A particle moves along a horizontal line so that its position at time t, t ≥ 0, is given by
s(t) = 40 + te^−t/20.
Find the minimum velocity of the particle for 0 ≤ t ≤ 100.
Answer:
The minimum velocity of the particle = [tex]-e^{-2 }[/tex] units
Step-by-step explanation:
Given - A particle moves along a horizontal line so that its position at time t,
t ≥ 0, is given by s(t) = 40 + te^−t/20.
To find - Find the minimum velocity of the particle for 0 ≤ t ≤ 100.
Proof -
Velocity, v(t) = [tex]\frac{d}{dt}(40 + te^{-\frac{t}{20} } )[/tex]
Now,
[tex]\frac{d}{dt}(40 + te^{-\frac{t}{20} } )[/tex] = [tex]\frac{d}{dt}(40 ) + \frac{d}{dt}(te^{-\frac{t}{20} } )[/tex]
= 0 + [tex]t\frac{d}{dt}(e^{-\frac{t}{20} } ) + e^{-\frac{t}{20} }\frac{d}{dt}(t )[/tex]
= [tex]t(-\frac{1}{20} )e^{-\frac{t}{20} } + e^{-\frac{t}{20} }[/tex]
⇒v(t) = [tex]-\frac{t}{20}e^{-\frac{t}{20} } + e^{-\frac{t}{20} }[/tex]
Now,
For minimum velocity, Put [tex]\frac{d}{dt}(v(t)) = 0[/tex]
Now,
[tex]\frac{d}{dt}[v(t)] = \frac{d}{dt} [ -\frac{t}{20}e^{-\frac{t}{20} } + e^{-\frac{t}{20} } ][/tex]
= [tex]-\frac{2}{20} e^{-\frac{t}{20} } + \frac{t}{400} e^{-\frac{t}{20} }[/tex]
Now,
Put [tex]\frac{d}{dt}(v(t)) = 0[/tex], we get
[tex]-\frac{2}{20} = - \frac{t}{400}[/tex]
⇒t = 40
Now,
Check that the point is minimum or maximum
Calculate [tex]\frac{d^{2} }{dt^{2} } [v(t)][/tex]
Now,
[tex]\frac{d^{2} }{dt^{2} } [v(t)][/tex] = [tex]\frac{d}{dt} [ -\frac{2}{20} e^{-\frac{t}{20} } + \frac{t}{400} e^{-\frac{t}{20} }][/tex]
= [tex]\frac{1}{400}e^{- \frac{t}{20} } [ 3 - \frac{t}{20}][/tex]
⇒[tex]\frac{d^{2} }{dt^{2} } [v(t)][/tex] = [tex]\frac{1}{400}e^{- \frac{t}{20} } [ 3 - \frac{t}{20}][/tex] > 0
∴ we get
t = 40 is point of minimum
So,
The minimum velocity be
v(40) = [tex]-\frac{40}{20}e^{-\frac{40}{20} } + e^{-\frac{40}{20} }[/tex]
= [tex]-2e^{-2 } + e^{-2 }[/tex]
= [tex]-e^{-2 }[/tex]
⇒v(40) = [tex]-e^{-2 }[/tex] units
∴ we get
The minimum velocity of the particle = [tex]-e^{-2 }[/tex] units
Answer this correctly I’ll give brainalist + 10 points
Answer:
x = 43
Step-by-step explanation:
Since these angles are inside a right angle, we know their sums are complementary (they add up to 90°.)
x + x + 4 = 90
2x + 4 = 90 | Combine x's
2x = 86 | Subtract 4 from both sides
x = 43 | Divide both sides by 2
If you partition ¼ into 6 equal segments, how long is each segment?
Answer:
1/24
Step-by-step explanation
I'm pretty sure that you just do 1/4 times 6 to get 1/24 so each segment will be 1/24.
Felicia and gabriella are on the hamilton middle school basketball team. The box plots show the number of points they scored in 8 basketball games.
Answer:
I
Step-by-step explanation:
I need the box plot to do the problem
A bag with 8 marbles has 4 red marbles, 3 blue marbles, and 1 yellow marble. A marble is chosen from the bag at random. What is the probability that it is red?
Write your answer as a fraction in simplest form.
Answer:
P = 4 / ( 4 + 3 +1 )
= 4 / 8
= 4 / 8 = 1 / 2
Hope it helps
Please mark me as the brainliest
Thank you
The probability that it is red is 1/2.
what is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
A bag with 8 marbles
4 red marbles,
3 blue marbles,
and 1 yellow marble.
So, the probability that it is red
= 4 / ( 8)
= 1/2
Hence, the probability that it is red is 1/2.
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Function lis defined by the equation r
R=5/8t - 9
Function 2 is defined by the following table,
I
Which function has a greater y-intercept?
Answer:
Both have the same y-intercept (-9)
Step-by-step explanation:
✔️Function 1, r = ⅝t - 9, is given in the slope-intercept form, y = mx + b.
b = y-intercept = -9
y-intercept for Function 1 = -9
✔️Function 2, using the table given, the y-intercept is the value of r when t = 0.
Thus, r = -9 when t = 0.
y-intercept for Function 2 = -9
✔️Both functions has the same y-intercept. None is greater than the other.
Need it now. I'll give you another 100 when done if all i right.
This it the test please do as fast as posible and show work. thank you and sorry
Factorise
7lm - 21lmn
Answer:
7lm - 21lmn
taking common 7lm
7lm(1-3n)
Find cos (P)
Q
74
70
P
24
R
A.
37
12
В.
35
37
C.
12
Answer:
cos P = 71.09
Step-by-step explanation:
cos = [tex]\frac{adajcent}{hypotenuse}[/tex]
cos P = [tex]\frac{24}{74}[/tex]
cos P = 0.324
cos-1 of 0.324 is 71.09
cos P = 71.09
cuánto es 567 + 678 es igual
Answer: 1245 :)
Step-by-step explanation:
Answer:
la respuesta es 1245
567+678=1245
How many minutes is 65% of 3 hours? ____ just write the number part of the answer.
Answer:
117
Step-by-step explanation:
There are 60 minutes in each hour, and to find how many minutes there are in 3 hours you would have to multiply 3 x 60.
3 x 60 = 180
To find 65% of 180 you can use the equation
65 x 180/100
65 x 180 divided by 100 is 117.
HELP ASAP!! In a right triangle, the longer leg is twice the shorter leg and the hypotenuse is 8 more than the shorter leg. Find the length of the shorter leg.
Answer:
We can't find an exact number, but the answer is x.
I need help and I don’t know how to check it
Answer:
y=2x+3
Step-by-step explanation:
Can someone help quick please
Answer:
PC = 4 cm
Step-by-step explanation:
AP = 4 cm
Because AB = BC, PB = PB, and we know that angle PBA = 90 degrees: triangle PBA is congruent to triangle PBC by the Side-Angle-Side theorem.
PC = AP because corresponding parts of congruent triangles are congruent.
What is the interquartile in the dot plot for Mrs. Orlando’s daycare? i need thisssss!!
Select all the expressions that are equivalent to 10x + 4 - (6x - 1)
Answer:
4x + 5
Step-by-step explanation:
10x + 4 - 6x + 1
= 4x + 5
What is the equation of the line that passes through the point (-5, 3) and has a
slope of
-6/5
find the area of the composite shape. quickly please
Answer:
4800 1 x 24 x 25 x 8
Step-by-step explanation: 1 x 24 x 25 x 8
What value of x is in the solution set of 2x - 3> 11 - 5x?
0 -3
O 0
O2
o 4
Answer:
The answer is x>2, x has to be greater than 2,
the answer is 4 since it is greater than 2
When a certain kind of bacterium takes a step, it moves 3 x 10^-7 meters. When
Joe takes a step, he moves 0.75 meters. How many times larger is Joe's step
than the bacterium's step?
Joe's step is[ ] x 10^[ ]
times larger than the bacterium's step
Answer:
Step-by-step explanation:
0.75/(3*10^(-7)) = 0.25*10^7 = 2.5*10^6
Please help ..........
Which table of ordered pairs represents a proportional relationship? I’m a timer please hurry thank you so much
х
-3
-4
-5
у
3
2
1
x
-1
-3
-5
у
1
3
5
-2.
-4
-6
y
1-5
1-7
-9
х
--2
-3
-4
у
0
-1
1-2
I
Answer:
I'd say the second one. the others are all showing a linear relatiknship
Someone please help me
Help ASAP pls I will give 10 points
Answer:
it is thr 3rd answer hope it help you
Janet is writing a book. She writes 3 pages every 2 days. If she continues at the same
pace, how long will it take her to write a 400-page book?
Which proportion could be used to solve this problem?
Mr. Ramone brought home 1/2 of an apple pie from work. He wants to share the apple pie equally among six friends. What is the amount of pie that each six people will receive.
Answer:
0.08
Step-by-step explanation:
i need help with this pls.
Answer:
The answer is D
Step-by-step explanation:
Plug all of the numbers in and they all work with the problem.
Which transformation could NOT be used to prove that two circles are congruent to one another?
a dilation with a scale factor of 2
a dilation with a scale factor of 1
a reflection
a rotation
Answer:
the congruent the congruent???
Step-by-step explanation:a dilation a dilation with two factors???
The transformation which could not be used to prove that two circles are congruent to one another is dilation with a scale factor of 2.
Option A is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
Dilation:
It changes the size of the figure so, the transformed figure is not congruent with the original figure.
Scale factor = 1 will not change the size of the figure.
Scale factor = 2 will change the size of the figure.
Reflection:
It does not change the size or the shape.
Rotation:
It does not change the size or the shape.
Thus,
The transformation of dilation with a scale factor of 2 could not be used to prove that two circles are congruent to one another.
Learn more about circle here:
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anime recommendations
Answer:
what genre babe♀️
Answer:
It depends on a lot what kind you like and if u have watched a lot
the promised Neverland
Black Clover
Aot
HxH
Monster
Code grass
The classroom of the elite
Psycho pass season 1 only
COMEDY
The disastrous life of saiki k
Kaguya sama love is war
if -3x-8=16 what is the value of -2(x-7)
Answer:
-3x-8=16
-3x = 16+8
-3x = 24
x = 24/-3
x = -8
= -2(x-7)
= -2(-8-7)
= 30
Hope this helps you. Do mark me as brainliest.