A rocket leaves the surface of Earth at time t=0 and travels straight up from the surface. The height, in feet, of the rocket above the surface of Earth is given by y(t), where t is measured in seconds for 0≤t≤600. Values of y(t) for selected values of t are given in the table above. Of the following values of t, at which value would the speed of the rocket most likely be greatest based on the data in the table?
(1) t=100
(2) t=200
(3)t=300
(4) t=400
Answers
Answer:
Remember that:
Speed = distance/time.
Then we can calculate the average speed in any segment,
Let's make a model where the average speed at t = t0 can be calculated as:
AS(t0) = (y(b) - y(a))/(b - a)
Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.
Then:
if t0 = 100s
AS(100s) = (400ft - 0ft)/(200s - 0s) = 2ft/s
if t0 = 200s
AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s
if t0 = 300s
AS(300s) = (3200ft - 400ft)/(400s - 200s) = 14ft/s
if t0 = 400s
AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s
So for the given options, t = 400s is the one where the velocity seems to be the biggest.
And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.
Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.
Speed is simply the rate of change of distance over time.
The greatest speed is at [tex]t = 400[/tex]
To calculate the time of the greatest speed, we simply calculate the slope between each interval.
The slope (m) of a line is:
[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]
When [tex]t = 100[/tex]
[tex](t_1,y_1) = (0,0)[/tex]
[tex](t_2,y_2) = (200,400)[/tex]
So, we have:
[tex]m = \frac{400-0}{200 -0}[/tex]
[tex]m= \frac{400}{200}[/tex]
[tex]m = 2[/tex]
When [tex]t = 200[/tex]
[tex](t_1,y_1) = (100,50)[/tex]
[tex](t_2,y_2) = (300,1360)[/tex]
So, we have:
[tex]m = \frac{1360-50}{300 -100}[/tex]
[tex]m = \frac{1310}{200}[/tex]
[tex]m = 6.55[/tex]
When [tex]t = 300[/tex]
[tex](t_1,y_1) = (200,400)[/tex]
[tex](t_2,y_2) = (400,3200)[/tex]
So, we have:
[tex]m = \frac{3200-400}{400 -200}[/tex]
[tex]m = \frac{2800}{200}[/tex]
[tex]m = 14[/tex]
When [tex]t = 400[/tex]
[tex](t_1,y_1) = (300,1360)[/tex]
[tex](t_2,y_2) = (500,6250)[/tex]
So, we have:
[tex]m = \frac{6250-1360}{500-300}[/tex]
[tex]m = \frac{4890}{200}[/tex]
[tex]m = 24.45[/tex]
From the above computation, the greatest speed (i.e. slope) is
[tex]m = 24.45[/tex]
The corresponding time at [tex]m = 24.45[/tex] is [tex]t = 400[/tex]
Hence, the greatest speed is at [tex]t = 400[/tex]
Read more about speed at:
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Related Questions
6.1+
4.55+
1.09 +
15.9+
3.771
Answers
Answer:
31.411
Step-by-step explanation:
6.1+4.55+1.09+15.9+3.771= 31.411
A television sells for $550. Instead of paying the total amount at the time of the purchase, the same television can be bought by paying $100 down and $50 a month for 14 months. How much is saved by paying the total amount at the time of the purchase? PLEASE HELP ME !
Answers
Answer:
250 Dollars
Step-by-step explanation:
100 down + 50 x 14
100 +700= 800
800-550= 250
$150 is saved by paying the total amount at the time of purchase.
In parallelogram RELA you are given that the measure of angle R = 110 degrees. Find the measure of angle L.
Answers
Answer:
L = 110 degrees
Step-by-step explanation:
all angles in a parallelogram are congruent
Answer:
How are you in college
Step-by-step explanation:
1 + 1 = 2
John left his house in Irvine at 8:35 a.m. to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50 a.m.. At 5:30 p.m. he left the meeting and drove home. He arrived home at 7:18 p.m.ⓐ What was his average speed on the drive from Irvine to Los Angeles? ⓑ What was his average speed on the drive from Los Angeles to Irvine? ⓒ What was the total time he spent driving to and from this meeting
Answers
A. The average speed was 36 mph.
B. The average speed on the drive from LA to Irvine was 25mph.
C. The total time he spent driving to and from the meeting was about 3 hours and 5 minutes.
Given below are a collection of scores on a spelling test: 5,6,10,8,3,5,9,8,7,4,6,5,3,7,9,5,6,4,5,6,7,5,4,6 a.) construct a frequency distribution b.) compute the relative frequencies. c.) compute the culmuative frequencies.
Answers
A coffee stand sells cups of coffee for $6 and cups of tea for $3. Tuesday a total of 75 cups were sold and the total money collected was $312. How many cups of coffee and how many cups of tea were sold
Answers
Answer:
46 Teas and 29 Coffees
Step-by-step explanation:
46×3= 138
29×6= 174
174+138=312
¿Cuántas libras de café “La Finca” que se vende a $5 la libra debe mezclarse con 80 libras decafé común que se vende a $2 la libra, para hacer una mezcla que se venda a $3 la libra?
Answers
Answer:
Necesitamos agregar 40 libras del café La Finca
Step-by-step explanation:
Sea x el número de libras de café de La Finca a mezclar.
Entonces, la cantidad total de libras que obtendremos en la mezcla será (x + 80) libras.
Ahora trabajemos con los precios; Tenemos x libras de La Finca a $ 5 por libra, con 80 libras de café a $ 2 por libra para dar una mezcla de (x + 80) a $ 3 Así, sumaremos el precio de La Finca más la otra variante para llegar al costo de la nueva mezcla.
Matemáticamente;
5 (x) + 2 (80) = 3 (x + 80)
5x + 160 = 3x + 240
5x -3x = 240-160
2x = 80
x = 80/2 x = 40
find the indicated unknown angle measure.
Answers
Answer:
Pretty sure it's 47°
which polynomial represents the company’s total output?
Answers
Answer:
C. 2b^3 + b^2 - 2b - 380
Step-by-step explanation:
Factory A: 2b^3 - 3b^2 + b - 120
Factory B: 4b^2 - 3b - 260
Add the polynomials:
2b^3 - 3b^2 + b - 120 + 4b^2 - 3b - 260 =
Be careful to combine like terms.
= 2b^3 - 3b^2 + 4b^2 + b - 3b - 120 - 260
= 2b^3 + b^2 - 2b - 380
Answer: C. 2b^3 + b^2 - 2b - 380
Name the set or sets of numbers to which the square root of 28 belongs to.
Answers
Hope this helped! Brainliest?
Solve the equation for y in terms of x
12x + 3y = 12
Answers
Answer:
y = 4 - 4x
Step-by-step explanation:
Step 1: Write equation
12x + 3y = 12
Step 2: Subtract 12x on both sides
3y = 12 - 12x
Step 3: Divide both sides by 3
y = 4 - 4x
Answer:
12x + 3y = 12
3y=12-12x
y=(12-12x)/3=3(4-4x)/3=4-4x
How many places do you need to move the decimal to the left to write the number below in the scientific notation?
Answers
Answer:
10
Step-by-step explanation:
in scientific notation a number cant be greater than 10. so you have to move the decimal to make it under 10.
.48 covert to fraction
Answers
Answer:
12/25
Step-by-step explanation:
explanation: Since there are 2 digits in 48, the very last digit is the "100th" decimal place. So we can just say that . 48 is the same as 48/100. terms by dividing both the numerator and denominator by 4.
Someone please help me.
Answers
Answer:
1 is good number 2 is wrong number 3 is good
Step-by-step explanation:
your welcome im juss writting more so it wont say issa short question!!
PLEASE HELP FAST...The dot plots show the numbers of children’s books purchased by customers at two different bookstores on one day which statement is supported by the information in the dot plots
Answers
Answer:
The mode of the data for Store 2 is greater than the mode of the data for Store 1.
Step-by-step explanation:
The mode of store 2 greater than mode of store 1.
What is box- plot?A box plot, commonly referred to as a box and whisker plot, is a form of chart that is frequently used in explanatory data analysis in descriptive statistics. Box plots use the data's quartiles (or percentiles) and averages to visually depict the distribution of numerical data and skewness.
Given:
Dot plots show the numbers of children’s books purchased by customers at two different bookstores.
Now, from the given figure
The mode of store 1 is 3
and, mode of store 2 is 4.
Hence, the mode of store 2 greater than mode of store 1.
Learn more about box- plot here:
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Pattern in this sequence
1,1+3,1+3+5,1+3+5+7, ...
Answers
Answer:25
Step-by-step explanation:
1 , 1+3 ,1+3+5 ,1+3+5+7,_
1 , 4 , 9 , 16 ,_
From 1 to 4 there is a difference of 3
From 4 to 9 there is a difference of 5
From 9 to 16 there is a difference of 7
From 16 to x there should be a difference of 9 because all the differences mentioned above are all odd numbers so that is the pattern in the sequence
16+9=25
g The following scatterplot shows the 20 top-selling cars with their weight on the horizontal axis and their miles per gallon (mpg) on the vertical axis. The overall direction of this data is __________. The strength of the association is __________. a.) positive; weak b.) positive; strong c.) negative; strong d.) negative; weak
Answers
scatterplot relating to the question is attached below.
Answer: Negative ; Strong
Step-by-step explanation:
From the picture of the scatter plot Given, it could be observed that the trend of the scatter points exhibits a negative gradient as the points on the graph slopes downward depicting that an inverse relationship exists between the two variables. With weight decreasing as miles per gallon increases. The relationship between the two variables depicted by the scatter plot is strong as the slope of the point is looks moderately steep.
Hi, can someone answer this?
Answers
Answer:
I think its D
Step-by-step explanation:
the 2 on top of the b equals 400.
400 times 400 = 160,000
( Hope this helps! )
The mean of data set A ls 43.5 and the MAD is 3.7. The mean of data set B is 12.8 and the MAD is 4.1.
1. Which data set shows greater variability? Explain your reasoning
Answers
Answer:
Data Set B
Step-by-step explanation:
Mean Absolute Deviation(MAD) can be defined as the distance between one data point (value) to the Mean in a give Data set
It can also be defined as the deviation of the mean from the data points or values given in a data set.
From the above question, we are told that:
The mean of data set A ls 43.5 and the MAD is 3.7.
The mean of data set B is 12.8 and the MAD is 4.1.
Comparing the two Data set, the Mean Absolute Deviation of Data set A is smaller than that of Data set B.
Hence, Data set B shows a greater degree of variability because the distance between a data point(value) and the mean is 4.1. This also means that the data points in Set B are more spread out compared to the data points in Set A.
Answer:
b
Step-by-step explanation:
0.0605 in standard form?
Answers
Step-by-step explanation:
Actually 0.0605 is already in standard form and it can be expressed in scientific notations as given below.
[tex] \huge0.0605 = 6.05 \times {10}^{ - 2} \\ [/tex]
What is 1+1 this is for those who need to answer questions to ask a question
Answers
Answer:
2
Step-by-step explanation:
1+1=2
(thank you dude!)
Answer:
2, and thank youuu:)
Step-by-step explanation:
A triangle measures 12 degrees and 40 degrees what is the measurement of the 3rd angle of the triangle
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{128°}}}}}[/tex]
Step-by-step explanation:
Sum of angles of triangle add up to 180°
Let the third angle be x
Create an equation and solve for x
[tex] \sf{x + 12° + 40° = 180°}[/tex]
[tex] \dashrightarrow{ \sf{x + 52° = 180°}}[/tex]
[tex] \dashrightarrow{ \sf{x = 180° - 52°}}[/tex]
[tex] \dashrightarrow{ \boxed{\sf{x = 128°}}}[/tex]
Hope I helped!
Best regards! :D
please help me answer this question
Answers
Answer:
false
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
In order for two triangles to be congruent, they must have the exact same side lengths and angle measures. In this case, you know that the angles of the triangles are equal, but you are not given side lengths. In math, you can never assume that the lengths are equal just because they look like it. Therefore, the answer is B. False because you do not know a single side length. In the future, review the rules of congruent triangles: SAS, ASA, SSS, AAS, HL where S = side, A = angle, H = hypotenuse, L = leg.
Solve for x: 3.8x − 2(x − 9) = 4.4x + 5
Answers
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
So we have the equation:
[tex]3.8x-2(x-9)=4.4x+5[/tex]
Distribute the -2:
[tex]3.8x+(-2x+18)=4.4x+5[/tex]
Combine like terms on the left:
[tex]1.8x+18=4.4x+5[/tex]
Subtract 1.8x from both sides. The left cancels:
[tex]18=2.6x+5[/tex]
Subtract 5 from both sides. The right cancels:
[tex]13=2.6x[/tex]
Divide both sides by 2.6:
[tex]x=13/2.6[/tex]
Simplify (multiply both layers by 10 to get rid of the decimal):
[tex]x=130/26[/tex]
Reduce (divide both layers by 26):
[tex]x=5[/tex]
So, the value of x is 5.
Answer:
5
Step-by-step explanation:
Step 1:
3.8x - 2 ( x - 9 ) = 4.4x + 5
Step 2:
3.8x - 2x + 18 = 4.4x + 5
Step 3:
1.8x + 18 = 4.4x + 5
Step 4:
18 = 2.6x + 5
Step 5:
13 = 2.6x
Answer:
5 = x
Hope This Helps :)
if I spend 6/11 of my money on books what fraction of it will remain
Answers
the number of hours you work in a week.
Answers
Answer:56 hours a week is what you have to work 8 hours a day 7 days a week
Answer and I will give you brainiliest
MATH
Answers
Answer:
I think that the answer would be question 3
Step-by-step explanation:
I think i remember doing this question
the floor of a house is shaped like a parallelogram the height of the parallelogram is 8 feet less than the base. the base is 48 feet. the length of the other side of the parallelogram is 45 ft what is the area of the floor?
Answers
Answer:
1920 ft^2
Step-by-step explanation:
base = 48 ft
height = 48 ft - 8 ft = 40 ft
area = base * height
area = 48 ft * 40 ft
area = 1920 ft^2
A construction worker estimates that a kitchen remodel will take 1 person 200 hours. If 5 people work on the job for 8 hours a day, how many days will it take for them to complete the job?
Answers
Answer:
5 days
Step-by-step explanation:
Multiply 8 hours by 5 people to get a total of an equivalent of 40 hours of work per day. 200/40 is equal to 5, so it would take them 5 days
Answer:
It will take them five days.
Step-by-step explanation:
So what I did was I multiplied 5 and 8 because there were 5 people and I'm taking it that each person worked 8 hours a day. So after multiplying that, I got 40. I then divided 40 by 200 and I got 5.
A company produces 4.56 times 10 Superscript 3 light bulbs each week. Written in scientific notation, which is the best estimate of how many light bulbs the company will make in 9.36 times 10 Superscript 2 weeks?
4.5 times 10 Superscript 1 light bulbs
1.4 times 10 Superscript 5 light bulbs
4.5 times 10 Superscript 6 light bulbs
45 times 10 Superscript 6 light bulbs
Answers
(C) 4.5 times 10 Superscript 6 light bulbs
Answer:
4.5 times 10 Superscript 6 light bulbs
Step-by-step explanation:
I took the test (: