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
write an integer for each
1- a deposit for $40
2- a loss of 25 pounds
please this assignment locks soon and it’s already over due,
Answer:
1. 40
2. -25
Step-by-step explanation:
I'm sure this is the answer
Olivia, the food stand manager, spends $210 per week on vegetable sandwich ingredients. She wants to earn $1870 per week.
Write an equation that can be used to determine x, the number of vegetable sandwiches Olivia needs to sell in order to earn $1870 per week.
Answer:
187
Step-by-step explanation:
1870/210=187
Also / means divide
2
Which of the following graphs represents a direct variation?
А
С
2
-4
-2
2
4
-2
2
-2
4
B
D
y
2
2
-2
2
4
2
4
-2
-2
Answer:
C & D
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!
Answer: 10x5
(10 blocks wide, 5 blocks long) or (5 blocks wide, 10 blocks long)
Step-by-step explanation:
3 blocks = 18 meters, so
1 block = 6 meters
60meters/ 6meters= 10 blocks
30 meters/ 6 meters = 5 blocks
How would you figure out how many samples of cookie dough can be given
out?
At the Fairview mall, a worker at an edible cookie dough store has
3 cups of cookie dough to give to customers for samples. The
worker places 1 cups of cookie dough in each sample. How many
samples can the worker give out if all the cookie dough is used?
Are 12/102 and 18/153 equivalent ratios?
Answer:
there are 2 ways:
[tex]\frac{12}{102}[/tex] ?= [tex]\frac{18}{153}[/tex]
1) try to simplify
[tex]\frac{12}{102}[/tex] (divide the numerator and denominator by 6) ?= [tex]\frac{18}{153}[/tex] (divide the numerator and denominator by 9)
2/17 = 2/17 so yes they are equivalent
2) use cross products
102x18 ?= 12x153
1836 = 1836 so yes they are equivalent
Al abrir su alcancía Beatriz encontró que entre monedas de 5, 10 y 25 centavos completaba $ 9.50. Encontró igualmente que el número de monedas de 10 centavos era el triple de las de 25 centavos y que las de 5 centavos era el doble de las de 10 centavos. ¿Cuántas monedas de cada denominación había en la alcancía?}
Answer:
67 monedas de 5, 34 de 10 y 11 de 25.
Step-by-step explanation:
Representemos el primer enunciado de manera algebraica:
[tex]5x+10y+25z =950[/tex] (1)
Donde:
x es el numero de monedas de 5y es el numero de monedas de 10 z es el numero de monedas de 25Ahora, el número de monedas de 10 centavos era el triple de las de 25 centavos y que las de 5 centavos era el doble de las de 10 centavos, se puede representar como:
[tex]y=3z[/tex] (2)
[tex]x=2y[/tex] (3)
Combinado las eacuaciones (1), (2) y (3) tenemos:
[tex]5(2y)+10y+25(\frac{y}{3}) =950[/tex]
[tex]10y+10y+\frac{25}{3}y =950[/tex]
[tex]\frac{85}{3}y =950[/tex]
[tex]y =34[/tex]
Por lo tanto el valor de x y z seran:
[tex]x=2(34)[/tex]
[tex]x=68[/tex]
[tex]z=11[/tex]
Si ponemos cada valor en la equacion (1), tenemos:
[tex]5(68)+10(34)+25(11) =955[/tex]
Como el resultado da 955 hay un excedente de 5 pesos, asi que finalmente tendremos.
x = 67
y = 34
z = 11
Espero te haya serrvido!
Brendan's mom bought him a new bes frame and wants to figure put the area.If Brendan's new bed frame is 5 1/4 feet long and 4 feet wide,What is the area of the bed frame?
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equation need multiplied by before adding the equations together?
Evaluate the expression: 8 ⋅ (1/2)^2
Answer:
8 × (1/2)²
8 × 0.25
2 Answer!
Hope this helps, thank you :) !!
Answer:
Step-by-step explanation:
The answer is : 2
Simplify
I added image with explation! Hope this helps!
A child is standing across the street from his apartment. His mother is on their balcony. The angle of elevation between the child's eyes and his mother's eyes is 28°. If the distance between their eyes is 35 ft, how far is the child standing from his apartment building? Round to the nearest foot.
Elena finds that the area of a house on a scale drawing is 25 square inches the actual area of the house is 2025 ft what is the scale of the drawing
Answer:
81 is the scale of drawing.
Step-by-step explanation:
Area of the house in drawing = A =
Let the factor by which scaling is present in the drawing be s.
Area of the house in reality = A' =
what is the answer to 3/4 x 5/6
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!
6. 1, 8, 5, 4, 1, 8, 5, 4
Mean
Median
Mode
Answer:
Mean 16.75
Median 15.5
Mode 13
Step-by-step explanation:
This is what I got .____.
help me please
bddbdbbdbd
5m=105 what is m in the equation
Answer:
m = 21
Step-by-step explanation:
5m = 105
5m ÷ 5 = 105 ÷ 5
m = 21
Is the formula for what?
A. Circle
B. Cone
C. Cylinder
D. Sphere
Answer: sphere
Step-by-step explanation:
Answer:
Sphere
Step-by-step explanation:
The formula given is the formula for volume of a sphere, where 'r' is the radius of the sphere.
The formula for volume of a sphere is the only formula with '4/3' in it, compared to the other option choices given.
Hope this helps.
I am bad at geometry please help
Answer:
3.9 in^2
Step-by-step explanation:
Split it up into a top rectangle and a bottom rectangle. Find the area of the top rectangle and subtract the combined area of the two quarter circles.
The area of the rectangle is 6 * 3 = 18. The area of the two quarter circles is the same as the area of one semicircle, and since the radius is 3 you can do:
3^2 * pi / 2 = 9pi/2. As a decimal this would be: 14.14.
Then, you can do rectangle - circle = 18 - 14.14 = 3.86. Rounded to the nearest tenth, this is 3.9
An employee at a store makes $6 an hour. If she has made $237.38 in a week, how
many hours, did she work that week? Write an equation showing how to solve for how
many hours she worked using "h"as the variable.
Answer:40 hours
Step-by-step explanation:divide 237.36 by 6 and you will get 39.5633
so basically what you're going to do is round it up and your answer will be 40
anyone know? its due tonight
Answer:
12 cm
Step-by-step explanation:
Well first we can cut the triangle in half and use the Pythagorean theorm
a^2+b^2=c^2
In this case we are going to be doing c^2-a^2=b^2
10^2-8^2=b^2
(10*10)-(8*8)=b^2
100-64=b^2
36=b^2
Now we just square root 36 (what number times itself is 36)
[tex]\sqrt{36}[/tex]
b=6
Since half of the one side equals 6 (DC) then the length of AC is 12!
Answer:
hey mate here is your answer...
Step-by-step explanation:
by using Pythagoras theorem...
BC² = BD² + DC²10² = 8² + DC²DC² = 100 - 64DC² = 36DC = 6DC is the half of AC.Therefore AC = 12 centimetres.hope it helps you ❣️
home security service. This private home security service guarantees to either dispatch one of their own five guards immediately if one of their customers sends in an alarm or, in the case that all five guards are responding to other calls, direct the alarm to the local police. The company receives 12 calls per hour, evenly distributed over the course of the day. The local police charges the home security company $500 for every call that the police responds to. It takes a guard, on average, 90 minutes to respond to an alarm. a. What fraction of the time are incoming alarms directed to the police? b. How much does the home security company have to pay the local police every month?
Answer:
a.
The fraction of the time is incoming alarms directed to the police is 74.02%
b.
The home security company has to pay $3,197,665 the local police every month.
Step-by-step explanation:
As per the given data
Numbers of guards = 5 guards
Calls received per hour = 12 calls per hour
Activity time = 90 minutes
First, calculate the inter-arrival time
Inter-arrival time = Minutes in an hour / Numbers of calls received per hour = 60 minutes per hour / 12 calls per hour = 5 minutes
a.
First, calculate the ratio of activity time to inter-arrival time
Ratio = Activity time / Inter-arrival time = 90 minutes / 5 minutses = 18
Now calculate the probability of all 5 servers are busy using ratio of activity time to inter-arrival time
Probability = [tex]P_{Servers}[/tex] ( ratio )
Probability = [tex]P_{5}[/tex] ( 18 )
Probability = 0.7402
Probability = 74.02%
Hence the probability of incoming calls directed to the police is 74.02%
b.
First, calculate the loss of customers
Loss of customers = Probability x ( 1 / Servers )
Loss of customers = 74.02% x ( 1 / 5 )
Loss of customers = 0.7402 x 0.20
Loss of customers = 0.14804 per minute
Loss of customers = 0.14804 per minute x 24 x 60 x 30 = 6,395.33 calls per month
Now calculate the total loss
Total loss = 6,395.33 calls x $500
Total loss = $3,197,665
Evaluate a--3° for Q = -3 and b = -3.
Answer:
Step-by-step explanation:
1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab
2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab
3. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
4. (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b)
5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b)
6. a2 − b2 = (a + b)(a − b)
7. a3 − b3 = (a − b)(a2 + ab + b2)
8. a3 + b3 = (a + b)(a2 − ab + b2)
9. an − bn = (a − b)(an−1 + an−2b + an−3b2 + ··· + bn−1)
10. an = a.a.a . . . n times
11. am.an = am+n
12. am
an = am−n if m>n
= 1 if m = n
= 1
an−m if m<n; a ∈ R, a 6= 0
13. (am)n = amn = (an)m
14. (ab)n = an.bn
15. a
b
n
= an
bn
16. a0 = 1 where a ∈ R, a 6= 0
17. a−n = 1
an , an = 1
a−n
18. ap/q = √q ap
19. If am = an and a 6= ±1, a 6= 0 then m = n
20. If an = bn where n 6= 0, then a = ±b
21. If √x, √y are quadratic surds and if a + √x = √y, then a = 0 and x = y
22. If √x, √y are quadratic surds and if a+ √x = b+ √y then a = b and x = y
23. If a, m, n are positive real numbers and a 6= 1, then loga mn = loga m+loga n
24. If a, m, n are positive real numbers, a 6= 1, then loga
m
n
= loga m−loga n
25. If a and m are positive real numbers, a 6= 1 then loga mn = n loga m
26. If a, b and k are positive real numbers, b 6= 1, k 6= 1, then logb a = logk a
logk b
27. logb a = 1
loga b where a, b are positive real numbers, a 6= 1, b 6= 1
28. if a, m, n are positive real numbers, a 6= 1 and if loga m = loga n, then
m = n
If you know the diameter of a given circle is 12, what is the area of the circle?
Answer:
The area is 113.1
Step-by-step explanation:
Hope this helped Mark BRAINLEST!!!
Help me please I’m stuck
Can someone please help me?
Answer:
#25 is left, #27 is between, #28 is below, and #26 is first i think.
Step-by-step explanation:
Answer: #25 is left, #27 is between, #28 is below, and #26 is first i think.
Step-by-step explanation:
10 If each equation below is solved for x, for which equation is x = 8 the solution?
Choose all that apply.
A 3x = 24
B 7x = 56
C 9x = 17
D 13 - X= 21
EX - 15 = -7
Which sum represents the partial fraction decomposition of 8x^ 4 + 3x^3- 115x^2- 39x+200/ 3x (x^2-10)^2
Answer:It's the last option again. You have 1 linear factor (3x) and 2 copies of a quadratic factor (x² + 10), and the partial fractions with the quadratic factor need to have a linear polynomial in the numerator.
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
edge 2021
Evaluate 150 - ( 2 +x)^ 3 when x - 2
Answer:
it's 86
Step-by-step explanation:
150-(2+x)^3=150-(2+2)^3
=150-4^3
=150-64
=86
The value of the expression 150 - (2 + x)³, when x = 2 is, 86.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 150 - (2 + x)³, when x = 2.
This can be obtained by replacing x = 2 in the expression.
Therefore, 150 - (2 + x)³.
= 150 - (2 + 2)³.
= 150 - 4³.
= 150 - 64.
= 86.
learn more about numerical expressions here :
https://brainly.com/question/29199574
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OKAY IM SORRY FOR ALL THESE- BUT I TRULY NEED HELP! THESE ARE CONFUSING! IF YOU KNOW WHAT THE ANSWER IS PLEASE HELP ME OUT!
Answer:
D
Step-by-step explanation:
A. Does not have to have symmetry
B. Opposite angles are congruent.
C. Opposite sides are parallel.
D. All sides are NOT congruent.
P(8,-3) T(x,y) = (x-4, y+7)
P'(?,?)
Answer:
P'(4,4)
Step-by-step explanation:
P(8,-3) T(x,y) = (x-4, y+7)
P'(8-4,-3+7)=P'(4,4)