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
Type your answer in the box.
r = 3 d = 5
Answer: 8.5
Step-by-step explanation:
I just took the quiz last week.
Can somebody help please #asap help w number 8
Answer:
y=4x bc each one is 4 so for one box it cost $4
Answer:
The expression will be y = 4x.
Step-by-step explanation:
First, we have to form expressions for number of boxes and total amount she earn :
Let x be the number of boxes,
Let y be the total amount,
Given that the costs of each box is $4 so in order to find the total amount, you have to multiply the number of boxes by 4 :
y = 4x
Find the area A of the sector of a circle of radius 50 feet formed by the central angle
5
radian.
Answer:
[tex]A=6250\ feet^2[/tex]
Step-by-step explanation:
Given that,
The radius of circle, r = 50 feet
The central angle, [tex]\theta=5\ radian[/tex]
We need to find the area of the sector of a circle. The formula for the area of sector is given by :
[tex]A=\dfrac{1}{2}r^2\theta\\\\=\dfrac{1}{2}\times 50^2\times 5\\\\A=6250\ feet^2[/tex]
So, the area f the sector of the circle is [tex]6250\ feet^2[/tex].
Can someone please help me ?
Answer:
m and p
p and q
Step-by-step explanation:
both m and q are 71° so what plus 71 = 90; 19. therefore, m and p are complementary as well p and q.
One of the legs of a right triangle measures 11 cm and its hypotenuse measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
4.8cm
Step-by-step explanation:
a²+b²=c² where c is the hypotenuse so
Let's plug in those values
11²+b²=12²
b²=12²-11²
b²=23
b=4.8
What transformation rule would represent a shift of 3 units to the left 4 units down?
Group of answer choices
(x,y) –> (x – 4, y – 3)
(x,y) –> (x – 3, y – 4)
(x,y) –> (4x, 3y)
(x,y) –> (x + 3, y + 4)
Given:
Shift of 3 units to the left 4 units down.
To find:
The transformation rule.
Solution:
The rule of transformation is
[tex](x,y)\to (x+a,y+b)[/tex] ...(i)
Here, a<0 if the figure shifts a units left and a>0 if the figure shifts a units right.
Similarly, b<0 if the figure shifts b units down and b>0 if the figure shifts b units up.
If a transformation represents shift of 3 units to the left 4 units down, then a=-3 and b=-4.
Putting a=-3 and b=-4 (i), we get
[tex](x,y)\to (x+(-3),y+(-4))[/tex]
[tex](x,y)\to (x-3,y-4)[/tex]
Therefore, the correct option is B.
is there estimates that her dinner has 48g of fat in it what percentage of her total daily allowance of fat does her meal contain her total daily allowance of fat is 70 grams
Answer: The meal contains 68.57% of her daily allowance of fat
Step-by-step explanation:
We know that in the dinner, there is a total of 48g of fat.
We also know that her daily dose of fat is 70g, so this will be "the 100%", then we can write:
70g = 100%
Under this point of view, we also can relate the 48g of the dinner to another percentage X%, such that:
48g = X%
Then we have two equations:
48g = X%
70g = 100%
To solve this, we can take the quotient of these two equations to get:
(48g/70g) = (X%/100%)
Now we want to solve this for X%, then we need to isolate X%:
(48g/70g)*100% = X%
68.57% = X%
This means that 48 grams of fat are 68.57% of her daily allowance.
-8c - 6 less than or equal to 10
What is the Voter Registration Act and how does it affect Gerrymandering?
Answer:
United States federal law signed into law by President Bill Clinton on May 20, 1993, and which came into effect on January 1, 1995.
Step-by-step explanation:
Hope It Helps :)
a number added to one third of itself equals 12 . what is the number
Answer:
9
Step-by-step explanation:
x+1/3x=12
(3x+1x)/3=12
4x/3=12
4x=12×3
4x=36
x=36/4
x=9
Answer:
1/3+x=12(cross multiply)
x+1=12*3
x+1=36(collect like terms)
x=36-1
x=35
Aldos coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Aldo $4.15 per pound, and type of B coffee costs $5.25 per pound. This month, Aldo made 119 pounds of the blend, for a total cost of $548.85. How many pounds of type B coffee did he use?
Let A represent amount of Type A coffee pounds used.
Let B represent amount of Type B coffee pounds used
A + B = 156
B = 156 - A
A = 156 - B
5.80A + 4.65B = 826.60
580 (156 - B) + 4.65B - 826.60 = 0
904.8 - 5.80B + 4.65B - 826.60 = 0
904.8 - 1.15B - 826.60 = 0
78.2 - 1.15B = 0
78.2/1.15 = 1.15B/1.15
68 = B
B = 68 pounds of Type B coffee
There's many more steps you can take to check and etc but am too lazy to put down sorry.
The drop down menu suggestions is true or false I need someone to help me plz
Answer:
Answer true or false and see what happens
Step-by-step explanation:
Can someone help me it’s due tomorrowwwww
Number one is straight angle
number two is obtuse
number three is acute
Number 4 is acute
number 5 is a right angle
number 6 is obtuse
number 7 is right angle
number 8 is obtuse
HOW TO CONSENTRATE ON STUDY?
Answer:
Listen to music or watch a video about what your about to study. Or do what I do... eat while studying
Step-by-step explanation:
i need help with everything please if you help you are a legend
Answer:
you got this
Step-by-step explanation:
go with your gut and you sure can win
Answer:
I can help.
Step-by-step explanation:
3a is closer to 1, because 12/12 is 1. and 6/12 is 1/2
3b is closer to 0, because 0/6 is o. and 3/6 is 1/2.
3c is 1 and 1 1/12
11/12 + 1/6
find the common denominator. 12. 6×2 and 1×2 then add straight across.
If X = 3 units, Y = 3 units, and Z = 4 units, then what is the surface area of the right triangular pyramid shown above?
Answer:
36
Step-by-step explanation:
you have to multiple and find the other area
Solve the equation.
q − 11 = 16
Answer:
q = 27
Step-by-step explanation:
Answer: 27
Step-by-step explanation: 16+11=27
if you know that there are 60 minutes in an hour how could you find the number of hours in 300 minutes
Answer:
300/60=5 Hours
Hope it helps
Answer:
5hours
Step-by-step explanation:
................
300÷60
in January 2010, Diana invested $4,500 in an account that paid interest compounded annually. the table showstopper balance of the account at different times. what was Diana's balance, in dollars and cents, in January 2014. the numbers on the table are, For the month Jan. 2011-$4,635.00
Jan. 2012-$4,774.05
Jan. 2013-$4,917.27
Answer:
500,000
Step-by-step explanation:
80-1
Which equation matches the hanger diagram?
Answer:
D
Step-by-step explanation:
You can see that the hanger is perfectly balanced
So that means that:
5 ones = 2 x's
So:
1+1+1+1+1=x+x
simplified
2x=5
D
I will give brainliest. any irrelevant awnsers will be flagged :). pls help.
Answer:
it is B
Step-by-step explanation:
hope it helps :) have a nice day!
Find the measure of 43.
43
77
<3 = [?]
Enter
Answer:
<3 = 77⁰
Step-by-step explanation:
Since 77⁰ and <3 are interior angles, angles inside the parallel line are in the same. This means that <3 will be 77⁰.
Hope this helps and stay safe, happy, and healthy, thank you :) !!
?=103°
Answer:
<3+77=180 co interior angle
<7=180-77=103°
Help please I give brainliest
Answer:
B
Step-by-step explanation:
Answer:11,15
Step-by-step explanation:
x axis is 11
y axis is 15
y axis stands talll
x axis lays down
100 POINTS AND WILL GIVE BRAINLIEST Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
x
2
-1
10
1
2
y
Use the function rule to complete the table.
- 10x + y = 4
In a multiple regression analysis, two independent variables are considered, and the sample size is 30. The regression coefficients and the standard errors are as follows. b1 = 2.815 Sb1 = 0.75 b2 = −1.249 Sb2 = 0.41 Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) H0: β1 = 0 H0: β2 = 0 H1: β1 ≠ 0 H1: β2 ≠ 0 H0 is rejected if t < −2.074 or t > 2.074
Answer:
There is a sufficient evidence that the coefficient b1 is not zero
There is a sufficient evidence that the coefficient b2 is not zero
Step-by-step explanation:
Given
[tex]n = 30[/tex]
[tex]b_1 = 2.815[/tex]
[tex]Sb_1 = 0.75[/tex]
[tex]b_2 = -1.249[/tex]
[tex]Sb_2 = 0.41[/tex]
[tex]\alpha = 0.05[/tex]
Claim: Coefficient is zero
The null and alternate hypotheses are:
[tex]H_0: \beta_1 =0\\\\H_1: \beta_1 \ne 0[/tex]
The test is two tailed because the alternate hypothesis contains [tex]\ne[/tex]
Calculate the rejection region
[tex]P(t < -t_0) = P(t > t_0) = \frac{\alpha}{2}[/tex]
[tex]P(t < -t_0) = P(t > t_0) = \frac{0.05}{2}[/tex]
[tex]P(t < -t_0) = P(t > t_0) = 0.025[/tex]
Calculate the degrees of freedom
[tex]df = n -2[/tex]
[tex]df = 30 -2[/tex]
[tex]df = 28[/tex]
On the student's T distribution table, the t value at 28 and column with [tex]\alpha = 0.05[/tex] (two tailed) is:
[tex]t\ value = 2.048[/tex]
The rejection value will contain all value lesser than -2.048 and all values greater than 2.048.
So: We reject [tex]H_0[/tex] when [tex]t < -2.048[/tex] and [tex]t >2.048[/tex]
Testing the first independent variable
Calculate test statistic
[tex]t = \frac{b_1 - 0}{Sb_1}[/tex]
[tex]t = \frac{2.815 - 0}{0.75}[/tex]
[tex]t = \frac{2.815 }{0.75}[/tex]
[tex]t = 3.753[/tex]
[tex]t = 3.753 > 2.048[/tex]
This implies that, we reject [tex]H_o[/tex] and accept [tex]H_1[/tex]
There is a sufficient evidence that the coefficient b2 is not zero
Testing the second independent variable
Calculate test statistic
[tex]t = \frac{b_2 - 0}{Sb_2}[/tex]
[tex]t = \frac{-1.249 - 0}{0.41}[/tex]
[tex]t = \frac{-1.249 }{0.41}[/tex]
[tex]t = -3.0463[/tex]
[tex]t = -3.0463 < -2.048[/tex]
This implies that, we reject [tex]H_o[/tex] and accept [tex]H_1[/tex]
There is a sufficient evidence that the coefficient b2 is not zero
Look at the image. Could someone please help me out? Only question B Thank you! WILL GIVE BRAINLYEST
Answer:
y = 3
Step-by-step explanation:
2x+6y=5x+4y if x=2
2(2)+6y=5(2)+4y
4+6y=10+4y
-4 =-4
6y=6+4y
-4y= -4y
2y=6
/2=/2
y=3
Which pair of triangles can be proven congruent by SAS?
Answer:
top choice
Step-by-step explanation:
For SAS, you need a side followed by an angle followed by another side of one triangle to be congruent to the corresponding parts of another triangle.
The top choice shows side-angle-side.
The middle choice shows angle-side-angle.
The bottom choice shows side-side-side.
Answer: top choice
Lilya bought 3 donuts for $2.97. At this rate, how much would 10 donuts cost?
Answer:
$9.90
Step-by-step explanation:
$2.97 divided by 3 equal 0.99 cents
0.99 multiplied by 10 equal 9.90
find the median for 24 27 17 19 23 39 20 29 33 33
Answer:
25.5
Step-by-step explanation:
Median calulater
Which of the following are dependent events? Select all that apply.
You draw a marble from a bag, replace it, and draw again.
You flip a coin and roll a number cube.
You draw two numbers from 1 to 10 from a hat without replacing them first.
You randomly choose two socks from a drawer, hoping they will match.
Answer: all
Step-by-step explanation:
Answer: You randomly choose two socks from a drawer, hoping they will match.
You draw two numbers from 1 to 10 from a hat without replacing them first.
Step-by-step explanation:
dependent events: compound events in which one event affects the likelihood of the other event
independent events:compound events in which one event does not affect the likelihood of the other event