How to sketch graph of

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Math

SAT dread. 1. If n and p are integers greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p? a. 3 b.7. c.10 d. 13. e 30 2. The company sends a team of 3 plumbers to work on a certain job. The company has 4 plumbers and 4 trainees. 1 team has 1 ...

statistics

What does the area corresponding to the critical value zcrt mean? There is a graph that has a normal bell shape curve that has a vertical arrow that intersects the x axis far from the y axis. then everything to the left of the the vertical arrow is colored in blue. The ...

physics

A car accelerates from rest at a constant rate A for some time after which it retards at a constant rate B to come to rest. If the time elapsed is T second,calculate the maximum velocity reached?(please try solving this problem by plotting velocity time graph and if you can ...

physics

A car accelerates from rest at a constant rate A for some time after which it retards at a constant rate B to come to rest. If the time elapsed is T second,calculate the maximum velocity reached?(please try solving this problem by plotting velocity time graph and if you can ...

Algebra Variation Constant

What does this mean? Do I graph this or what? Find the variation constant and an equation of variation where y varies directly as x and y=12 when x=2 The variation constant =? The equation of variation is y=?

MATH

The height h (in meters) of a cannonball t seconds after it is fired into the air is given by h=-4t^2+16t+9. a) What is the initial height of the cannonball? What feature does this correspond to on the graph? b) Find the height of the cannonball after 1 second. c) What is the ...

calc volumes

the basse of a solid S is the region enclosed by the graph of y=square root (ln x), the line x=e, and the x-axis. if the cross sections of S perpendicular to the x-axis are squares, then the volume of S is. how do i find the side of the squares. because i got square root(lnx) ...

Chemistry

I am unsure exactly how to set up this calculation. From a graph that we got from getting different absorbances we took those points we got and got a equation for the best fit line. The equation was y = 760.8x + .02014 and the unknown absorbance equalled .254. We than wanted ...

English Speech

Derrick's social studies teacher assigned Derrick to present a report about the life of the nomadic peoples who live in Mongolia. Derrick decided that he would focus his report on their traditional homes, called gers. Which visual aids are most likely to be helpful? Select all...

Algebra

11. The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales. a) Write and graph a system of four inequalities that ...

statistics

An experiment with results acquired showed that at the beginning the temperature was 20 degrees and the size of bacteria was 1 mm long. 12 hours later the temperature was 56 degrees and the size of the bacteria was 12 mm long. Create a graph showing the size of the bacteria ...

calculus

This is from our problem set. f(x)= 2(x^3)-3(x^2)-12x+20 write an equation of the line perpendicular to the graph of f at x=0 I think i'm supposed to take the derivate of f and then find the slope of the tangent line at x=0. Then take the opposite reciporcal of that and put ...

CAlculus

The graph of the derivative, f '(x), is given. Determine the x-coordinates of all points of inflection of f(x), if any. (Assume that f(x) is defined and continuous everywhere in [-3, 3]. If there are more answer blanks than inflection points, enter NONE in any remaining spaces...

physics

A Bainbridge mass spectrometer is shown in the figure. A charged particle with mass m, charge |q|=3.2 ×10−19C and speed v=3 ×10@6 m/s enters from the bottom of the figure and traces out the trajectory shown in the fields shown. The only electric field E=11 ×103 V/m is...

physics

extrapolation is the process whereby we extend an established numerical relationship between two variables beyond the limits of our observed and recorded data. why extrapolation would not be useful and wise to use in force-elongation graph? In force-elongation, as one ...

math 157

For each set, develop and appropriately label a graph. Then write a short paragraph justifying your selection. Stress Units of Various Life Experiences Experience Stress Units Death of spouse 100 Divorce 73 Marital separation 65 Jail term 63 Death of family member 63 Personal ...

Physics

If object A starts 5m to the right of the orgin and moves to the right at 5m/s. And Object B starts 2m to the right of the orgin and moves to the left at 3 m/s. how do you draw a distance vs time graph for that?

Calculus

Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t - e^-t, correct? dy/dt = -t^2 - 5t, correct? So: Integral from 0 to 3 of Sqrt[(e^t - e^-t)^2 + (-t^2 - 5t)^2] Then what ...

Ed Tech Connexus

1.in Microsoft®️ execel graphs are refered to as? a. sparklines b. illustrations c. tables d. charts 2. What is one of the strengths of line graphs? a. line graphs show percentage of a whole b. line graphs show change over time c. line graphs compare values of individual ...

math help

can someone give me an example of what they mean about this problem. I have to come up with a real-world example where we can apply the concept learned within our chapter that the data could be linear which it talks about solving equations using the method of least squares ...

finite 2

A plant can manufacture 30 tennis rackets a day for a daily cost of $2100 and 50 rackets a day for $3000. Let y represent the cost and x represent the number of rackets. How much more does it cost to produce 31 than 30 rackets per day? Write your equation in the slope ...

Math

Student tickets to the Homecoming game cost $5 each. General admission tickets cost $8 each. So far, 150 tickets have been sold. $900 has been collected. A. Write a system of equations for this model in standard form. B. Graph the system. ( let each square represents 20 units...

chemistry

Cl2O2 (g)---> 2ClO (g) Time [Cl2O2] (M) 0....... 6.60*10^-8 172..... 5.68*10^-8 345..... 4.89*10^-8 517..... 4.21*10^-8 690..... 3.62*10^-8 862..... 3.12*10^-8 Determine the value of the first-order rate constant. For this question, you need to graph it on excel in order to...

Geometry

How do I write an equation of a line perpendicular to the graph of -2y + x =-5 that passes through the point at (1,2) Given the line -2y + x =-5, solve for y so the equation is in this form: y = mx + b Once you know the slope, m, you also know the slope of the perpendicular ...

math axis of symmety

What is the equation of the axis of symmetry of the graph with the order pairs of (-2,0) and (6,0). How would I do this since? I thought perhaps I could do -2+__=6 which would be 8 then 8/2 =4 so x=4 my brother says I'm suppose to do 6-2=4/2=2 so x=2 who's right or are we both...

Physics

The location of a car at times t1 and t2 is given by the position vectors r1= 15km due east + 20km due north (time t1) and r2= 13km due west + 25km due north (time t2) The units of distance are kilometers a. What is the magnitude l^rl of the displacement? b. What angle does ...

calculus

Please help me solve. I think increase = concave up and decrease = concave down? On the graph y = x^5-15x^3+10 for x what intervals is the function increasing, decreasing, concave up and concave down. Plot the critical points, plot and label the inflection points. Solve for ...

Math

Use the following table to answer the questions. (Give your answers correct to two decimal places.) x 1 1 3 3 5 5 7 7 9 9 y 3 2 6 1 3 3 3 2 5 3 (a) Find the equation of the line of best fit. y hat = + x (ii) Graph this equation on a scatter diagram. (Do this on paper. Your ...

Math

School is planning to purchase a new copy machine. The principal has narrowed the choice to two models. Superfast Deluxe and Quick Copies. He plans to purchase the machine that copies the quickest rate. Use this info to determine which one is faster. Quick copies: c=1.5t where...

physics

A car is stopped at a set of traffic lights. It takes off, accelerating at 4.5m/s2 until it is travelling at 60km/h. It maintains this velocity for 3 minutes before braking to a halt over 60m at another set of traffic lights. How far has the car travelled in this trip and how ...

Math

A survey of 594 studnets about the sports program at a school finds the following results: 495 students like the program 99 students think the program is inadequate. If a circle graph were made from the data, what would the measure of the central angle be for the group that ...

PHYSICS

In heavy rush-hour traffic you drive in a straight line at 12 m/s for 1.5 minutes, then you have to stop for 3.5 minutes, and finally you drive at 15 m/s for another 2.5 minutesPlot a position-versus-time graph for this motion. Your plot should extend from t=0 to t=7.5 minutes...

Calculus

Estimate the area under the graph of f(x) = 2x^3 + 3 from x= -1 to x=5, first using 6 approximating rectangle and right endpoints, and then improving your estimate using 12 approximating rectangles and right endpoints. When using the left and right endpoints, is there a ...

Physics

An object travels with a constant acceleration for 10 s. The vectors in Figure 3-41 represent the final and initial velocities. carefully graph the x component of the velocity versus time, the y component of the velocity versus time and the y component of the acceleration ...

Math

For the equation y = -6x, what is the slope and y intercept? The formula is y = mx + B. I know that m = the slope and B = the y intercept. So in the equation y = -6x, what is the slope and y intercept? Is -6 the y intercept or the slope? Because if it's the slope, How am I ...

Math

For the equation y = -6x, what is the slope and y intercept? The formula is y = mx + B. I know that m = the slope and B = the y intercept. So in the equation y = -6x, what is the slope and y intercept? Is -6 the y intercept or the slope? Because if it's the slope, How am I ...

statistics

The data set for the study is a sample of a survey conducted on the population of the American Intellectual Union (AIU). It is available via the following link: Excel 2007 DataSet with DataSet Key which contains the following nine sections of data that will be used throughout ...

statistics

The data set for the study is a sample of a survey conducted on the population of the American Intellectual Union (AIU). It is available via the following link: Excel 2007 DataSet with DataSet Key which contains the following nine sections of data that will be used throughout ...

ALgebra 1

4. Write the equation of a line whose slope is 6 and whose y intercept is -3. The answer would be y=6x-3 This is the y-intercept formula (y=mx+b) where m is the slope and b is the y-intercept. Thanx What about this one?Can you plz help? 6. What happens to the graph of the line...

Math 115 # 19

The following information shows a relationship between the speed of a certain car over a 100-mi test trip and the gas mileage obtained: Speed 40 45 50 55 60 gas millage 35 33 28 25 22 Use this information to make a line graph and then predict the gas mileage associated with a ...

Find the center (h,k) and radius

Find the center (h,k) and radius r of the circle and then use these to (a) graph the circle and (b) find the intercepts, if any. 3x^2+36x+3y^2=0

algebra

I NEED HELP ! Match the inequality to its graph. A. less than or equal to -1 B. less than 3 C. less than 1 D. less than or equal to -3 7. 4y + 3 *less than or equal to* y+6 8. -2y > 2 9. y over 3 < -1 10. 3y *less than or equal to* 2y +3

Math plz fast i really need it

Archie rolls two number cubes each with sides numbered 1 through 6 he then finds the sum of the numbers on the tops of the cubes which two sums have the same probabillity? A. 3 and 4 B. 5 and 9 C. 5 and 8 D. 10 and 12 i need the work involved and i have another question The ...

Math!

Let h(x)=4-x. Use h, the table, and points on graph to evaluate the expression. x 2 3 4 5 6 f(x) −1 0 1 2 3 g(x) points (-1,1), (2,3), (3,5) (a) (g^−1 compose f^ −1)(2) (b) (g^−1 compose h)(1) (c) (h^−1 compose f compose g^-1)(3)

Math Help Please

Solve and graph(using words)the inequalities.Then describe the graphs using words. Example:x>5andx<9.[There would be an open circle on the 5 and an open circle on the 9.The shading is between the 2numbers. My Problem: -6<x+3<6(Remember,this is an "and" statement) ...

math

Dental services. The national cost C in billions of dollars for dental services can be modeled by the linear equation C=2.85n+30.52, where n is the number of years since 1900 (Health Care Financing Administration,.a) find and interpret the C-intercept for the line.b)find and ...

Math Problem (please help)

Find all the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to discard any rational zeros that are obviously not zeros of the function. (Enter your answers as a comma-separated list.) f(x...

pre-calculus 11

I have a question that two ski decide to have a race. I need show a graph of height versus time of the two skiers going over a jump. I am assuming that both skiers graphs would be parabola's and have a maximum height with both graphs opening downward.

algebra the slope- intercept form

Find the slope and y-intercept for the graph of each equation: y=x-7 how would you solve this type of equation? i know that with an equation like: y=2x+4 that it would be m=2/1 and b=4. but how would you solve the first one.

math

What is the connection between the solutions of the equation ax^2 + bx + c = 0 and the x intercepts of the graph of f(x) = ax^2 + bx + c? The solution says: The solutions of the equation are the first coordinates of the x intercepts. I did the solutions to the formula but do ...

physics

The question has three parts, it looks like a lot but it is just description, trying to understand relationships. 1. You toss a coin straight up into the air. Sketch on the axes below the velocity-time acceleration-time graphs of the coin from the instant it leaves your hand ...

college

For each set of parameter values: - Calculate the optimal time to extract the resource - How do you find switchpoint/ transition point? - Calculate the Extraction path (Q0, Q1, etc.) - Calculate the MUC in each period - HOW DO U FIND MUC? - Calculate the optimal price in each ...

Statistics

create a report with the following: the mean score for each question, the mean score for the entire test, a graph that represents the scores for each question. Evaluate the test by using the information in your report and conducting qualitative item analysis and quantitative ...

Physics 141

A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is 100 s per increment, and the scale for the velocity axis is 110 m/s per increment.

algebra

what is the graph of 6X^2+6X-12>0? My solution is: an open circle over -2 going to infinite an open circle over +1 going to infinite is this correct?

math!

what is the vertical and horizontal difference between the two eqautions on a graph? Here are the eqautions... y=2x+3 y=2x-4 please help me on this. These two eqautions when graphed are parralell to each other. But im not sure how to calculate the difference in vertical and ...

math

what is the vertical and horizontal difference between the two eqautions on a graph? Here are the eqautions- y=2x+3 y=2x-4 please help me on this. These two eqautions when graphed are parralell to each other. But im not sure how to calculate the difference in vertical and ...

algebra

an advertising company made 15 million in 2002 and 22 million in 2003. in a bar graph of this data, the bar for 2002 is 3 inches high. How high should the bar for 2003 be to represent the data proportionally?

Algebra

Can you please check my answers? Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. x-2/x+1 <0 my answer: (-infinity,-1) u (2, infinity) -x+8/x-3 > or equal to 0 my answer: (3,8] 2/x-2<1 my ...

Calculus

Consider the function below. f(x) = [1-(4/x)]^x (a) Use a graph to estimate the value of the limit of f(x) as x approaches infinity. (Round the answer to two decimal places.) (b) Use a table of values of f(x) to estimate the limit. (Round the answer to four decimal places.)

Calculus

The altitude (in feet) attained by a model rocket t seconds into flight is given by the function h(t) = -1/3t^3 + 4t^2 + 20t + 2,for t _> 2 a)Find the maximum altitude attained by the rocket. b)Why does it not make sense to use this function after t = 16 seconds? Use the ...

Physics

A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is 100 s per increment, and the scale for the velocity axis is 330 m/s per increment.

science

The position-time graph for a tennis ball thrown vertically upwards from the second floor of a school building is shown below.ignore all effects of air friction.The height of the second floor is 6,5m.The ball rises 0,9 m from the point of projection before it starts to fall to...

Finance

Your 401 (k) Account at East Coast Yachts You have been at your job for East Coat Yachts for a week now and have decided you need to sign up for the company’s 401(k) plan. Even after your decision with Sarah Brown, the Bledsoe Financial Services Representative, you are still...

calculus

Consider a differentiable functionf having domain all positive real numbers, and for which it is known that f'(x)=(4-x)^-3 for x.0 a. find the x-coordinate of the critical point f. DEtermine whether the point is a relative maximum or minomum, or neither for the fxn f. justify ...

Geometry

How do I find the distance between (-9,3) and (-1,-5) By using the Pythagorean theorem. The line between the two points is the hypotenuse of a triangle with perpendicular side lengths of 8 in the x direction and 8 in the y direction. The 8's come from the differences in x and ...

Parabola/Hyperbola

Not really for homework help, but just for curiousity. Is there a way to distinguish whether the graph is a parabola or a hyperbola if you do not know the equations and one side of the hyperbola is missing (so there's just one U shape) by restricting the domains or ranges. I ...

Algebra

2. The Sugar Sweet Company is going to transport its sugar to market. It will cost $4200 to rent trucks, and it will cost an additional $150 for each ton of sugar transported. Let C represent the total cost (in dollars), and Let S represent the amount of sugar (in tons) ...

math

The Sugar Sweet Company is going to transport its sugar to market. It will cost 4550 to rent trucks, and it will cost an additional 175 for each ton of sugar transported. Let c represent the total cost (in dollars), and let s represent the amount of sugar (in tons) transported...

Algebra

For each diagram find the relationship between the number of shapes and the perimeter of the figure they form. Represent this relationship using a table, words, an equation, and a graph. Below there are 3 sets of Pentagon's there is one by itself with the number one on each of...

math help needed bad

I'm really confused on how to answer this question. Can someone help me to figure this out? Thank you A survey about the student government program at a school finds that of 245 students: -218 like the program -27 students think this program is unnecessary. If a circle graph ...

math-inequalities

Hi, I am having some problems with inequalities. It is asking us to solve and graph on a number line and then write it in interval notation and set notation. X>2 and X>4 I graphed them in a number line already and i have the following: Interval notation (2,infinity) and ...

Calculus (Normal Line, please check my work)

The slope of the line normal to the graph of 4 sin x + 9 cos y = 9 at the point (pi, 0) is: Derivative: 4cosx - 9siny(dy/dx) = 0 (dy/dx) = (-4cosx) / (-9siny) (dy/dx) = (4) / 0 Normal line = -1 / (4/0) Does this mean that the slope of the normal line is undefined, or did I do ...

Physics

A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is 60 s per increment, and the scale for the velocity axis is 270 m/s per increment.

ecoc

i can not figure this out the economist for the grand corporation has estimated the company's cost function, using time series data, to be TC=50+16Q-2Q2+0.2Q3 a.plot this curve for quantites 1 to 10 b.calculate the average total cost,average variable cost, and marginal cost ...

Graph constraints

Suppose that there is a model with two constraints 1) 120x1+160x2 <=(less than or equal to)450 2) 3x1+10x2 <= 25 and there is a third constraint called min. requirement, orginally this constraint is: 37x1+65x2 >= (greater than or equal to)120 I have to find all values...

Math

Tino conducted a survey of all the eighth graders in his school for his math project.  He asked each student how much he or she spent on school supplies at the beginning of the year (rounded to the nearest dollar).  He also calculated the average amount spent and found it to...

Chemistry

I am doing a lab on enthaply of vaporization of water, I got everything else on the post lab but these two questions, please help. The deltaHvap data from the handbook reference vary with temp. 1) if your data were perfect, but deltaHvap is not constant, how would this show up...

Math(Please help)

1) where is the function f(x)= 5 / (2x-4)^3 increasing. I know the answer is for all of x but I do not know how to get this. I know that you can write the equation as 5(2x-4)^-3 2) Let a, b, and c be fixed with a>0 and let f(x)=ax^2 + bx + c. Which of the following ...

Math-Help

A rock is tossed straight up into the air. The height h (in feet) t seconds after it is tossed is given by the function: h(t)=-16t^2+100.4t+5.1 (a) Make a table of values for 0 to 10 seconds. (b) Graph the function. (c) What is the initial height of the rock? (d) When did the ...

Physics

On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.30 N/cm. The graph in the figure shows the acceleration of the glider as a function of time. Find the mass of the glider. Find the maximum displacement of the glider ...

economics

Suppose 15 peaches and 20 oranges need to be divided between fred and ethel. Fred's utility function is U=Max(#of peaches, #of oranges) ethels utility function is U=Max(2# peaches, # of oranges). Carefully draw a graph showing the set of Pareto efficient allocations.

Math (equation of tangent line)

Consider the implicit equation 2xy-1=(x+y+1)^2 a) Compute and solve for the derivative dy/dx as a function of x and y. b) Find the equation of the tangent line to the graph of the above when y=-1. For part a, I found the derivative being equal -(x+1)/(y+1) but how would I find...

Physics please clarify

Posted by Mary on Monday, September 24, 2007 at 10:11pm. A cube is located with one corner at the origin of an x, y, z, coordinate system. One of the cube's faces lies in the x, y plane, another in the y, z plane, and another in the x, z plane. In other words, the cube is in ...

chemical kinetics

2H2O2 --->2H2O + O2 What is the instantaneous rate of formation of O2 at 50s? THeres a graph with the concentration of H2O2 as a function of time. at 50s the conc. is .2 But isnt this the concentration of H2O2, I don't understand. Also what is the difference between ...

math

how are and 3 4th bours and the distance traveled in 2 3 4th hours represented in the table?how are they shown on the graph? Having read the next four or five posts, I suggest you do two things: 1. Start over and write a complete question for each post. Fragments of questions ...

Math

Graph the equations below accurately. Find the point of intersection of the two lines. You will type your x value in the first part and the y value in the second part of the question. If the answer if no solution then type NS in both parts and if the the answer is infinite ...

Graph Theory/ Algorithms / Computer science

I am working on this problem from the book, Data Structures & Algorithm Analysis in C++. The problem is: 9.40 Give a polynomial-time algorithm that finds ceil(V /2) vertices that collectively cover at least three-fourths (3/4) of the edges in an arbitrary undirected ...

algebra 2

1) In the general second-degree equation Ax^2 + Bxy + Cy^2 + Dx + Ey = F = 0, what is the discriminant and what does it tell you about the graph of the equation? 2) Which terms in a general second-degree equation (Ax^2 + Bxy + Cy^2 + Dx + Ey = F = 0) are used to find the ...

physics

A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is 30 s per increment, and the scale for the velocity axis is 50 m/s per increment.

algebra

You are trying to compare the Farenheit and Celcius scales and you have two examples; Temperatur A is 50 degrees Celcius and 122 Farenheit. Temperature B is 100 degrees Celcius and 212 degrees Farenheit. What graph models the relationship between Farengeit and Celcius scales? ...

calculus

A trough is 9 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x4 from x=−1 to x=1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water ...

college geomrtry

What are the differences between linear and quadratic equations? How are these differences displayed in a graph? Write a brief scenario that can be modeled with a linear equation. Summarize a situation modeled by a quadratic equation. Are there equations that are neither ...

Alg 1

You have 60 megabytes of space left on your portaable media player. You can choose to download song files that use 3.5 megabytes or video files that use 8 megabytes. You want to download at least 12 files. What is a graph showing the numbers of songs and video files you can ...

precalc

For the graph y=2, what is the: A) Domain B) Range C) X values of all zeroes D) Equations of all asymptotes E) 1 to 1 or not F) Continuous or not (if continuous tell where) G) Increasing, decreasing, both (if both tell where), or neither H) Bounded above, bounded below, ...

Algebra2

Complete parts a – c for each quadratic function: a. Find the y-intercept, the equation of the axis of symmetry and the x- coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. 1. f(x) = 2x^2 2. f(x) = x^...

probability

Make a histogram showing the binomial probability distribution for the following: A waiter at the Green Spot resturant has learned from long experience that the probability that a lone diner will leave a tip is only 0.7. During one lunch hour he serves six people who are ...

Math

Question: A tunnel with a parabolic arch is 12 m wide. If the height of the arch 4 m from the left edge is 6 m, can a truck that is 5 m tall and 3.5 m wide pass through the tunnel? Justify your decision. I drew the graph of the arch with x-intercepts (0,0) and (12,0) , and ...

Calculus grade 12 exam review PLEASE HELP ASAP !!

PLEASE HELP ME! Exam is in an hour and i need to finish this exam pre-test to help me ! consider the function y = 2sinx a) determine dy/dx b) calculate the exact value of x for which the slope of the tangent to the graph is √2 in the interval [0, pie] c) determine the ...

physics

I'm suppose to draw velocity time and acceleration time graph for a rocket that is launched vertically into the air and falls back down to its initial height. We are to assume that x axis is up. So would I draw an curved figure like a downward parabola or a straight vertical ...

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