Jeremy analyses one of his parachute jumps. He draws a graph showing his velocity up to the opening of his parachute. a) Estimate Jeremy's acceleration at t = 10s to 1 decimal place. b) Estimate his average speed for this part of the jump. Give your answer to two significant figures.
Answers
Answer:
Jeremy's acceleration is about [tex]1\,\frac{m}{s^2}[/tex] at t =10 s
His average speed is about 44.5 m/s in this section of his jump approximating with points on the curve (under-estimate)
His average speed is about 46 m/s if using the tangent line (over estimate)
Step-by-step explanation:
Jeremy's acceleration can be estimated by the curve's derivative at that point. That is the slope of the tangent line to the velocity curve at x = 10 sec. Please see attached image where the tangent line is drawn in orange, and the points to use to calculate its slope are drawn in green.
These points are : (6, 42) and (14,50) which using the slope formula give:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}= \frac{50-42}{14-6}=\frac{8}{8} \frac{m}{s^2} = 1\,\frac{m}{s^2}[/tex]
So his acceleration at that point is about [tex]1\,\frac{m}{s^2}[/tex]
Now, using about the same interval of x-values (from 6 to 14), the corresponding speeds are approximately: 40 (for time 6 seconds) and 49 (for time 14 seconds (look for the red dots on the attached image). Since the average velocity is given by the integral of the function between those points divided by the length of the interval where it is calculated:
[tex]v_{average}=\frac{area}{interval\,\,length}[/tex]
and we don't have the actual velocity function to estimate the integral, we can approximate this area by that of a trapezoid that connects the red dots with the bottom of the horizontal axis (see red trapezoid in the image). Clearly from the image, this approximation would give us an under-estimate of the actual average speed.
The area of this trapezoid is: approximately:
[tex]Trapezoid\,\, area=(49+40)\,8/2=356[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{356}{8} \frac{m}{s} =44.5\,\frac{m}{s}[/tex]
If the area is approximated instead with the trapezoid form by the green points we used to calculate the acceleration (this would give us an over-estimate):
[tex]Trapezoid\,\, area=(50+42)\,8/2=368[/tex]
Then the average velocity estimated from it is:
[tex]v_{average}=\frac{368}{8} \frac{m}{s} =46\,\frac{m}{s}[/tex]
while his actual instantaneous velocity seems to be about 46 m/s from the graph
Answer:
a) 1.0
b) s=45
Step-by-step explanation:
Related Questions
Given f(x) = 4x3 − 12x2 + 40x + 12, find f(–2).
Answers
Hey there! :)
Answer:
f(-2) = -148.
Step-by-step explanation:
To calculate f(-2), simplify substitute -2 for x in the equation. Therefore:
f(x) = 4x³ -12x² + 40x + 12
Becomes:
f(-2) = 4(-2)³ - 12(-2)² + 40(-2) + 12
Simplify:
f(-2) = 4(-8) - 12(4) - 80 + 12
f(-2) = -32 - 48 -80 + 12
Finally, you get:
f(-2) = -148.
The Retained earnings account has a credit balance of $54,000 before closing entries are made. Total revenues for the period are $72,200, total expenses are $48,300, and dividends are $15,800. What is the correct closing entry for the revenue accounts?
Answers
Answer: $62100
Step-by-step explanation:
The following can be deduced from the information given in the question:
Credit balance = $54000
Total revenues = $72,200
Total expenses = $48,300
Dividends = $15,800
Closing entry= Credit balance + Total revenues - (Total expenses + Dividends)
= $54000 + $72,200 - ($48300 + $15800)
= $126200 - $64100
= $62100
Determine the exact value of sin 0
Answers
Answer:
36.87°
Step-by-step explanation:
[tex] \sin \theta = \frac{3}{5} \\ \\ \sin \theta = 0.6 \\ \\ \theta = {sin}^{ - 1} (0.6) \\ \\ \theta = 36.869897646 \degree \\ \\ \theta = 36.87 \degree[/tex]
Same-side interior angles form when a transversal intersects with two parallel lines, making the same-side interior angles supplementary.
O True
O False
Answers
select all that are equal to 5^3*5^-7
a. 1/5^-4
b. 1/5^4
c. 5^-4
d. 5^4
e. 1/-625
Answers
Answer:
5^3*5^-7 = 1/5^4 b. is true = 625
5^3*5^-7 = 5^-4 c. is true = 625
Step-by-step explanation:
b. Left hand side
Simplify the following:
5^3/5^7
Combine powers. 5^3/5^7 = 5^(3 - 7):
5^(3 - 7)
3 - 7 = -4:
5^(-4)
5^4 = (5^2)^2:
1/(5^2)^2
5^2 = 25:
1/25^2
| 2 | 5
× | 2 | 5
1 | 2 | 5
5 | 0 | 0
6 | 2 | 5:
Answer: 1/625
Right hand side:
Simplify the following:
1/5^4
5^4 = (5^2)^2:
1/(5^2)^2
5^2 = 25:
1/25^2
| 2 | 5
× | 2 | 5
1 | 2 | 5
5 | 0 | 0
6 | 2 | 5:
Answer: 1/625
_____________________________
c. Left hand side (see above)
Right hand side:
Simplify the following:
5^(-4)
5^4 = (5^2)^2:
1/(5^2)^2
5^2 = 25:
1/25^2
| 2 | 5
× | 2 | 5
1 | 2 | 5
5 | 0 | 0
6 | 2 | 5:
Answer: 1/625
Answer:
The answers are B and C. The other person is wrong.
Step-by-step explanation:
it’s two multi choice questions please help
Answers
Answer:
see below
Step-by-step explanation:
a) They could be congruent because having the same angles doesn't necessarily mean that they are congruent.
b) These triangles are congruent by ASA because using the sum of angles in a triangle they have the same angles and one congruent side.
Answer:
a) F
b) C
Step-by-step explanation:
Brainliest please?
For a) it only tells you all the angles, which makes them similar triangles, but none of the sides are given, so it cannot be determined whether they are congruent.
For b) it is not to scale and using a little subtraction, you can quickly use the fact that there are 180 degrees in a triangle, you can determine that the 2 triangles have the same angles, with the side with 9.2 cm between 58 and 68 degree vertices on both triangles, making the 2 triangles congruent by ASA.
QED
Uma lousa digital possui uma forma retangular e tem sua largura expressa pelo polinômio b+2. Sendo sua área igual ao polinômio B ao quadrado + 5b+ 6, qual é o polinômio que expressa a altura dessa lousa?
Answers
Answer:
b+3
Step-by-step explanation:
Largura : b+2
Área: b² +5b +6
Sabe-se que a área de um retângulo é dada pela largura multiplicada pela altura.
A partir dos zeros da equação da área é possível encontrar o polinômio da altura:
[tex]b^2 +5b +6\\b=\frac{-5\pm \sqrt{25-4*1*6} }{2} \\b'=-2\\b''=-3[/tex]
Visto que o polinômio da largura é b+2, para que a equação da área seja válida, o polinômio da altura deve ser b+3.
A prova pode ser feita pela multiplicação dos polinômios:
[tex]A = L*H\\A=(b+2)*(b+3)\\A=b^2+5b+6[/tex]
Find the next three terms in the geometric sequence: 72, 36, 18,... (sorry for bothering a lot)
Answers
Answer:
18 / 2 = 9
9 / 2 = 4.5
4.5 / 2 = 2.25
The next three terms are 9,4.5,2.25
Hope this helps
Step-by-step explanation:
Suppose a group of 24 people bought tickets to the American Kennel Club Museum of the Dog. Tickets cost $15 each for adults, $10 each for students, and $5 each for children under age 12. There were twice as many adults as children under age 12. If the total cost of the tickets was $260, how many tickets were purchased for children under age 12? *
Answers
Answer: 50
Step-by-step explanation:
In order to participate in the end of the year filed trip, the students at Francis Scott Key need
to fundraise $1200. They plan to have a fajita dinner. They have enough food to serve 240
people. They are charging adults $6 per plate, and students only have to pay $2 per plate.
How many adults and children need to buy a plate in order for them to exactly meet their
goal?
Answers
Answer: 60 kids, 180 adults
Step-by-step explanation:
Let x be the number of children and y be the number of adults eating.
If they have 240 people eating then x+y=240.
If they have to fundraise 1200 then 2x+6y=1200.
Solving the system of equations, we can multiply the first equation by 2 to get 2x+2y=480. Then subtract the two equations and get -4y=-720, so y=180. Substitute y=180 back in to get x=60.
Hope that helped,
-sirswagger21
anyone know thus multiple question.... yes you , i know you've saw this , your reading now ... please help (if you can of course )
Answers
Answer:
if union, U means plus,+
if intersect means minus, -
A bag contains 2 red, 5 blue, and 2 white marbles. Find the probability of randomly picking a red marble, keeping the marble, and then picking a blue marble.
A) 7/8
B) 10/81
C) 5/36
D) 1/9
Answers
Answer:
5/36
Step-by-step explanation:
There are 9 marbles in the bag
P( red) = number of red / total
= 2/9
Keep the marble
1 red, 5 blue, and 2 white = 8 marbles
P( blue) = number of blue / total
= 5/8
P(red, keep,blue) = 2/9 * 5/8 = 10/72 = 5/36
Jonathan bought a table and some chairs and a furniture store. The equation that models the situation is Y equals 25X +80, where why is the amount of money he spends and X is the number of chairs he bought. What does the Y intercept mean in the situation?
Answers
Answer:
Step-by-step explanation:
The equation modeling the situation is ;
y = 25x + 80
We want to know what the y-intercept mean in this question
Mathematically, the equation of a straight line is ;
y = mx + c
where c is the y intercept and m is the slope
What we should understand is that at the y intercept which is 80 here, the value of x is 0
Now since y means the amount of money spent and x is number of chairs bought, the value 80 means that the amount spent when he bought 0 number of chairs is 80
Now going by the question, since he bought 0 chairs here and we still have some cost, definitely he spent the money on other things which of course might be the amount spent in purchasing some tables
Picture attachment is below
Answers
Answer:
0.04
Step-by-step explanation:
Answer:0.04
Step-by-step explanation:4/100
Elsa sold 37 pairs of earrings for $20 each at the craft fair. She is going to use 1/4 of the money to buy new CDs and is going to put the rest of the money in her savings account. How much money will she put in her savings account?
Let “s” stand for he amount of money saved
1. Equation:
2. How much money did she spend on CDs?
3. How much money did she out in her savings account?
Answers
Answer:
185 -> Spent on new CD's
$ 555 -> Savings Account
Steps:
37*20 = 740/4 = 185 -> Spent on new CD's
740 - 185 = $ 555 -> Savings Account
Description:
The 2 question is asking that how much money did she spend on her CD. We times 37 and 20 = that will equal 740 then we divide 740 by 4 = 185. Meaning we just solved for question 2. Answer is 185 spent on new CD.
For question 3 this time we get 740 again we do it by 37 times 20 equal 740. we minus it by 185 the spent on new CD answer. so 740-185= $555. So answer for question 3 is $555 to her saving account.
Please mark brainliest
Hope this helps.
AOV is a right angle and the ratio AOB: BOC= 2:3 what is the size of angle BOC ?
Answers
BOC = 3/5 of the right angle
= 3/5 x 90
= 54 degree
2) solve for h: a = 1/2 bh
(area of triangle)
Answers
Answer:
h = 2a/b
Step-by-step explanation:
a = 1/2 bh
2*a = 2* 1/2 bh
2a = bh
2a/b = bh/b
2a/b = h
Which equation is equivalent to 4 x = t + 2
Answers
Answer:
Its supposed to be x = s
like its in the picture
So we divide both sides by 4
we get t+2 / 4
That means the answer is C
Answer:
the correct answer for this question is c. s= t+2/4
source. edge.
HELPPPP ME PLZZZZ!!!!!!
Answers
14. Each leg is [tex]21\sqrt{2}[/tex] units long.
15 (a). The longer leg is [tex]7\sqrt{3}[/tex] units long
15 (b). The hypotenuse is [tex]14[/tex] units long
=====================================================
Explanations:
For a 45 degree right triangle, aka 45-45-90 triangle, the hypotenuse is equal to sqrt(2) times the short leg. Algebraically we can say
[tex]y = x\sqrt{2}[/tex] where x is the leg and y is the hypotenuse
Let's solve for x
[tex]y = x\sqrt{2}\\\\x\sqrt{2} = y\\\\x = \frac{y}{\sqrt{2}}\\\\x = \frac{y\sqrt{2}}{\sqrt{2}*\sqrt{2}} \ \text{rationalizing denominator}\\\\x = \frac{y\sqrt{2}}{2}\\\\[/tex]
Now plug in the given hypotenuse y = 42, this leads to,
[tex]x = \frac{y\sqrt{2}}{2}\\\\x = \frac{42\sqrt{2}}{2}\\\\x = \frac{42}{2}\sqrt{2}\\\\x = 21\sqrt{2}\\\\[/tex]
---------------------------
For a 30-60-90 triangle, the hypotenuse is double that of the short leg. So the hypotenuse is 2*7 = 14.
The longer leg is equal to sqrt(3) times the short leg. The longer leg is [tex]7\sqrt{3}[/tex]
What are the domain and range of this graph
Answers
Answer:
As shown in picture, the graph starts from 0 and goes to + infinity.
=> Domain: [0, + infinity)
=> Range: [0, + infinity)
Hope this helps!
:)
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. A graph titled Temperature Conversion has Degrees Fahrenheit on the x-axis and Degrees Celsius on the y-axis. The line goes through points (50, 10) and (64, 18). If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
Answers
Answer:
10 degrees Celsius
Step-by-step explanation:
Since the line goes through point (50, 10) and x represents Fahrenheit, y represents Celsius, then 50 F= 10 C
Answer:
10 degrees
Step-by-step explanation:
i need to solve this wink wink 5-6+8*674/2
Answers
Answer: 2,695
Step-by-step explanation:
5-6+8*674/2
Multiply 8 and 674
5-6+5,392/2
Divide 5,392 by 2
5-6 + 2,696
Subtract 6 from 5
-1 + 2,696
Add
2,695
Step-by-step explanation:
5 - 6 = -1
-1 + 8 = 7
7 x 674 = 4,718
4,718 / 2 = 2,359
Mrs. Schroeder, a school principal, drove her own car for a class trip, taking a different route. The principal’s car can travel 32 miles per gallon of gas, and it used 12 gallons for the trip. How many miles did the principal drive? ____miles
Answers
Answer: 384 miles
Step-by-step explanation:
From the question, Mrs. Schroeder, a school principal, drove her own car for a class trip, by taking a different route and we are told that the principal’s car can travel 32 miles per gallon of gas, and it used 12 gallons for the trip.
Since it used 1 gallon of gas for 32 miles, 12 gallons will be for:
= 32miles × 12
= 384 miles
The principal drove for 384 miles.
Which of the following equations have infinitely many solutions? Choose all answers that apply:
Answers
Answer:
Options B, C and D.
Step-by-step explanation:
Those are the answers because when you solve the equation, the same values are on both sides of the equation. example option B;
-19x -19 = -19x-19
Add 19 to both sides of the equation to get rid of -19
-19x -19 +19 =-19x -19 +19
Divide both sides by -19
[tex]\frac{-19x}{-19} = \frac{-19x}{-19}[/tex]
x = x
How many triangles can be formed
Answers
Answer:
2
Step-by-step explanation:
2
John would like to go on a ski trip with his friends. In order to go on the trip, John needs to save more
than $350 dollars. Write an inequality that describes, M, the money that John needs to save.
Answers
Answer:
$350 < M
Step-by-step explanation:
c 21/
D 101
2
Ms. Gartland bought x number of shirts for the new members of her chorus. The cost
for x number of shirts, including $3.99 shipping, was $77.49. Each shirt cost $12.25.
There was no sales tax on this purchase. Which equation could be used to find x?
Answers
How do outliers affect data analysis? A.They may significantly affect the mean of the data. B.Not enough information. I would need to know what the data points are. C.They afect the mode of the data. D.They do not, just calculate them with the data the same as all the other data. PLEASE HELPPP!!!!!!
Answers
Answer:
A.They may significantly affect the mean of the data.
Step-by-step explanation:
The outliers may significantly affect the mean of the data.
What is outlier?The extreme values in the data are called outliers.
Example: For a data set containing 2, 19, 25, 32, 36, 38, 31, 42, 57, 45, and 84.
In the above number line, we can observe the numbers 2 and 84 are at the extremes and are thus the outliers.
The outliers are a part of the group but are far away from the other members of the group.
For example:
Consider the data: 70, 73, 77, 71, 7, 73, 72, and 78
Let's calculate the mean to understand how the outlier affects the results.
Here, the datapoint 7, is an outlier.
Mean (with outlier)
=70+73+77+71+7+73+72+78/8
=521/8
=65.1
Mean (without an outlier) = 70+73+77+71+73+72+78/7 = 514/ 7 =73.4.
the outlier creates a variation in the mean value of the data.
As, from the example discussed above we have seen that outliers depends on mean of the data.
Hence, outliers may significantly affect the mean of the data.
Learn more about outliers here:
https://brainly.com/question/26958242
#SPJ5
Does anyone get this?
Answers
Answer: B
Step-by-step explanation:
In the systems of equation it already gives you the solution for x which is -2 so all you have to do is substitute -2 into the first equation and solve for y.
y= 2/3x + 3
x= -2
Substitute x for -2
y = [tex]\frac{2}{3}* \frac{-2}1} + 3[/tex]
y= [tex]\frac{-4}{3}[/tex] + [tex]\frac{3}{1}[/tex]
y = [tex]\frac{5}{3}[/tex]
so now you have the solution like this [tex](-2,\frac{5}{3})[/tex]
Can someone help? Thanks :D
Answers
Answer:
[tex]y\leq -x+4[/tex]
Step-by-step explanation:
The first thing that we can do is look at the equation of the line and then worry about the inequality afterwards.
This line has a y-intercept of 4 and a slope of -1.
This means that the equation of this line would be [tex]y=-x+4[/tex]
Now that we have the equation of the line, we just need to determine which inequality sign to use.
As the shaded region is BELOW the line, we will use a less than (<) sign.
As the line is fully shaded, I can only assume that it is meant to include the line, which would mean that [tex]y\leq -x+4[/tex] would be the equation for this inequality.
