × 15²

= 112.5m .

After this, the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. The distance traveled during this time can be evaluated applying  the formula

\(s = ut + (1/2)at^2\)

Here,

s = distance traveled,

u = initial velocity (the final velocity of the previous step),

a = acceleration (-0.05m/s2)

t = time (10s).

Placing in these values we get

s = 112.5 + (1/2) × (-0.05) × 10²

= 87.5m.

Finally, brakes are applied and it stops after 5s. The distance traveled during this time can be evaluated using the formula \(s = ut + (1/2)at^2\)

Here,

s = distance traveled,

u = initial velocity (the final velocity of the previous step),

a = acceleration (-0.05m/s2)

t = time (5s).

Placing in these values we get s = 87.5 + (-0.05)× 5² = 85m.

Therefore, total distance traveled by car can be calculated by adding all three distances together which gives us

112.5m + 87.5 + 85

= 285m.

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The complete question is

A car starts from rest and moves with an acceleration of 1m/s2 for 15. Then the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. then the brakes are applied and it stops 5s after calculating the total distance traveled?

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer:

t = 32,5 minutes

Step-by-step explanation:

Volume to fill =  13000000 Gal

5 pumps delivering  80000 gal/min

5 * 80000 = 400000 gal/min

If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then

t =  13000000/ 400000

t = 32,5 minutes

The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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Answer:

A

Step-by-step explanation:

5 feet 9 in inches=69

86-69=17

Answer:

A right triangle is always an isosceles triangle.An equilateral triangle is never an obtuse triangle.

Answer:

A right triangle is always an isosceles triangle.

Step-by-step explanation:

The value of the distance across the sea is 302 feet

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

Two triangles are said to be similar if the ratio of their corresponding sides are in the same proportion.

Triangle PRE and triangle POC are similar triangles based on the angle - angle similarity. Hence:

PR / PO = RE/OC

substituting:

x/ (x + 135) = 185 / 335

335x = 185x + 45225

150x = 45225

x = 302 feet

The value of PR is 302 feet

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The triangle has a perimeter of 48 units.

Triangles are figures with three sides, the perimeter is the sum of the lengths of the three sides. The length of each side is determined by Pythagorean theorem:

l = √(x² + y²)

Where:

First, determine the horizontal and vertical length of each side:

Side 1

x = 18, y = 0

Sides 2, 3

x = 9, y = 12

Second, determine the side lengths:

Side 1:

l = 18

Sides 2, 3

l = √(9² + 12²)

l = 15

Third, calculate the perimeter of the triangle:

p = 18 + 15 + 15

p = 48

The perimeter of the triangle is equal to 48 units.

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Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

-4x/-2y

Step-by-step explanation:

16x - y - 4x + 1

---------------------

16x - y - 2y - 1

= - 4x/- 2y

Hope this helped!

Therefore , the solution of the given problem of unitary method comes out to be any other restrictions or criteria would determine how many possible methods there are to shade 3/8 of the square.

Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.

Here,

The phrase "shade 3/8 of the square" might be interpreted in a variety of ways, which might result in various solutions. Here are a few potential explanations and their accompanying responses:

1) The most straightforward interpretation is to shade 3/8 of the square as a single, continuous area.

There are countless ways to shade precisely 3/8 of the square in this interpretation.

2) Discrete Interpretation: Using a grid or discrete cells to shade 3/8 of the square.

The number of alternative ways relies on the size of the grid or the number of discrete cells if the square is divided into a grid or cells and the requirement is to shade exactly 3/8 of the cells. F

3) Interpretation based on constraints: Shading 3/8 of the square with specific restrictions.

In conclusion, the exact interpretation and any other restrictions or criteria would determine how many possible methods there are to shade 3/8 of the square. It is challenging to estimate the precise number of potential solutions in the absence of more details.

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Answer:

Town B

Step-by-step explanation:

-3 2/5 is equal to -3.4 and -3.4 is smaller than -3.33 therefore it is colder

Step-by-step explanation:

1 / 9 is the correct answer

Answer:

The answer is 1/9

Step-by-step explanation:

Hope it helps.

Answer:

x = 45 degrees

Step-by-step explanation:

All angles in a triangle will add up to 180 degrees.  So far we have 57 degree of 180.  We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180.  We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.  

Now, follow this equation to find x:

57 + 78 + x = 180

135 + x = 180

-135        -135

x = 45

Let:

Using elimination method:

Replace the value of y into (1):

The solution is:

Therefore the system has one solution

Answer:

2.5 inches

Step-by-step explanation:

Using Alfonso's scale of the drawing, which is 1in=10 ft, we can conclude the height of the tower to be 2.5 inches because

the actual height of the tower is 25 feet

10+10=20, which by following the scale, is 2 inches

we then have 5 left, 5 being half of 10, and .5 being half an inch.

Therefore the height of the tower using Alfonso's scale is 2.5 inches.

Hope this helps and take care

Answer:

-6

Step-by-step explanation:

Answer: 6.4 :)

Step-by-step explanation:

6.358

Step-by-step explanation:

To round a number to the nearest tenth, look at the hundredth number .If that number is greater than 5,add 1 to the tenth value.If is less than 5 , leave the tenth place value as it is, and remove all the numbers present after the tenth's place.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

See explanation

Step-by-step explanation:

\(6 {c}^{2} + 2 {c}^{4} - c \\ \\ standard \: form = \red{ \boxed{ \bold{2 {c}^{4} + 6 {c}^{2} - c}}} \\ \\ degree = \purple{ \boxed{ \bold{4}}} \\ \\ leading \: coefficient = \orange{ \boxed{ \bold{1}}}\)

The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.

(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.

Step 1: Sum up the number of movies watched by all 25 students:

\(0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70\)

Step 2: Divide the sum from Step 1 by the number of students (25):

70 / 25 = 2.8

So the sample mean X = 2.8

(b) The sample standard deviation s can be calculated using the formula:

\(s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }\)

Where \(X_{mean}\) is the sample mean, n is the sample size, and Σ represents the sum of all values.

Step 1: Calculate \((X - X_{mean})^2\)for each data point and sum up the values:

\((0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36\)

Step 2: Divide the sum from Step 1 by (n - 1) = 24:

31.36 / 24 = 1.31

Step 3: Take the square root of the result from Step 2:

\(\sqrt{1.31} = 1.15\)

So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).

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