If a projectile is launched at an angle # with the horizontal, its parametric equations are as follows. x= (50 cos(deltha)t and y = (50 sin(deltha)}t – 16t2 Find the angle that maximizes the range of the projectile.

Answer:

(6/11, 16/11)

Step-by-step explanation:

While it's fairly obvious that you're supposed to "solve this system of equations," it'd be clearer if you were to say so specifically.  Also, reduce ambiguity by using parenthes:  You meant either (5/3)x or 5/(3x).  Which one?  I'm assuming it's (5/3)x.

Then our system is:

(5/3)x - 2y = -2

      x  +  y =  2

Let's eliminate y through addition/subtraction.  Multiply the 2nd equation through by +2:

(5/3)x - 2y = -2

     2x  + 2y = 4

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

(11/3)x       =  2

Multiplying both sides by 3 eliminates the fractional coefficient:

11x = 6

Then x = 6/11.  Now we must solve for y:

-(6/11) + y = 2

Multiplying 2 by 11/11 yields:

-(6/11) + y = 22/11.

This simplifies to y = 16/11

Thus, the solution of this system is

(6/11, 16/11)

To solve the equation 7 sin(x) = 5 - sin(x), we can first simplify it by adding sin(x) to both sides:

8 sin(x) = 5

Then we can solve for sin(x) by dividing both sides by 8:

sin(x) = 5/8

In the given interval of 0 < pi < 2pi, there are two possible solutions for x where sin(x) = 5/8. These solutions can be found using the inverse sine function (also known as arcsine):

x = arcsin(5/8)

Using a calculator, we can find that:

x ≈ 0.77 (in radians)

or

x ≈ 2.36 (in radians)

Therefore, the solutions to the equation 7 sin(x) = 5 - sin(x) in the interval 0 < pi < 2pi are:

x ≈ 0.77, 2.36 (in radians)
To find all solutions of the equation 7 sin(x) = 5 - sin(x) in the interval 0 < x < 2π, follow these steps:

1. Isolate sin(x):
7 sin(x) + sin(x) = 5
8 sin(x) = 5

2. Solve for sin(x):
sin(x) = 5/8

3. Find the principal solutions in the interval 0 < x < 2π:
x₁ = arcsin(5/8)
x₂ = π - arcsin(5/8)

4. Check if both solutions are in the interval 0 < x < 2π. If they are, list them as comma-separated values.

Your answer: x₁ ≈ 0.7297, x₂ ≈ 2.4119

learn more about sine functions here: brainly.com/question/12595712

#SPJ11

Answer:D

Step-by-step explanation: The answer would be 3b+6 and when you solve 3(b+2) you get 3b +6)

3 times b is 3b and when you add 6 it becomes 3b+6 or 3(b+2)

Answer:

A seems correct

Step-by-step explanation:

so 6 must be multiplied b times and added to 3

The step of data storytelling that describes showing the story of the data to highlight the meaning behind the numbers is "Visuals". The correct answer is option (d).

Visuals are an important aspect of data storytelling because they can help to convey complex information in a simple and easy-to-understand way. Visuals can include graphs, charts, diagrams, and other types of visual aids that appeal to the sight and are used for effect or illustration.

By using visuals, a data analyst can help their audience to better understand the story that the data is telling and to see the patterns and trends that might not be presently alleged from the raw numbers alone.

Hence, the correct answer is option (d).

Learn more about data storytelling here:

https://brainly.com/question/30097516

#SPJ12

The complete question is as follows:

A data analyst wants to tell a story with data. As a second step, they focus on showing the story of the data to highlight the meaning behind the numbers. which step of data storytelling does this describe?

a. Primary message

b. Engagement

c. Narrative

d. Visuals

The number of kilometers are 1,3.5,0.5,0.075,0.001.

Meters are 1000,3500,500,75,1.

The number of meters is x.

The number of kilometers is y.

kilometer = 1/1000×meter

y = 1/1000×x

The units of length and distance are meters and kilometers, respectively. The kilometer, or 1,000 meters, serves as the unit of distance measurement in the metric system. Therefore, one meter is equivalent to a thousandth of a kilometer.

A meter is denoted by the letter m, whereas a kilometer is denoted by the letter km. The default unit of length measurement in the metric system. Between the length of a ruler and the spacing between objects in a room, meters are used to measure everything.

Therefore the number of kilometers are 1,3.5,0.5,0.075,0.001.

To learn more about Kilometers, visit:

https://brainly.com/question/13987481

#SPJ1

Answer:

The rule to calculate the dilation by a scale factor 1/3 centered at the origin

(x, y) → (3/2x, 3/2y)

Hence, option D is correct.

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

The coordinates of the image can be determined by multiplying the coordinates of the original point by a given scale factor.

Given that the point M was located at (4, -2) and was dilated to M'(6,-3).

It means if we multiply the coordinates of the original point M(4, -2) by 3/2, we get the image point M'(6, -3).

i.e.

M(4, -2) → M'(3/2(4), 3/2(-2)) → M'(6, -3)

In other words, the image M'(6, -3) is obtained after the dilation by a scale factor 3/2 centered at the origin.

Therefore,

The rule to calculate the dilation by a scale factor 1/3 centered at the origin

(x, y) → (3/2x, 3/2y)

Hence, option D is correct.

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

To know more about demographics visit:

brainly.com/question/32805670

#SPJ11

The expression (f(x+h) - f(x)) / h simplifies to 2x + h - 3.

To find and simplify the expression (f(x+h) - f(x)) / h for the given function f(x) = x^2 - 3x + 2, we follow these steps:

1. Substitute f(x+h) and f(x) into the expression:

  (f(x+h) - f(x)) / h = [(x+h)^2 - 3(x+h) + 2 - (x^2 - 3x + 2)] / h

2. Expand and simplify the numerator:

  [(x^2 + 2xh + h^2) - 3(x+h) + 2 - (x^2 - 3x + 2)] / h

  = [x^2 + 2xh + h^2 - 3x - 3h + 2 - x^2 + 3x - 2] / h

  = [2xh + h^2 - 3h] / h

3. Factor out h from the numerator:

  h(2x + h - 3) / h

4. Cancel out the h in the numerator and denominator:

  2x + h - 3

Therefore, the expression (f(x+h) - f(x)) / h simplifies to 2x + h - 3.

To know more about simplifying expressions, click here: brainly.com/question/14649397

#SPJ11

Based on the results of the linearhypothesis function, we can conclude whether the hypothesis in part (b) is supported or not.

Linear hypothesis is a method of testing statistical hypotheses by estimating the parameters of a linear equation. This method of testing hypotheses involves estimating the parameters of a linear equation using a sample of data to determine if the parameters differ significantly from zero.

We can estimate the given model using the data in vote1. To do this, we will fit a linear regression model with the two independent variables (a's expenditures and b's expenditures) and the dependent variable (outcome). We can then use the model to determine whether a's expenditures have an effect on the outcome. We can do this by testing whether the coefficient for a's expenditures is statistically significant. If the coefficient is not statistically significant, then this means that a's expenditures do not have an effect on the outcome. We can also use the model to determine whether b's expenditures have an effect on the outcome. We can do this by testing whether the coefficient for b's expenditures is statistically significant. If the coefficient is not statistically significant, then this means that b's expenditures do not have an effect on the outcome. These results can be used to test the hypothesis in part (b). We can use the linearhypothesis function to test the hypothesis at a 5% significance level. If the test is found to be statistically significant, then this means that the hypothesis is supported. If the test is not statistically significant, then this means that the hypothesis is not supported.  Based on the results of the linearhypothesis function, we can conclude whether the hypothesis in part (b) is supported or not.

To learn more about hypothesis
https://brainly.com/question/15980493
#SPJ1

Answer:

232.5 ft

Step-by-step explanation:

Bounce

1      
2          

3           
4          
5

80   +   40X2  +  20 x 2   + 10 x 2   + 5 x 2  + 2.5   = 232.5 ft 

From the correlation table , based on the correlation values , then the predictor that would lead to least prediction error in predicting happiness using simple regression is stats class .

What is Predictor Variable ?

The predictor variable is used to predict the future outcome based on some given circumstances. The Other names by which predictor variable is known as "criterion variable" and "explanatory variable" .

the best predictor from the given correlation table is the highest value in the table ; irrespective of the sign .

We have to predict happiness using the simple regression ;

So to find the predictor , we select the row in the happiness row ,

we can see that the biggest value for the happiness row is 0.41 , which is the stats class .

Therefore , The predictor that lead to least prediction error is Stats Class .

Learn more about Regression here

https://brainly.com/question/28217629

#SPJ4

Answer:

By adding n = 10 to the calculation, we can determine the tenth component in the sequence denoted by the expression a(n) = 5n - 1:

a(10) = 5^10 - 1

= 976,5624

The sequence's tenth term is 976,5624 as a result.

The dual linear program is as follows:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The primal linear program is:

x1 + 2x2 - x3 + x4 >= 0

4x1 + 3x2 + 4x3 - 2x4 <= 3

-x1 - x2 + 2x3 + x4 = 1

x2, x3 >= 0

To find the dual, we introduce dual variables y1, y2, and y3 for the primal's three constraints, and w1 and w2 for the primal's two non-negativity constraints on x2 and x3, respectively.

The dual linear program is:

maximize 0y1 + 3y2 + y3

subject to:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The objective function of the dual is the sum of the products of the primal's objective coefficients and the dual variables, which gives 0y1 + 3y2 + y3. The new objective is to maximize this expression subject to the dual constraints.

Note that the dual program is also written in standard form, with all inequality constraints replaced by equality constraints and non-negativity constraints.

Know more about linear program here:

https://brainly.com/question/14161814

#SPJ11

Answer:

Add 6 to both sides.

Step-by-step explanation:

Remember you are trying to isolate the variable

The function returns the resulting vector of y values as a NumPy array.

Here is a Python implementation of a piecewise function that takes in a scalar or a vector and returns the corresponding y values:

import numpy as np

def piecewise_function(x):

   if isinstance(x, (int, float)):  # Check if scalar

       if x < -2:

           return x**2 - 1

       elif -2 <= x < 2:

           return np.exp(x)

       else:

           return np.sin(x)

   elif isinstance(x, np.ndarray):  # Check if vector

       y = []

       for elem in x:

           if elem < -2:

               y.append(elem**2 - 1)

           elif -2 <= elem < 2:

               y.append(np.exp(elem))

           else:

               y.append(np.sin(elem))

       return np.array(y)

   else:

       raise ValueError("Invalid input type. Must be a scalar or a vector.")

# Example usage

x_scalar = 3

y_scalar = piecewise_function(x_scalar)

print("Scalar output:", y_scalar)

x_vector = np.array([-3, 0, 3])

y_vector = piecewise_function(x_vector)

print("Vector output:", y_vector)

In this implementation, the function piecewise_function checks the type of the input (x) to determine whether it is a scalar or a vector. If it is a scalar, the function evaluates the corresponding piecewise equation and returns the resulting y value. If it is a vector, a for loop is used to iterate over each element of the vector, applying the piecewise equations and storing the y values in a list. Finally, the function returns the resulting vector of y values as a NumPy array.

Learn more about vector

https://brainly.com/question/28028700

#SPJ11

Answer:

It may be B

Step-by-step explanation:

2.5x means to multiply 2.5

The equation that describes the number of cups of food she eats in terms of days is

y = 5x.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation

We have,

Amount of food per day.

= 2 x 2.5

= 5 cups

Now,

The amount of food y in x days.

y = 5x

Thus,

The equation is y = 5x

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

The statement is TRUE. Extrapolation in regression analysis refers to using the line of best fit to predict values that lie outside the range of the observed data.

It involves extending the regression line beyond the observed data points to estimate values for variables that are beyond the range of the data. However, it's important to note that extrapolation can be risky because it assumes that the relationship between the variables continues outside the observed range, which may not always be valid. Extrapolation should be done with caution and its results should be interpreted carefully.

To know  more about variables visit:

brainly.com/question/29583350

#SPJ11

The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

For similar question on vertex.

https://brainly.com/question/1217219  

#SPJ8

Answer:

c

Step-by-step explanation:

Answer:

The total percentage loss would be 67%.

Step-by-step explanation:

Since we have given that

Rate of decline each year = 20%

Number of years = 5

We need to find the total percentage loss in value of the house at the end of 5 years.

So, Total percentage loss would be

Answer:

b

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 1 ← is in slope- intercept form

with slope m = 2

y = - \(\frac{1}{2}\) x - 7 ← is in slope- intercept form

with slope m = - \(\frac{1}{2}\)

• Parallel lines have equal slopes

the slopes are not equal thus not parallel

• the product of the slopes of perpendicular lines is equal to - 1

2 × - \(\frac{1}{2}\) = - 1

Thus the 2 lines are perpendicular to each other.

Answer:

0 ≤ t ≤ 18

Step-by-step explanation:

The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.

Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.

According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:

5t ≤ 93

This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.

Simplifying the inequality:

5t ≤ 93

Dividing both sides by 5 (since the coefficient of t is 5):

t ≤ 93/5

t ≤ 18.6

Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:

t ≤ 18

0 ≤ t ≤ 18

Answer: 0≤t≤12

Step-by-step explanation:

(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)

If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.

Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.

Answer:

Graph #1

Step-by-step explanation:

In this distance v time graph, a negative slope means moving toward Mr. Wilson, a positive slope means moving away from Mr. Wilson, and a flat section means staying at a particular location without moving.

Answer:

it's d

Step-by-step explanation:

≤ may refer to:

Inequality (mathematics), relation between values; a ≤ b means "a is less than or equal to b"

so the answer D is right because the face always ponit to the bigger number if x is -14 then this stament would be true

The present value of the continuous stream of income over 4 years, rounded to the nearest dollar, is $952,390.

To find the present value of a continuous stream of income, we can use the formula:

PV = C / r

where PV is the present value, C is the constant stream of income, and r is the interest rate.

In this case, C = $34,000 per year and r = 4%.

We need to find the present value over 4 years, so we can use the formula:

\(PV = C / r * [1 - 1/(1+r)^n]\)

where n is the number of years.

Plugging in the values, we get:

\(PV = $34,000 / 0.04 * [1 - 1/(1+0.04)^4]\)

\(PV = $34,000 / 0.04 * (1 - 0.8227)\)

\(PV = $34,000 / 0.04 * 0.1773\)

PV = $952,390.10.

For similar question on continuous stream.

https://brainly.com/question/28556500

#SPJ11

To determine the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base, we need to consider similar triangles.

Let's denote the radius of the smaller cone as 'r'. We can create a right triangle using the height of the smaller cone (4 feet), the height of the larger cone (10 feet), and the radius of the larger cone (11 feet).

In the larger cone, the ratio of the radius to the height remains constant. Therefore, we can set up the following proportion:

(r / 4) = (11 / 10)

Cross-multiplying the proportion, we have:

10r = 4 * 11

10r = 44

Dividing both sides by 10, we find:

r = 44 / 10

r = 4.4 feet

Therefore, the radius of the smaller cone created when a horizontal plane passes through the cone at exactly 4 feet from the base is 4.4 feet.

Learn more about: horizontal plane

brainly.com/question/30630905

#SPJ11

Answer:

128

Step-by-step explanation:

6 / 3 + 32 * 4 - 2.

We first calculate 6/3 and 32 * 4:

6 / 3 = 2

32 * 4  = 128

Our expression then becomes 2 + 128 - 2.

We can evaluate, getting 128.

Answer:

36

Step-by-step explanation:

6 ÷ 3 + 3^2 · 4 − 2

= 2 + 9 · 4 - 2

= 2 + 36 - 2

= 38 - 2

= 36

Answer:

  11.4

Step-by-step explanation:

You want the distance between C(-5, 5) and D(4, -2).

The distance formula is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, the distance is computed to be ...

  d = √((4 -(-5))² +(-2 -5)²) = √(81 +49) = √130

  d ≈ 11.4

The length of CD is about 11.4 units.

__

Additional comment

The distance formula is an application of the Pythagorean theorem. It computes the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.

Answer:

75 more people came from Wales than from Scotland.

Step-by-step explanation:

300 people attend

5 percent from scotland

300 * 0.05 = 15

30 percent from Wales

300 * 0.30 = 90

The term how "many more" means we are substracting scotland from wales

90 - 15 = 75