Answer: (0,4)
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
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 if Yk the answer.
Answer:25
Step-by-step explanation:
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
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
Solve for h
h – 5 = -30
Make sure to show your work for full points!
Answer:
h = -25
Step-by-step explanation:
h - 5 = - 30
+5 +5
h = -25
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%
-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
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:
What is the value of y in the following equation? -10y + 4(3y – 8) = -64
Answer:
y=-16
Step-by-step explanation:
Answer:
y = -16
Step-by-step explanation:
−10y+4(3y−8)=−64
Step 1: Simplify both sides of the equation.
−10y+4(3y−8)=−64
−10y+(4)(3y)+(4)(−8)=−64(Distribute)
−10y+12y+−32=−64
(−10y+12y)+(−32)=−64(Combine Like Terms)
2y+−32=−64
2y−32=−64
Step 2: Add 32 to both sides.
2y−32+32=−64+32
2y=−32
Step 3: Divide both sides by 2.
2y
2
=
−32
2
y=−16
Answer:
y=−16
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?
I don’t know the answer
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)
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)
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.
what is 4 and half hours in minutes
Share £747 in the ratio 2:7 between Tom and ben
Tom will get
Dan will get
2+7x=747 X83 83(2)=83 83(7)= 581
Step-by-step explanation:
Find the area of the shape shown below.
Answer: 256
Step-by-step explanation:
Answer:
256cm² is the correct answer
In a sale the price of a bike is reduced by 40% the sale price of the bike is £192 how much did the bike cost before the sale?
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
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:
1. Line A ang Line B are parallel lines cut by Transversals x and y. 2 = 57° and 3 = 85°, Find the measure of 5.
Answer:
Step-by-step explanation:
∠1 = 180° - ∠2 - ∠3 = 38°
∠5 = ∠1 = 38°
Many studies have investigated the question of whether people tend to think of an odd or an even number when they are asked to think of a single-digit number (0 through 9). Combining results from several studies, Kubovy and Psotka (1976) used a sample of 1,770 people, of whom 741 thought of an even number and 1,029 thought of an odd number. Would a one-sided or a two-sided alternative hypothesis be more appropriate in this case
Answer:
A two-sided alternative hypothesis would be more appropriate in this case
Step-by-step explanation:
A one-sided hypothesis is one that asserts that a given parameter is either smaller than the null hypothesis value or larger than the value presented by the null hypothesis.
However in a two sided hypothesis, the claim is made that a given parameter is not equal to the parameter given in the null hypothesis, such that the parameter can be either larger than than or lesser than the value of the null hypothesis and still satisfy the condition of the hypothesis
Therefore, given for that for there to be a conclusion, the test should be weather the number of people that think of an odd number are equal to the number of people that think of an even number, or weather the number of people that think of an odd number are not equal to the number of people that think of an even number
Therefore, a two-sided hypothesis should be used since the claim (that the numbers are not equal) is not equal to the value of the parameter in the null hypothesis (that the numbers are equal)
11 and 3/8 pounds of cat food were donated to the shelter
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
1/2 of 2/2 = ???????????
Answer:
0.5
Step-by-step explanation:
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:
Write the difference in factored form. (24x4 - 15x2 + 6x) - (10x4 + 5x2 - 4x)
Answer:
The factored difference is: [tex]2x(7x^3 - 10x + 5)[/tex]
Step-by-step explanation:
Difference in non factored form:
To find the difference in non-factored form, we subtract the common terms. So
[tex]24x^4 - 15x^2 + 6x - (10x^4 + 5x^2 - 4x) = 24x^4 - 10x^4 - 15x^2 - 5x^2 + 6x + 4x = 14x^4 - 20x^2 + 10x[/tex]
Greatest common factor:
Of the exponents: Between [tex]x^4, x^2[/tex] and [tex]x[/tex], it is the one with the lowest exponent, so x.
Between 14, 20 and 10:
14 - 20 - 10|2
7 - 10 - 5
So 2
The gcf is 2x, which means that the factored expression is:
[tex]2x(\frac{14x^4}{2x} - \frac{20x^2}{2x} + \frac{10x}{2x}) = 2x(7x^3 - 10x + 5)[/tex]
The factored difference is: [tex]2x(7x^3 - 10x + 5)[/tex]
For the polynomial function, describe the end behavior of its graph.
f(x) = 2x3 + 5x
I need help with this question please
Answer:
C.
Step-by-step explanation:
Given
[tex]A =(x_1,y_1)[/tex]
[tex]B =(x_2,y_2)[/tex]
[tex]C =(x_3,y_3)[/tex]
[tex]D =(x_4,y_4)[/tex]
Required:
Which condition proves that AB is perpendicular to CD
First, calculate the slopes of both.
For AB
[tex]m_1 = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
For CD
[tex]m_2 = \frac{y_4 -y_3}{x_4 - x_2}[/tex]
The condition of perpendicularity is:
[tex]m_1 * m_2 = -1[/tex]
Substitute values for m1 and m2
[tex]\frac{y_2 -y_1}{x_2 - x_1} * \frac{y_4 -y_3}{x_4 - x_2} = -1[/tex]
Option (c) is correct