Answer:
2(x - 3)
Step-by-step explanation:
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
Mary purchased a prepald phone card for $30. Long distance calls cost 8 cents a minute using this card. Mary used her card only once to make a long distance
call. If the remaining credit on her card is $26.16, how many minutes did her call last?
HELPPPP!!!!!!!!!!!!!
Answer:
Its A
Step-by-step explanation:
ez
Answer:
A
Step-by-step explanation:
y= -3x + 7
HELP!!!!!!!
Functions f(x) and g(x) are shown:
f(x) = x2 g(x) = x2 + 8x + 16
In which direction and by how many units should f(x) be shifted to match g(x)?
A. Left by 4 units
B. Right by 4 units
C. Left by 8 units
D. Right by 8 units
Answer:
Option A, Left by 4 units
Step-by-step explanation:
Step 1: Convert g(x) to a function square
We currently have g(x) in this order: [tex]ax^2 + bx + c[/tex]
However, we want g(x) to be in this order: [tex](ax + c)^{2}[/tex]
The first thing we have to do is to factor it out:
[tex]g(x)=x^{2}+8x+16[/tex]
[tex]g(x) = (x + 4)(x + 4)[/tex]
[tex]g(x) = (x+4)^{2}[/tex]
Step 2: Now we can see which way we need to move it
The original form is: [tex]f(x) = (ax - b)^{2}[/tex]
Since the - has changed to a +, that means that we moved -4 spaces down the x-axis. This means that we move left by 4 units.
Answer: Option A, Left by 4 units
Look at the graphs below to make sure:
Answer:
A.) Left By 4 Units
Step-by-step explanation:
Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 + 8x + 16
The direction in which and by how many units the f(x) should be shifted to obtain the g(x) is given by as follows.
Given,
f(x) = x²
g(x) = x² + 8x + 16
we have to consider, the dependent term while selecting the direction.
Therefore, except x², only x term is dependent term.
In g(x), the x term is given by 8.
Therefore, we need to shift the f(x) left by 4 units.
Therefore, option A is correct.
You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. What is the probability of NOT picking a green marble out of the bag randomly?
Answer:
hey there
The answer is 7/10
this is true because we have two green marbles and five blue
2+5=7
Step-by-step explanation:
Answer:
20% or 2/10
Step-by-step explanation:
10 marbles in total. We want to find the probability of not picking a green marble. 10marbles-3red-5blue=2marbles left.
So the probability of picking a green marble is 2/10 or 20%
Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)
Answer:
a) 10
b) 3
c) 16
Step-by-step explanation:
Count the squares and the half ones match them with each other to get a full square... so so sorry if im wrong i did this a while ago! Currently Yr 9 x
What type of information would you find in a hunting regulations publication?
A.typical weather for each hunting season
B.number of people arrested for poaching
C.number of animals found in each hunting location
D.license, permits, and stamp requirements
Answer:
D
D. license, permits, and stamp requirements
The type of information that determine the hunting regulations publication is option D.
The following information should be considered:
The typical weather should not required. The number of people arrested is not considered.Only license, permits and requirement of stamp should be required.Learn more: brainly.com/question/16911495
1. Find the value of
sec Θ if tan Θ = -2 90° ≤ Θ ≤ 180°
a. - sqrt(5)
b. sqrt(5)
c. -5
d. 5
2. Find the value of cos Θ if sec Θ = s/3 270° ≤ Θ ≤ 360°
cos =
3. Find the value of
csc Θ of cos Θ = -3/5 180° ≤ Θ ≤ 270°
csc =
9514 1404 393
Answer:
-√53/5-4/5Step-by-step explanation:
The relevant relations are ...
sec = ±√(tan² +1)
cos = 1/sec
csc = 1/sin = ±1/√(1 -cos²)
Sine and Cosecant are positive in quadrants I and II. Cosine and Secant are positive in quadrants I and IV.
__
1. sec(θ) = -√((-2)² +1) = -√5
2. cos(θ) = 1/sec(θ) = 1/(5/3) = 3/5
3. csc(θ) = -1/√(1 -(-3/5)²) = -√(16/25) = -4/5
Find the slope of a line that passes through the points (3,3) and (9, 1). Please simplify any fractions if you have them in your answer.
Answer: -1/3
Step-by-step explanation: slope is the difference in the y values over the difference in the x values
How many gallons of pure water should be added to 10 gallons of a solution containing 15% juice so that the remaining solution contains 5% juice?
Answer:
20 gallons
Step-by-step explanation:
10 gallons of solution w/ 15% juice means 1.5 gal of juice
to make it into 5%, multiply 1.5 by 20
1.5 x 20 = 30
5% of 30 gallons is 1.5 since 10% of 30 is 3.
Since there was already 10 gallons, the # of gallons of pure water added should be 20 gal.
I hope this helps thanks
Answer:
What is the amount of juice in the original solution? a =
✔ 1.5
What is the original amount of solution in gallons? b =
✔ 10
How much juice is added? c =
✔ 0
How much total solution is added? d =
✔ x
Step-by-step explanation:
Simplify the following:
(-4x^3-14x^2+10x-1) ÷(2x-1)
Show your work.
Can someone please help for college prep math
Answer:
[tex]1-8x-2x^2[/tex]
Step-by-step explanation:
(-4x^3-14x^2+10x-1)÷(2x-1)
Factor the expressions that are not already factored.
[tex]\frac{(2x-1)(2x^2-8x+1)}{2x-1}[/tex]
Cancel out 2x−1 in both numerator and denominator.
[tex]2x^2-8x+1[/tex]
Swap terms to the left side.
[tex]1-8x-2x^2[/tex]
Graph if needed:
Which triangles are similar?
23
23
13/12
673
Trianglo A
36
39
15
28
6217
67
15
Triangle c
Trianglo B
O A. Triangles A, B, and C
OB. Triangles B and C
O C. Triangles A and B
D. Triangles A and C
PREVIOUS
Answer:
D. Triangles A and C
Step-by-step explanation:
We can see whether the figures are congruent or not by checking out the similarity ratio
For triangle A and C the side lengths and angle measures are proportional so we can say that these two angles are congruent.
let p= fg where f (0,5) and g (-4,-3). what is the direction angle of -3/2p?
Answer: its B) 63
Step-by-step explanation:
On edge 2021
-12(x - 3) - (2x - 6) = 60
Answer:
x=-9/7
Step-by-step explanation:
Answer:-12(x - 3) - (2x - 6) = 60
= -12 OJHORZHOEHFOSDHSKDKCDEZIAIFDNSQDKFFFFFFFFFFFFZIDJAZIFJOIJF
Step-by-step explanation:
EFKJNDOIDNOIEFJOAIZFOUJFNJBVJFNVJNZJCN
E/f + f/e if e is 15 and f is 9
Answer:
34/15
Step-by-step explanation:
15/9 + 9/15 = 34/15
Answer:
2 4/15 or 2.27 (rounded up)
Step-by-step explanation:
15/9 + 9/15
75/45 + 27/45
102/45
2 12/45
2 4/15
Helpppppppppppppppp
Answer:
∠QRT = 42°
Step-by-step explanation:
arc QT + 2(∠QPT = 2(42°) = 84°
arc QT = arc TQ
arc TQ = 2(∠QRT)
84° = 2(∠QRT)
∠QRT = 42°
Through part of the 2017-18 National Basketball Association (NBA) season,
two players had these statistics for the number of points they scored.
Anthony Davis Kevin Durant
Points per game (mean): 25.9 26.0
Mean average deviation: 6.6
Based on these data, which statement is true?
4.3
A. On average, Kevin Durant scored many more points. The number
of points Durant scored also varied more.
B. On average, Anthony Davis scored many more points. The number
of points Davis scored also varied more.
C. On average, the two players scored about the same number of
points. The number of points Davis scored varied more.
D. On average, the two players scored about the same number of
points. The variation in the number of points scored was also
about the same
PLEASE HELP! The AHS football team did a weigh-in at the start of training camp. The weights of the players were distributed normally with a mean of 98kg and a standard deviation of 6kg. What percentage of players are under 86kg?
Answer:
2.28% of players are under 86kg
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The weights of the players were distributed normally with a mean of 98kg and a standard deviation of 6kg.
This means that [tex]\mu = 98, \sigma = 6[/tex]
What percentage of players are under 86kg?
The proportion is the pvalue of Z when X = 86. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{86 - 98}{6}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.0228*100% = 2.28%
2.28% of players are under 86kg
A university class has 29 students: 14 are accounting majors, 9 are business majors, and 6 are history majors. The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is an accounting major and the second student is a history major
Answer:
0.1034 = 10.34% probability that the first student selected is an accounting major and the second student is a history major
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
14 account majors from a set of 29 students.
Then, 6 history majors from a set of 29 - 1 = 28 students.
So
[tex]p = \frac{14}{29}*\frac{6}{28} = \frac{14*6}{29*28} = 0.1034[/tex]
0.1034 = 10.34% probability that the first student selected is an accounting major and the second student is a history major
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
comparing both equations
-2x-1=3x+4
or, -1-4 =3x+2x
or, -5=5x
or, X= -1
Y= -2x-1
or, Y= -2(-1)-1
or, Y=1
hence, ( -1,1)
Please help if Yk the answer.
Answer:25
Step-by-step explanation:
-3 (4b + 7) > 3. Plz help I have 5 mins
☁️ Answer ☁️
Inequality Form:
b < −2
❤️
Interval Notation:
(− ∞, −2)
Hope it helps.
Explanation: Have a nice day!~ ￣▽￣
Answer:
b < -2
Step-by-step explanation:
-3 (4b + 7) > 3
-12b -21 > 3
-12b > 3 + 21
-12b > 24
b < 24/-12
b < -2
Cindy read 240 minutes last week she read 378 minutes this week how many minutes did she read altogether
Answer:
618
Step-by-step explanation:
They are added
Answer:
240 + 378 = 618
Step-by-step explanation:
an easy way to add big numbers s to break it up into smaller pieces.
Example: 240+378 = (200 + 300 = 500) + (40 + 70 = 110) + (0 + 8 = 8) = 618
Seth invested a certain amount of money and got back an amount of $ 8400. If
the bank paid an interest of $ 700, find the amount Sam invested. *
Answer:
$7700
Step-by-step explanation:
amount invested + interest = total
amount invested + 700 = 8400
Subtract 700 from both sides.
amount invested = 7700
Answer: $7700
What is the value of 7m – 3n when m = 3 and n = 2?
Answer:
It's 15.
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
Plug in m = 3 & n = 2 into the equation.
7(3) - 3(2)
21 - 6
15
Hope this helps & have a great rest of your day!
how do I find a midpoint between (4,-1) and (-8,3)
Answer:
(-2,1)Step-by-step explanation:
Midpoint formula:
(x1 + x2)/2, (y1 + y2)/2
Substitute needed values.
4 + -8 = -4
-4/2 = -2
Now for the y's
-1 + 3 = 2
2/2 = 1
MIDPOINT: (-2,1)
I need to multiply 10,170 by 0.775
Answer:
7881.75
Step-by-step explanation:
10,170x0.775
Answer:
7881.75
Step-by-step explanation:
Please help me to see if this is correct
Answer:
You are correct
Step-by-step explanation:
Answer: yes, you are correct :)
Step-by-step explanation:
A store is having a sale in which the cost of any item is 35% off. Which expression can be used to find the cost, x, of an item AFTER DISCOUNT?
Answer:
73373773737477374747373738
Distance between the object you were looking out in the hands lens is the ____.
Answer:
Focal length
Step-by-step explanation:
Not sure tbh