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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:

A B C F

Step-by-step explanation:

Answer:

x=1 must satisfy both equations.

Step-by-step explanation:

1)Y=X+4

2)Y=3X+2

IT Means x+4=3x+2

3x-x=4-2;

2x=2 ;  x=1 must satisfy both equations

If the rainfall was recorded on 36 (instead of 9) randomly selected days throughout the year, the standard error of the mean would be equal to 0.195 inches.

The standard error measures the variability or uncertainty in an estimate or statistic based on a sample. It is often denoted as SE or SE(θ), where θ represents a population parameter of interest.

Given that

the standard error of the mean, SE = 0.39 (when sample size,n = 9).

Let s be the standard deviation around the mean, then

Since SE = [tex]\dfrac{s}{\sqrt n}[/tex]

In this sample,

0.39 = [tex]\dfrac{s}{\sqrt9}[/tex]

s = 0.39 × 3

s = 1.17.

If the sample size is increased from 9 to 36,

SE = [tex]\dfrac{1.17}{\sqrt36}[/tex]

SE = [tex]\frac{1.17}{6}[/tex]

SE = 0.195 inches.

Thus, the standard error of the mean changes from 0.39 inches to 0.195 inches.

Learn more about Standard Error here:

https://brainly.com/question/13179711

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Answer:

[tex]P(x<810)=0.5[/tex]

[tex]P(x<800) = 0[/tex]

[tex]P(x>808.40) = 0.58[/tex]

[tex]P(x\le805.40\ or\ x\ge 808.40) = 0.85[/tex]

Step-by-step explanation:

Given:

[tex]F(x) = \left\{\begin{array}{ll}{0} &; {x&lt;800^{\circ} \mathrm{C}} \\ {0.05 x-40} &; {800^{\circ} \mathrm{C} \leq x&lt;820^{\circ} \mathrm{C}} \\ {1} &; {x&gt;820^{\circ} \mathrm{C}}\end{array}[/tex]

Solving (a): P(x < 810)

To solve this, we make use of:

[tex]P(x<810) = F(x) = 0.05x - 40[/tex]

Because

[tex]800^\circ C \le 810 \le 820^\circ C[/tex]

So:

[tex]F(x) = 0.05 * 810 -40[/tex]

[tex]F(x) = 40.5 -40[/tex]

[tex]F(x) = 0.5[/tex]

Hence:

[tex]P(x<810)=0.5[/tex]

Solving (b): P(x < 800)

To solve this, we make use of:

[tex]P(x<800) = F(x) = x[/tex]

Because:

[tex]x < 800^\circ C[/tex]

So:

[tex]P(x<800) = 0[/tex]

Solving (c): P(x > 808.40)

Here, we make use of complement rule:

[tex]P(x>808.40) = 1 - P(x \le 808.40)[/tex]

Where:

[tex]P(x\le808.40) = 0.05x - 40[/tex]

[tex]P(x\le808.40) = 0.05*808.40 - 40[/tex]

[tex]P(x\le808.40) = 0.42[/tex]

So:

[tex]P(x>808.40) = 1 - 0.42[/tex]

[tex]P(x>808.40) = 0.58[/tex]

Solving (d) The probability that the temperature lies outside 805.60 and 808.40

First, we calculate the probability that it lies within.

This is represented as:

[tex]P(805.40 < x < 808.40)[/tex]

This is calculated using:

[tex]P(805.40 < x < 808.40) = F(808.40) - F(805.40)[/tex]

[tex]P(805.40 < x < 808.40) = 0.05*808.40-40 - (0.05*805.40-40)[/tex]

[tex]P(805.40 < x < 808.40) = 0.42 - (0.27)[/tex]

[tex]P(805.40 < x < 808.40) = 0.42 - 0.27[/tex]

[tex]P(805.40 < x < 808.40) = 0.15[/tex]

Using complement rule, the required probability is:

[tex]P(x\le805.40\ or\ x\ge 808.40) = 1 - 0.15[/tex]

[tex]P(x\le805.40\ or\ x\ge 808.40) = 0.85[/tex]

Answer:

Step-by-step explanation:

-4.4 + (5-2)(-6) = -4.4 + (3)(-6) = -4.4 + (-18) = - 22.4

Answer:

q = 114

Step-by-step explanation:

q/19 > 5

q > 19 * 5 = 95

==> q = 114 works

Answer:

rrerer

Step-by-step explanation:erewqwdqwdqd noo hlp me

Answer: [tex]73^{\circ}[/tex]

Step-by-step explanation:

Angles in a triangle add to 180 degrees.

Answer:

Step-by-step explanation:

To find the number of hours for each, divide the amount of money he had received by the amount he would receive for 1 hour of work. (Answers are in the image below) I hope I wasn’t too late to help:)

Answer:

B. 76 square centimeters

Step-by-step explanation:

Edg 2021 it's correct

Answer:

Step-by-step explanation:

b

Answer:

6 students are wearing blue shirts

Step-by-step explanation:

you divide 36 by 6 and that equals 1/6 of the students.

Answer:

A and F

Step-by-step explanation:

Answer:

1) 180 degrees; straight angle

2) (5x-18)+(4x+45)=108

3) x=17

4) 90 degrees; right angle

5) (3x+6)+(5x+4)=90

6)x=10

Step-by-step explanation:

Answer:

5+4=9

and the second one is right

Step-by-step explanation:

;)

Answer:

the first one is incorrect but the second one is correct!

Step-by-step explanation:

5 + 4 = 9

if you have 5 apples and you want to add 4 more

5 + 1 + 1 + 1 + 1 = 9

Answer:

18

Step-by-step explanation:

32-14=18

Answer:

C.9

Step-by-step explanation:

2 doz =3eggs

4 doz = 6 eggs

6 doz = 9 eggs

Answer:

x=5/2, x=-4/3

Step-by-step explanation:

Answer:

The vertex is (-1.5, 11.25)

Step-by-step explanation:

Step-by-step explanation:

When x=36, only the first statement is true (x is a multiple of 3). this is because 12×3= 36

36 is not odd, making the other statement false

Answer:

3×[tex]10^{-6}[/tex]

Step-by-step explanation:

Hope it helps ;)

Answer:

3x10^-6

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. The sign of the exponent will depend on the direction you are moving the decimal.

Answer:

12

Step-by-step explanation:

4 times 3 = 12

Answer:

A because when you add the angles up it has to equal 180

Step-by-step explanation:

Answer:

A) ∠ABC and ∠DEF

Step-by-step explanation:

Supplementary angles add up to 180 degrees total. So if you take 180 and subtract 118 you get 62.

∠ABC = 62

∠DEF = 118

180 - 118 = 62

180 - 62 = 118

118 + 62 = 180

Answer:

44

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

because you take 3 pulse 2

Answer:

Option (1)

Step-by-step explanation:

Given inequality is.

4x + 5 ≥ 13

We will further solve this inequality,

(4x + 5) - 5 ≥ 13 - 5

4x ≥ 8

[tex]\frac{4x}{4}\geq \frac{8}{4}[/tex]

x ≥ 2

Therefore, on a number line solution of x will be all values of x greater than equal to 2.

Which will be represented by and arrow starting with a solid point from x = 2 directing towards numbers greater than 2.

Option (1) will be the answer.

Step-by-step explanation:

I hope this helps. Ans:41/16 alternate form: 2 9/16, 2.5625

Answer:

First: 105

Second: 65

Third: 133

Fourth: 129

Fifth: 60

Answer:

ok

Step-by-step explanation:

Answer:

suppersize my fries...

Answer:

[tex] \frac{3}{4} \times \frac{5}{6} [/tex]

[tex] \frac{3 \times 5}{4 \times 6} [/tex]

[tex] \frac{15}{24} [/tex]

[tex] \frac{5}{8} [/tex]

Answer:

5/8

Step-by-step explanation:

Sorry for the messy handwriting.

Hope this helps! Have a great day!