help pls offering 95 points and if brainliest if 2 people answer

Help Pls Offering 95 Points And If Brainliest If 2 People Answer

Answers

Answer 1

Answer:

126*2/(5+2+)

252/7=36

Step-by-step explanation:

Hope this helps! =D

Sorry again


Related Questions

explain what function (in mosaic ) and what parameters you should you use to find the value of z* for a specified confidence level c

Answers

This would give you a z* value of approximately 1.96.

To find the value of z* for a specified confidence level c in a mosaic function, you should use the inverse cumulative

distribution function (also called the quantile function or the z-score function). The parameters you need are the

desired confidence level (c) and the standard normal distribution.

Here are the steps to find the value of z*

1. Determine the desired confidence level (c). This is usually given as a percentage, like 95% or 99%.

2. Calculate the area under the curve corresponding to the confidence level. This is equal to (1 - c)/2.

3. Use the inverse cumulative distribution function (quantile function) with the standard normal distribution to find the z

score corresponding to the calculated area.

4. The resulting value is the z* value for the specified confidence level c.

For example, if you need to find the z* value for a 95% confidence level, you would calculate (1 - 0.95)/2 = 0.025, and

then use the inverse cumulative distribution function with the standard normal distribution to find the z-score

corresponding to 0.025. This would give you a z* value of approximately 1.96.

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dominique is building a flower box for her yard. the outline of the box is shown in the diagram. if she wants to cover the box with burlap to protect it, how much burlap does she need to buy?

Answers

Once we have the total surface area, we will know how much burlap Dominique needs to buy to cover the flower box.

To determine how much burlap Dominique needs to buy to cover the flower box, we need to calculate the surface area of the box. Unfortunately, without the specific dimensions or a provided diagram,

I cannot give you an exact number.
However, here are the general steps to calculate the surface area of a rectangular flower box:
1. Identify the dimensions: length (L), width (W), and height (H).
2. Calculate the surface area of each face:
  - Top/Bottom: 2 x (L x W)
  - Sides: 2 x (L x H)
  - Front/Back: 2 x (W x H)
3. Add the surface areas of all faces together to get the total surface area.
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I need to find the general equation for the circle that passes through the given points

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The general equation for a circle with center (a,b) and radius r is:

[tex](x-a)^2 + (y-b)^2 = r^2[/tex]. By substituting the values and simplifying the equation, we will get 0.

What is circle ?

In math, a circle is a closed, two-dimensional shape made up of all elements that are spaced uniformly apart from the centre. The radius of something like the circle refers to this distance. Often, the letter "O" or "" is used to represent a circle. The circle is really a fundamental geometric shape and includes a number of significant characteristics, including its radius, which is the distance it around circle, or its area, which is the volume of the circle's interior. A circle's area is equal to 2 times its radius square, and its circumference is equal to 2 times its radius.

To find the equation for the circle that passes through the points (-5,0), (0,4), and (2,4), we need to find the center (a,b) and radius r.

First, we find the midpoint of the line segment between (-5,0) and (0,4), which is:

[tex]((-5+0)/2, (0+4)/2) = (-2.5,2)[/tex]

Next, we find the midpoint of the line segment between (0,4) and (2,4), which is:

[tex]((0+2)/2, 4/2) = (1,2)[/tex]

Since the circle passes through all three points, its center must be equidistant from all three points. Using the distance formula, we can set up three equations:

[tex](-2.5 - a)^2 + (2 - b)^2 = r^2[/tex]

[tex]a^2 + (4 - b)^2 = r^2[/tex]

[tex](1 - a)^2 + (2 - b)^2 = r^2[/tex]

Simplifying the equations and setting them equal to each other, we get:

[tex](-2.5 - a)^2 + (2 - b)^2 = a^2 + (4 - b)^2 = (1 - a)^2 + (2 - b)^2[/tex]

Expanding the squares and simplifying, we get:

[tex]6a - 10 = 0[/tex]

[tex]2b - 12 = 0[/tex]

Solving for a and b, we get:

a = 5/3

b = 6

Now we can find the radius of the circle by plugging in the values of a and b into one of the equations we set up earlier:

[tex]a^2 + (4 - b)^2 = r^2[/tex]

[tex](5/3)^2 + (4 - 6)^2 = r^2[/tex]

[tex]25/9 + 4 = r^2[/tex]

[tex]r^2 = 61/9[/tex]

Therefore, the equation of the circle is:

[tex](x - 5/3)^2 + (y - 6)^2 = 61/9[/tex]

Simplifying, we get:

[tex]4x^2 + 4y^2 - 40x + 48y + 167 = 0.[/tex]

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Below is a table giving the fox and rabbit populations in a national park
during a 12-month period. Note that each value of t corresponds to the beginning of
the month

According to the data in the table, is F a function of R? Is R a function of F? Explain.

Is either R or Fa function of t? Explain.

Answers

The table only gives us information about the values of R and F at certain points in time, but it does not give us a functional relationship between the two variables. To determine whether F is a function of R, we would need to know the number of foxes for each value of R.

What is function ?

A function in mathematics is a rule that converts each element from one set, known as the domain, into a particular element in another set, known as the range. The domain of a function is the set of all potential inputs, whereas the range is the set of all potential outputs. A graph, a table of values, or an equation can all be used to describe a function. In science, engineering, economics, and other disciplines, functions are used to represent the connections between variables.

Neither R nor F is a function of t because there are multiple values of R and F for some values of t. For example, at t=2, the number of rabbits is 750, and at t=3, the number of rabbits is 567.

From the data in the table, we cannot determine whether F is a function of R or whether R is a function of F. To determine whether F is a function of R, we would need to know the number of foxes for each value of R. Similarly, to determine whether R is a function of F, we would need to know the number of rabbits for each value of F. The table only gives us information about the values of R and F at certain points in time, but it does not give us a functional relationship between the two variables.

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Razak's mother weighs, 64.8kg. If she weighs 4 times the weight of Razak, What is Razak's weight?​

Answers

Razak weighs 16.2 kg. To find Razak's weight, we need to use the information given in the problem that his mother weighs 4 times his weight.

Let's use the variable "R" to represent Razak's weight in kilograms. According to the problem, Razak's mother weighs 4 times Razak's weight, so we can write an equation:

Mother's weight = 4 * Razak's weight

64.8 = 4R

To solve for R, we can divide both sides by 4:

64.8 / 4 = R

16.2 = R

Therefore, Razak weighs 16.2 kg.

It's important to note that in solving this problem, we assumed that the weight of Razak's mother was accurately given in the problem. Additionally, we assumed that the units of measurement were in kilograms. If the problem used different units, we would need to convert them to kilograms before solving the equation.

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Pls im begging you do my math hw I just got back from a track meet

Answers

Answer:

x = 71

Step-by-step explanation:

180 degrees is how many degrees were in a triangle.

Add up the angles then subtract by 180 and there is your answer.

Two pools are being filled with water. To start, the first pool contains 1900 liters of water and the second pool contains 1501 liters of water. Water is being added to the first pool at a rate of 21.25 liters per minute. Water is being added to the second pool at a rate of 35.5 liters per minute.

Answers

To find the amount of water in each pool at any given time, we need to use the formula:

Amount of water = Initial amount of water + (rate of inflow × time)

Let's say we want to find the amount of water in each pool after 10 minutes. Using the formula, we get:

Amount of water in first pool = 1900 + (21.25 × 10) = 2125 liters

Amount of water in second pool = 1501 + (35.5 × 10) = 501 liters

Therefore, after 10 minutes, the first pool contains 2125 liters of water and the second pool contains 501 liters of water.

8. A square and its dimensions are shown below. What is the perimeter of the square?

Answers

Step-by-step explanation:

Perimeter is the sum of all of the sides

  add all of the    3x + 3  's

3x+3    +   3x +3     +  3x+3    +  3x + 3 = 12x + 12  units

I have a question,what is 3x + 2 = 17

Answers

Answer: x=5

Step-by-step explanation:

First you gotta box the variable so you don't get confused. The opposite of adding 2 is subtracting so you subtract 2-2 which gives you 0 and subtract 17-2 which gives 15. THEN, you will have left 3x=15 in order to get rid of the three you have to divide by the 3 on both sides. Lastly, you get your answer! Hope this helps :D

What is 2^2000
2 to the power of 2000

Answer in number form. Not scientific notation or e notation.

Answers

Step-by-step explanation:

Not sure why you would want this...here is the result using a big number calculator on the internet:

2^2000 =

114,813,069,527,425,452,423,283,320,117,768,198,402,231,770,208,869,520,047,764,273,682,576,626,139,237,031,385,665,948,631,650,626,991,844,596,463,898,746,277,344,711,896,086,305,533,142,593,135,616,665,318,539,129,989,145,312,280,000,688,779,148,240,044,871,428,926,990,063,486,244,781,615,463,646,388,363,947,317,026,040,466,353,970,904,996,558,162,398,808,944,629,605,623,311,649,536,164,221,970,332,681,344,168,908,984,458,505,602,379,484,807,914,058,900,934,776,500,429,002,716,706,625,830,522,008,132,236,281,291,761,267,883,317,206,598,995,396,418,127,021,779,858,404,042,159,853,183,251,540,889,433,902,091,920,554,957,783,589,672,039,160,081,957,216,630,582,755,380,425,583,726,015,528,348,786,419,432,054,508,915,275,783,882,625,175,435,528,800,822,842,770,817,965,453,762,184,851,149,029,376

Faith kicks a football. The graph below shows the height of the football ℎ h in feet after � t seconds.

Answers

Answer:

faith

Step-by-step explanation:

you are a Beautiful human being

Graph triangle DEF with vertices D (6,2), E (6,6), and F (10,4) and its image after a dilation centered at the origin with a scale factor of 1/2. Then find the difference between the area of the image and the area of the preimage.

Answers

Answer:

The graph is below.

The area of the pre-images is 8 and the area of the image is 2.  The difference is 6 [tex]units^{2}[/tex]

Step-by-step explanation:

Area of the large triangle

a = [tex]\frac{bxh}{2}[/tex]  I am going to choose the vertical line to be the base because I can count the base to be 4 and the height straight up from the base to be 4.

a = [tex]\frac{4x4}{2}[/tex] = 8

I found the base for the image in the same way

a = [tex]\frac{2x2}{2}[/tex] 2

Helping in the name of Jesus.

fix her error, please help!!!

Answers

The trigonometric ratios of sine, cosine, and tangent can be used  to find the lengths of the sides of the triangle.

How do you solve the right triangles?

A right triangle has one angle that measures exactly 90 degrees. Identify this angle in the triangle.

Label the sides of the triangle as the hypotenuse, adjacent, and opposite sides, relative to one of the non-right angles. The hypotenuse is always the side opposite the right angle.

We know that;

Tan 45 = 5.9/w

w = 5.9/Tan45

w = 5.9

Then;

Tan 35 = 5.9/w + x

0.7 = 5.9/5.9 + x

0.7(5.9 + x) = 5.9

4.13 + 0.7x = 5.9

x = 2.5

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On your own sheet of paper, make a stem-and-leaf plot of the following set of data and then find the range of the data.
83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92.

can I get the range in a graph form?

Answers

The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45

what is range ?

The range of a number collection or data points in mathematics is the difference here between biggest and smallest values. It is a measurement of the data's dispersion or variability. The range is frequently employed in descriptive statistics and can serve to provide information about the data's distribution.

given

Certainly! The data are shown in a stem-and-leaf plot as follows:

5 | 4

6 | 0 1 2 2

7 | 1 2 4 6 8

8 | 2 3 4 4 6 7

9 | 0 5 5 9

The difference between the largest and smallest values is the data's range.

The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45

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Emily got her monthly credit card statement, which showed a bill of $156. She paid the minimum payment due, which was $30. If the interest rate was 15.5%, then Emily had to pay interest on the amount of $ _________ and the amount of interest to be paid would be __________.

Answers

Emily had to pay interest on the amount of $126 and the amount of interest to be paid would be $16.41.

What is interest rate?

Interest rate is the percentage charged by a lender to a borrower for the use of money, usually expressed as an annual percentage of the principal borrowed.

Emily had to pay interest on the remaining balance after making the minimum payment of $30.

Remaining balance = $156 - $30 = $126

The amount of interest to be paid would be calculated as:

interest = (interest rate/12) * remaining balance

Where 12 is the number of months in a year.

So,

interest = (15.5/12) * $126 = $16.41

Therefore, Emily had to pay interest on the amount of $126 and the amount of interest to be paid would be $16.41.

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the function f(x)=-5x^2 + 17x + 21 models the predicated sales of a pen after x price increase. use the table showing actual and predicted sales to find the residual for the models

Answers

To find the residual for each data point, we subtract the predicted sales from the actual sales. The residuals for the model are 1, 0, 1, and 1 for x=0, 1, 2, and 3 respectively.

To find the residual for each data point, we need to subtract the predicted sales from the actual sales:

For x=0: Residual = Actual sales - Predicted sales = 22 - 21 = 1

For x=1: Residual = Actual sales - Predicted sales = 33 - 33 = 0

For x=2: Residual = Actual sales - Predicted sales = 36 - 35 = 1

For x=3: Residual = Actual sales - Predicted sales = 28 - 27 = 1

Therefore, the residuals for the model are 1, 0, 1, and 1 for x=0, 1, 2, and 3 respectively.

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A rectangle garden has one side that is 6 feet longer than the other. A lawn care company installs synthetic grass that costs $8 per square foot in the entire.

If x represents the length, in feet, of the shorter side of the garden, and y represents the total cost, in dollars, to install the synthetic grass, which equation correctly shows the relationship between x and y?

Answers

Answer:

Step-by-step explanation:

The area of the rectangle garden can be expressed as:

Area = Length × Width

Since one side is 6 feet longer than the other, we can express the length as:

Length = Width + 6

Substituting this expression for length into the area formula, we get:

Area = (Width + 6) × Width

Simplifying this expression, we get:

Area = Width² + 6Width

The cost to install synthetic grass is given as $8 per square foot, so the total cost y can be expressed as:

y = 8(Area)

Substituting the expression for area that we found earlier, we get:

y = 8(Width² + 6Width)

Simplifying this expression, we get:

y = 8Width² + 48Width

Therefore, the equation that correctly shows the relationship between x (the length of the shorter side of the garden) and y (the total cost to install synthetic grass) is:

y = 8x² + 48x

i need help badly because im confused

Answers

Answer:

92in²

Step-by-step explanation:

A= 1/2(b1+b2)h = 1/2 (18+5)8=

1/2 (23)8= 1/2 184 = 92in²

P ( rolling a composite number and the coin landing on heads and tails )

Answers

Assuming a standard six-sided die and a fair coin, the probability of rolling a composite number (any number that is not a prime number) on the die is 3/6 or 1/2, since there are three composite numbers (4, 6, 8) out of six possible outcomes (1, 2, 3, 4, 5, 6).

The probability of the coin landing on heads is 1/2, and the probability of it landing on tails is also 1/2. Therefore, the probability of both events happening together is:

P(composite number and heads and tails) = P(composite number) x P(heads) x P(tails)

P(composite number and heads and tails) = (1/2) x (1/2) x (1/2)

P(composite number and heads and tails) = 1/8

So the probability of rolling a composite number and the coin landing on heads and tails is 1/8.

Emilio flipped a pair of fair coins 60 times. On 24 occasions, heads appeared on both coins. How is this outcome different from the expected outcome?

Answers

Emiliο's οutcοme οf getting heads οn bοth cοins 24 times in 60 flips is 9 mοre than the expected οutcοme.

What is prοbability?

Prοbability is simply hοw likely sοmething is tο happen.

The expected οutcοme fοr flipping a pair οf fair cοins οnce is that there is a 1/4 (οr 0.25) prοbability οf getting heads οn bοth cοins.

Therefοre, the expected number οf times that heads wοuld appear οn bοth cοins in 60 flips is:

Expected number = (Prοbability οf heads οn bοth cοins) x (Number οf flips)

Expected number = 0.25 x 60

Expected number = 15

Emiliο οbserved that heads appeared οn bοth cοins 24 times, which is greater than the expected number οf 15.

The difference between the οbserved οutcοme and the expected οutcοme is:

Difference = Observed number - Expected number

Difference = 24 - 15

Difference = 9

Therefοre, Emiliο's οutcοme οf getting heads οn bοth cοins 24 times in 60 flips is 9 mοre than the expected οutcοme.

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Max went to the store and bought a new iPad that was 45% of the original price he saved $135 because of the sale how much was the original price of the iPad

Answers

Answer:

$245.45

Step-by-step explanation:

.45c = $135, so c = $245.45

.45 × $245.45 = $110.45, a $135 savings.

Please help I’ve posted this question twice and it’s due tonight

Answers

Based on the Venn diagram, the results in order are:

Students who do not like DC superheroes: 117Students who like Marvel superheroes: 358Students who like both DC and Marvel superheroes: 155Students who like DC but not Marvel superheroes: 85Students who like Marvel but not DC superheroes: 203Students who do not like the DC or Marvel superheroes: 117

How do we solve this?

To solve this problem, we can use a Venn diagram to represent the information given.

Total students surveyed = 560

395 like superheroes from either company

240 prefer DC superheroes

358 do not like Marvel superheroes

To find how many students did not like DC superheroes, we need to find the number of students who do not fall into the DC circle:

Students who do not like Marvel superheroes = 358

Students who like both DC and Marvel superheroes = (395 - 240) = 155

Students who like Marvel superheroes only = ?

Students who like DC superheroes only = (240 - 155) = 85

To find how many students like Marvel superheroes, we need to find the number of students who fall into the Marvel circle:

Students who do not like DC superheroes = ?

Students who like both DC and Marvel superheroes = 155

Students who like Marvel superheroes only = ?

Students who like DC superheroes only = 85

To find how many students like both DC and Marvel superheroes, we can use the information we already have:

Students who like both DC and Marvel superheroes = 155

To find how many students like DC but not Marvel superheroes, we can use the information we already have:

Students who like DC superheroes only = 85

To find how many students like Marvel but not DC superheroes, we can use the information we already have:

Students who like Marvel superheroes only = (358 - 155) = 203

Finally, to find how many students do not like the DC or Marvel superheroes, we need to find the number of students who do not fall into either circle:

Students who do not like DC superheroes = ?

Students who like both DC and Marvel superheroes = 155

Students who like Marvel superheroes only = 203

Students who like DC superheroes only = 85

We can now use the formula for the total number of students surveyed to find the number of students who do not like DC or Marvel superheroes:

Total students surveyed = Students who do not like DC superheroes + Students who like both DC and Marvel superheroes + Students who like Marvel superheroes only + Students who like DC superheroes only

560 = Students who do not like DC superheroes + 155 + 203 + 85

Students who do not like DC superheroes = 117

Similarly, we can use the same formula to find the number of students who like Marvel superheroes:

560 = Students who do not like DC superheroes + 155 + Students who like Marvel superheroes only + 85

Students who like Marvel superheroes = 203 + 155

Students who like Marvel superheroes = 358

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Find the angle measure indicated. Assume that lines which appear tangent are tangent. A. 110 degrees B. 175 degrees C. 155 degrees D. 120 degrees

Answers

Therefore, the angle measure indicated 110° that is option A.

What is angle?

An angle is the measure of the amount of rotation between two intersecting lines or planes. It is defined as the space between two intersecting lines or planes measured in degrees, radians, or other units of angular measurement. Angles are often represented by a symbol that looks like a small arc, with three letters labeling the points that define the angle, such as "ABC." The vertex of an angle is the point where the two lines or planes intersect, and the sides of an angle are the two rays that extend from the vertex. Angles are used in geometry, trigonometry, and other mathematical fields to measure and analyze the relationships between shapes and objects.

Here,

Since sector PF has a measure of 90 degrees, then angle PAF must also have a measure of 90 degrees since it is an inscribed angle that intercepts the same arc.

To find the angle measure of QSR, we first need to find the measure of angle QPR.

Since sector PF is a 90 degree sector and line QR is tangent to the circle at point R, we know that angle QRP is a right angle (90 degrees).

Similarly, since sector QR is a 150 degree sector and line PS is tangent to the circle at point S, we know that angle QPS is a right angle (90 degrees).

Therefore, angle QPR + angle QPS = 90 + 90 = 180 degrees.

Since angle QPS and angle QRP share ray QR, they are adjacent angles.

So, angle QSR = 360 - (angle QPR + angle QPS)

= 360 - 180 -70

= 110 degrees

Therefore, the measure of angle QSR is 110 degrees, which is equivalent to a straight line.

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Pls help! This is due today!

Answers

Answer:
3(a - 1) / (a + 1)

Step-by-step explanation:

I double checked, its right

Find the least-squares regression line y^=b0+b1x through the point
(−3,0),(2,9),(5,13),(9,19),(10,23).

For what value of x is =0?

Answers

Answer:

3

Step-by-step explanation:

or differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

Answers

The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.

To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:

s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

where s is the arc length, t is the parameter, and (x, y, z) is the position vector.

We want the arc length to be 2, so we can set up the following equation:

2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

We can then choose a function for each component of the position vector, such as:

x = t

y = t²

z = sin(t)

We can now find the derivatives with respect to t:

dx/dt = 1

dy/dt = 2t

dz/dt = cos(t)

We can substitute these into the arc-length formula:

2 = ∫√(1)² + (2t)² + (cos(t))² dt

Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.

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The question is -

Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

A player kicks a football off the ground so that if travels with a velocity of 32 miles per hour at an angle of 34° with the ground. Find the magnitude of the horizontal and vertical components.

Answers

As a result, the horizontal component of velocity has a magnitude of 11.8 m/s\ while the vertical component of velocity has a value of 8.0 m/s.

What is velocity?

The pace at which an item changes its position is described by a vector quantity called velocity. It is described as the rate at which displacement changes in relation to time The amount and direction of velocity are both present. Speed refers to the velocity's magnitude.

The football's velocity in this scenario is 32 miles per hour, or around 14.3 meters per second.

We can use trigonometry to determine the sizes of a velocity vector's horizontal and vertical components.

Vₓ = V cos (theta), where V is the magnitude of the velocity vector and theta is the angle that the velocity vector makes with the horizontal axis, gives the horizontal component of velocity.

Vy = V sin (theta), where V is the magnitude of the velocity vector and theta is the angle that the velocity vector makes with the horizontal axis, gives the vertical component of velocity.

In this instance, we are aware of the football's velocity, which is 32 miles per hour, or around 14.3 meters per second6. It makes a 34 degree 6 angle with the ground.

Therefore,

Vₓ= V cos (theta) * cos (34 degrees) = 14.3 m/s * 11.8 m/s

Vy = V sin (theta) * sin (34 degrees) = 14.3 m/s * 8.0 m/s

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(Using trig to find an angle)
Solve for x. Round to the nearest tenth of a degree, if necessary.

Answers

Step-by-step explanation:

For a RIGHT triangle   Sin = opposite LEG / Hypotenuse

           sin x = 45/ 83

                 x = arcsin (45/83)  = use calculator = 32.8 degrees

How many square centimeters are in the total surface area
of this cylinder? Express your answer to 2 decimal places?
4.0 cm
2.5 cm

Answers

Total surface area of this cylinder, the answer is (C) 163.36 cm².

What is an area ?

The total surface area of a cylinder can be found using the formula:

surface area = 2πr² + 2πrh

where r is the radius and h is the height.

Substituting the given values, we get:

surface area = 2π(4.0)² + 2π(4.0)(2.5)

= 2π(16.0) + 2π(10.0)

= 32π + 20π

= 52π

Using the approximation 3.14 for π and rounding to 2 decimal places, we get:

surface area ≈ 52(3.14) ≈ 163.36 cm²

Therefore, the answer is (C) 163.36 cm².

What is cylinder?

A cylinder is a three-dimensional shape that has two circular bases that are parallel and congruent to each other. The sides of a cylinder are curved, and they connect the bases. A cylinder has a constant cross-sectional area throughout its height, and it is a type of prism. The height of a cylinder is the perpendicular distance between the bases.

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. The surface area of a cylinder can be calculated using the formula A = 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder. Cylinders are commonly found in everyday objects such as cans, pipes, and containers.

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evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) ∫ (3x^2 + 2x – 3) / (x^3 – x) dx
_____________

Answers

The integral ∫ (3x^2 + 2x – 3) / (x^3 – x) dx evaluates to:
-ln(|x|) + ln(|x - 1|) + ln(|x + 1|) + C, where C is the constant of integration.

How to evaluate the integral?

To evaluate the integral ∫ (3x^2 + 2x – 3) / (x^3 – x) dx, follow these steps:

Factor the denominator.
The denominator (x^3 - x) can be factored as x(x^2 - 1). Further, (x^2 - 1) can be factored as (x - 1)(x + 1). So, the denominator becomes x(x - 1)(x + 1).Perform partial fraction decomposition.
Write the integrand as a sum of partial fractions:
(3x^2 + 2x - 3) / (x(x - 1)(x + 1)) = A/x + B/(x - 1) + C/(x + 1) Clear the denominators.
Multiply both sides by x(x - 1)(x + 1) to get:
3x^2 + 2x - 3 = A(x - 1)(x + 1) + Bx(x + 1) + Cx(x - 1)Solve for A, B, and C.
By comparing coefficients or plugging in suitable x values, we find:
A = -1, B = 1, and C = 1 Rewrite the integral.
Now the integral becomes:
∫ (-1/x + 1/(x - 1) + 1/(x + 1)) dxEvaluate the integral.
The integral can be evaluated by finding the anti-derivative of each term:
∫ (-1/x) dx = -ln(|x|) + C1
∫ (1/(x - 1)) dx = ln(|x - 1|) + C2
∫ (1/(x + 1)) dx = ln(|x + 1|) + C3
Combine all three anti-derivatives and the constants:
- ln(|x|) + ln(|x - 1|) + ln(|x + 1|) + C
Thus, the integral ∫ (3x^2 + 2x – 3) / (x^3 – x) dx evaluates to:
-ln(|x|) + ln(|x - 1|) + ln(|x + 1|) + C, where C is the constant of integration.

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