please I need some help with both questions.

your answer would be A. 122/27

(a) The initial speed of the projectile - 28.2m/s

(b)The total time interval the projectile was in flight - 4.07s.

a) When a projectile is launched with speed \(v_{i}\) at an angle above the horizontal, the initial velocity components are \(v_{xi}\) = \(v_{i}\) cos\(θ\) and                  \(v_{yi}\)= \(v_{i}\) sin\(θ\) . Neglecting air resistance, the vertical velocity when the projectile returns to the level from which it was launched (in this case, the ground) will be \(v_{y} = - v_{yi}\) .

From this information, the total time of flight is found  \(v_{yf} = v_{yi} + a_{y}\) to be

         \(t_{total} = \frac{v_{yf} - v_{yi} }{a_{y}}\)   = \(\frac{-v_{yi} - v_{yi} }{-g}}\)  = \(\frac{2v_{yi} }{g}\)

         \(t_{total} = \frac{2v_{i}sinθ }{g}\)

Since the velocity of a projectile with no air resistance is constant, the horizontal distance it will travel in this time is given by

R = \(v_{xi} t_{total} = (v_{i} cosθ_{i}) \frac{2v_{i}sinθ }{g}\)  =  \(\frac{v^{2}_{i}}{g}( 2sinθ_{i} cosθ_{i} )\) = \(\frac{v^{2} _{i} (sin2θ_{i} ) }{g}\)

Thus, if the projectile is to have a range of R=81.1m when launched at an angle of \(θ_{i}\)=45.0°, the required initial speed is

\(v_{i} = \sqrt{\frac{81.1 * 9.80}{sin90} }\) = 28.2 m/s

Therefore, the initial speed of the projectile - 28.2m/s

b) With \(v_{i}\)=28.2m/s and \(θ_{i}\) = 45.0°, the total time of flight (as found

above) will be

        \(t_{total} = \frac{2v_{i}sinθ }{g}\)  = \(\frac{2(28.2 m/s) sin45}{9.80m/s^{2}}\) = 4.07s

∴The total time interval the projectile was in flight - was 4.07s.

c) Note that at \(θ_{i}\) =45.0° that sin(2\(θ_{i}\)) will decrease as \(θ_{i}\) is increased above this optimum launch angle. Thus, if the range is to be kept constant while the launch angle is increased above 45.0°, we see from \(v_{i}\) = \(\sqrt{\frac{Rg}{sin2θ_{i}} }\)that the required initial velocity will increase.

Observe that for \(θ_{i}\) <90°, the function sin\(θ_{i}\) increases as \(θ_{i}\) it increased. Thus, increasing the launch angle above 45.0° while keeping the range constant means that both \(v_{i}\) sins will increase. Considering the expression  \(t_{total}\) given above, we see that the total time of flight will increase.

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The correct question is :

The record distance in the sport of throwing cowpats is 81.1m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time interval the projectile was in flight. (c) How would the answers change if the range were the same but the launch angle was greater than 45°? Explain.

Answer:

a = 18

Step-by-step explanation:

3(x+6)-x = 2x + a

Distribute

3x +18 -x = 2x+a

2x +18 = 2x+a

Subtract 2x from each side

18 = a

The given data points ara

To find a 3rd degree polynomial using least squares regression to fit the given data, follow these:The general equation of the 3rd degree polynomial is\(y = ax³ + bx² + cx + d.\)

We need to find a, b, c and d by solving the following equations using the given data points:

∑y = \(Na + b∑x + c∑x² + d∑x³  ∑xy\)

= \(a∑x³ + b∑x² + c∑x + dN∑x²y\)

=\(a∑x⁴ + b∑x³ + c∑x² + d∑x²∑x³y = a∑x⁵ + b∑x⁴ + c∑x³ + d∑x³\)

Here N is the number of data points, which is 4 in our case.

∑x =\(-10 + (-8) + 1 + 3 = -14∑x²\)

=\((-10)² + (-8)² + 1² + 3²\)

= \(174∑x³\)

= \((-10)³ + (-8)³ + 1³ + 3³\)

= \(-210∑x⁴\)

= \((-10)⁴ + (-8)⁴ + 1⁴ + 3⁴\)

=\(2716∑x⁵\)

=\((-10)⁵ + (-8)⁵ + 1⁵ + 3⁵\)

= \(-36430∑y\)

= \(1 + 7 - 4 - 7\)

=\(-3∑xy\)

= \((-10)×1 + (-8)×7 + 1×(-4) + 3×(-7)\)

= \(-85∑x²y\)

=\((-10)×1 + (-8)×49 + 1×(-4) + 3×(-49)\)

=\(-545∑x³y\)

=\((-10)×(-1) + (-8)×(-343) + 1×(-4) + 3×(-2187)\)

= 24055

Solving the above four equations, we get the values of a, b, c and d as follows:

a = 0.1043,

b = -2.0107

c = 2.8804

and

d = -3.3071

The required 3rd degree polynomial is

y = \(0.1043x³ - 2.0107x² + 2.8804x - 3.3071.\)

The required 3rd degree polynomial that best fits the given data is

`y =\(0.1043x³ - 2.0107x² + 2.8804x - 3.3071`.\)

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Answer:

f(x) = -100(1.05)^(x+5) + 50

Step-by-step explanation:

Here, we want to write an equation that represents the transformation

5 units right means 5 units on the positive x-axis

50 units up means we add this to the total y value

So the resulting equation will be;

f(x) = -100(1.05)^(x+5) + 50

Answer:

b

Step-by-step explanation:

acellus sucks

Answer:

B

Step-by-step explanation:

(6, 5) lies on the graph of the linear equation while (9, 8) is not on the line.

(6, 5) is a solution, (9, 8) is not.

To determine if an ordered pair is a solution to a linear equation, substitute the values into the linear equation to check if it makes the linear equation true.

Another way of confirming if they are solutions to the linear equation, plot the graph of the linear equation. If the points are on the line of the linear equation, then they are solutions to the linear equation.

Substitute (6, 5) into y = 2/3x + 1:

5 = 2/3(6) + 1

5 = 5 [true, it is a solution]

Substitute (9, 8) into y = 2/3x + 1:

8 = 2/3(9) + 1

8 = 2(3) + 1

8 = 7 [not true, it is not a solution].

The graph of the linear equation also shows that (6, 5) is on the line while (9, 8) is not.

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Answer:

median

Step-by-step explanation:

in a box plot, it does not represent the mean, just so you know.

mode =  largest number.

range =  difference between largest number and smallest number

Answer:

2,620.

Step-by-step explanation:

thats the answer. have a nice day!

Answer:

64,339 = π(r^2)(20)

r^2 = 1,023.987

r = 32 ft

Using the bottom rules, we can conclude that Ethan's mistakes are: shapes C and F are placed in the wrong groups.

The image showing the two groups is as shown in the brainly link attached at the end.

From the attached file in the brainly link, we see that the shapes are grouped using the following criteria:

Using the above rules, we can conclude that Ethan's mistakes are: shapes C and F are placed in the wrong groups.

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On solving the question, we can say that the, naresh knows how to play 8 songs on the sitar each month he learns how to play 2 new songs equation will be y = 8x + 2

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation will be

y = 8x + 2

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The correct question is -

The sitar is a popular Indian classical string instrument. Naresh plays this instrument at cultural events that he and his family attend. Naresh knows how to play 8 songs on the sitar. Each month, he learns how to play 2 new songs. Write an equation to model the of songs Naresh knows hot" to play on the sitar, y, as a function of the number of months, x.

Answer:

49

Step-by-step explanation:

The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.

Therefore, let the number of red marbles be \(x\).

We have the following equation:

\(\frac{x}{84}=\frac{7}{12}\)

Cross-multiplying, we get:

\(12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}\)

Therefore, there are 49 red marbles in the bag.

The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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✩ Answer:

 ✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

  \(\bold{Hello!}\\\bold{Your~answer~is~below!}\)

✩ Step-by-step explanation:

 ✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

✺ Subtract \(5\) from both sides:

✺ Subtract \(5\) from \(17\) to get \(12\):

✺ Divide both sides by \(3\). Since \(3\) is positive, the inequality direction remains the same:

✺ Divide \(12\) by \(3\) to get \(4\):

\(Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex\)

             "ටᆼට"

Answer:

M means measure so you're finding what PQR is

m∠PQR = about 60°

Mary's living room is rectangular and measures 27 feet by 36 feet.  Mary has walked 90 feet in total.

Mary strides the 27-foot length of the main room. She then does a 180-degree turn and walks the 36-foot breadth. After another 27 feet, she finally makes her way back to the corner where she began.

She has therefore traveled the following distance:

90 feet is equal to 27 feet in length, 36 feet in width, and another 27 feet for the return, i.e,

27 feet (length) + 36 feet (width) + 27 feet (return length) = 90 feet

Mary has now covered a total distance of 90 feet.

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Answer:

3.) x=3

4.) x=11

Step-by-step explanation:

3.) 80= 27x-1

x=3

4.) 5x+5+9x+21= 180

14x+26= 180

x=11

Answer: #3) x= 3. #4) x= 11

Step-by-step explanation:

For #3 these angles are alternate exterior angles. (Opposite sides of the transversal and outside of the parallel lines) Alternate exterior angles are equal, so set these two equal to each other to solve for x. 27x-1 = 80 Add 1 to both sides. 27x = 81. Divide both sides by 27. X = 3. For #4, these angles are same side interior angles. (Same side of the transversal and inside the parallel lines) Same side interior angles sum to 180 degrees. (5x+5) + (9x+21) = 180. Combine like terms. 14x + 26= 180. Subtract 26 from both sides. 14x = 154. Divide both sides by 14. X = 11

If a researcher needed to determine whether random assignment to groups was effective in creating equivalent groups, s/he might useT-tests. The correct answer is T-tests.

T-tests are statistical tests used to compare the means of two groups and determine if there is a significant difference between them. They are commonly used to assess group equivalence resulting from random assignment.

To determine whether random assignment to groups was effective in creating equivalent groups, researchers commonly use statistical tests like T-tests. T-tests are used to compare the means of two groups and assess whether there is a statistically significant difference between them.

By conducting a T-test on relevant variables between the groups, researchers can evaluate if there are any significant differences that might indicate that random assignment was not successful in creating equivalent groups. If the T-test results in a non-significant p-value, it suggests that there is no significant difference between the groups, providing evidence that random assignment was effective in creating equivalent groups.

Regression analyses, quartiles, and Pearson correlations are not specifically designed to evaluate the effectiveness of random assignment in creating equivalent groups. Regression analyses are used to model relationships between variables, quartiles are used to divide a dataset into equal quarters, and Pearson correlations assess the strength and direction of linear relationships between variables.

While these techniques can be valuable for different research questions and analyses, they are not primarily used for assessing group equivalence resulting from random assignment.

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Complete Question:

If a researcher needed to determine whether random assignment to groups was effective in creating equivalent groups, s/he might use:

Group of answer choices

T-tests

Regression analyses

Quartiles

Pearson correlations

Answer:

48 member did not vote

Step-by-step explanation:

32 is 40% of 80

80-32=48

is there a picture to help me underdtsnd what we are trying to do with the questionAnswer:

Step-by-step explanation:

Fair dealing is a legal concept that allows for the limited use of copyrighted materials without obtaining permission from the copyright holder. However, the extent of fair dealing varies depending on the purpose and amount of the material being used.

In the case of making photocopies of a book in the library for personal research, fair dealing may allow for the copying of a section of the book for the purposes of research or private study, but permission would need to be obtained for copying the entire book. Fair dealing also allows for the making of a copy of a video for personal use at home, but not for distribution or public performance.

It is important to note that fair dealing does not allow for the copying of software without permission, as software is typically protected by licenses rather than copyright law. Additionally, making multiple copies of a work for personal use or research may not be considered fair dealing if it infringes on the rights of the copyright holder.

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x = −12/5 and y = −58/15

Step-by-step explanation:

x+3y=−14

4x−3y=2

Add these equations to eliminate y:

5x = −12

Then solve 5x = −12 for x:

5x = −12

5x/5 = −12/5 (Divide both sides by 5)

x = −12/5

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

x + 3y = −14

Substitute −12/5 for x in x + 3y = −14:

−12/5 + 3y = −14

3y + −12/5 = −14

(Simplify both sides of the equation)

3y + −12/5 + 12/5 = −14 + 12/5

(Add 12/5 to both sides)

3y = −58/5

3y/3 = −58/5/3

(Divide both sides by 3)

y = −58/15

Answer:

3.7252903e-9

Step-by-step explanation:

(((128^(negative 3)) / 4)*(2^(negative 3))) / 4 = 3.7252903e-9

According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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(-8+10i)(-9+3i) simplifies to 102 - 96i in the form of a + bi.

Expression (-8+10i)(-9+3i) is to be simplified as the expression to a + bi form, we can expand the given expression using FOIL method:

(-8+10i)(-9+3i) = 72 - 6i - 90i - 30i²= 72 - 96i + 30 (as, i² = -1)= 102 - 96i (On combining)

Hence, (-8+10i)(-9+3i) simplifies to 102 - 96i in the form of a + bi.

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Podemos utilizar la ley de cosenos para aproximar la distancia entre las cometas. Primero, necesitamos encontrar la longitud de la tercera cuerda, que conecta los puntos donde se cruzan las dos cuerdas que sostienen las cometas. Podemos usar trigonometría para encontrar la altura de este triángulo.

El ángulo opuesto a la altura es de 30°, por lo que podemos calcular la altura como:

Ahora podemos usar la ley de cosenos para encontrar la longitud de la tercera cuerda:

Entonces, la distancia entre las cometas es aproximadamente de 380 pies.

in the sample of 100 respondents from Vermont, 65.3% of them reported exercising for at least 30 minutes a day for three days out of the week.

The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as:

sample proportion = 65.3% = 0.653

what is minute?

In this context, "minute" likely refers to the amount of time spent exercising per day. Specifically, the survey asked if participants had exercised "more than 30 minutes a day for three days out of the week."

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After learning the difference between Roth and traditional retirement plans such as IRA, 401(k), and 403(b), I would prefer a {choose either "Roth" or "Traditional"} retirement plan.

My preference is based on {provide reasons for your preference, such as tax implications, investment options, and anticipated future income tax bracket}.

Overall, the decision between a Roth and traditional retirement plan depends on individual financial circumstances and future goals. It is important to consult with a financial advisor to determine the best option for your specific situation.