Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.a (t) = 8t i + sin t j + cos 2t k, v(0) = i, r(0) = jr(t) = ?(b) On your own using a computer, graph the path of the particle.
Answers
Answer:
remember that:
a*i + b*j + c*k can be written as a vector: (a, b, c)
We know the acceleration of the particle, and we want to find the velocity of the particle, so we just need to integrate two times.
a(t) = (8*t, sin(t), cos(2*t))
integrating that, we get:
V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + v0
where v0 is the vector that defines the velocity at t = 0
in the question you wrote:
V(0) = i
so i suppose that this is:
V(0) = (1, 0, 0)
Then the velocity equation gives:
V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + (1, 0, 0)
V(t) = (4*t^2 + 1, -cos(t), sin(2*t)/2)
Now to get the position equation, we integrate it again
r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + r0
where r0 is the initial position, in the question you wrote:
r(0) = j
so we get:
r(0) = (0, 1, 0)
replacing that we get:
r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + (0, 1, 0)
r(t) = ((4/3)*t^3 + t, -sin(t) + 1, -cos(2*t)/4)
Writing this in the same notation than in the question, we get:
r(t) = [(4/3)*t^3 + t}*i + [-sin(t) + 1]*j + [-cos(2*t)/4]*k
b) Now we want to graph this:
The image isn't really good but can be used to understand the motion of the particle.
Related Questions
Alex wants to arrange chairs in such a way that the number of chairs in a row is equal to the number of columns. He has ordered 5100 tables.
a)How many more tables needed to arrange in such a way that he planned? Justify your answer
2)How many chairs can he remove to arrange in a way that he wants? Justify your answer.
Answers
Answer:
84
59
Step-by-step explanation:
In other to have the same number of chayes in both rows and columns ;
If the Number of chairs per row = x ; then number of chairs per column = x
Then the total number of chairs needed = x * x = x²
Hence, if there are 5100 chairs ;
Number of chairs needed more ;
Take the square root of 5100 ;the round to the next whole number :
B.) For number of chairs to be removed ;
Take the square root of 5100 and round down to the whole number.
Hence,
A.) = √5100 = 71.414 = 72
72² - 5100 = 84
B.) 5100 = 71.414 = 71
5100 - 71² =
Help will give brailiest to first answer
Answers
question isn't loading
Step-by-step explanation:
Answer:
i think it is b but don't take my word
Step-by-step explanation:
When g(x) = 3x, what is g(5)?
Answers
Answer:
g(5) = 15
Explanation:
If the x in g(x) is 5 then the x beside 3 would also be 5.
g(5) = 3(5)
g(5) = 15
Hope this helps, good luck!
Answer:
g(5)= 15
Step-by-step explanation:
g(x) = 3x and in this situation x =5 ( g(5) )
so substitute x for 5 in the original equation:
g(x) = 3x --> g(5) = 3(5)
which gives you 15. Hope this helps!
I need help please anyone
Answers
Answer:
base: 3units
height: 5units
Area:15units square
Step-by-step explanation:
you can count the squares in the figure to know the base and hight.
Area of parallelogram= base x height= 3x5= 15 units square.
please give me brainliest, thanks!
Help please (pre algebra)
Answers
Answer:
Step 1: 3t = 51
Step 2: 3t/3 = 51/3
Step 3: t = 17
Step 4: The Green Garage has 17 tires
Hope this helps!
Answer:
3t=51
[tex]\frac{3t}{3}[/tex]=[tex]\frac{51}{3}[/tex]
t=17
The Green Garage has 17 tires.
Step-by-step explanation:
Look at the question carefully
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?
Answers
Answer:
Step-by-step explanation:
The general equation of the circle is:
(x-h)²+(y-k)²=r²
(h, k)=(-3,-5) are the coordinates of the center of the circle.
r=6 is the radius
The equation of the circle is:
(x+3)²+(y+5)² = 36
for the function x^2+8x+7
evaluate f(4)
Answers
Answer:
I think you would have to plug in 4 as X so it would be 4^2 +8(4)+ 7
that would be 16+ 32 +7 and that would equal 55
2. The cost of oranges varies directly with the total mass bought. 2 kg of oranges costs $4.50. Describe the relationship between cost and mass in words. You may want to calculate a unit rate first.
Answers
Answer:
The relationship between the cost/mass is $2.25/kg.
Step-by-step explanation:
You first need to divide $4.50 / 2, to know what a single kilogram mass costs.
$4.50 / 2 = $2.25
Now that you have this unit rate $2.25, You can multiply/add it.
$4.50 + $2.25 is $6.75, + another $2.25 = $9.00, and so on.
3. Two dice are rolled. What’s the conditional probability that both dice are 5’s if it’s known that the sum of points is divisible by 5?
Answers
Answer:
[tex]Pr =\frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)\}[/tex] --- sample space
First, list out all outcomes whose sum is divisible by 5
[tex]A = \{(4,6), (5,5),(6,4)\}[/tex]
So, we have:
[tex]n(A) = 3[/tex]
Next, list out all outcomes that has an outcome of 5 in both rolls
[tex]B = \{(5,5)\}[/tex]
[tex]n(B) =1[/tex]
The required conditional probability is:
[tex]Pr =\frac{n(B)}{n(A)}[/tex]
[tex]Pr =\frac{1}{3}[/tex]
please help me find the area
Answers
Answer:
320 square feet.
Step-by-step explanation:
For the moment, let's put the square back in place. That would make the length 16 + 8 = 24 and the width 16.
L = 24
W = 16
Area = L * W
Area = 24 * 16
Area = 384
Now the next step is to take out the square. It is 8 * 8 = 64
The area of the figure = 384 - 64 = 320 square feet, and that's the answer.
Answer:
320 in^2
Step-by-step explanation:
we need to find the area of this figure
Firstly divide above picture in two parts
1st figure = (16*16)in.
2nd figure = (8*8)in.
Area of 1st figure = 16*16 = 256 in^2
Area of 2nd figure = 8*8 = 64 in^2
Area of whole figure = ( 256 + 64 )in^2
= 320 in^2
solve for this square.
Answers
Answer:
a2
b4
c16 brainliest plzz
Answer:
a) SV = 2
The line that is SV actually is not the full slash. It is halfway, and we know that half of four would be two.
b) RT = 4
This time RT is a full line going all the way down. So it would be 4.
c) p = a + b + c
The lengths are all the same because we calculated in the first question that two is half of four. So the base, height, and hypotenuse are the same, 2.
2 + 2 + 2 = 6
So the perimeter of the triangle RVS is 6.
Solve the following system. If the system's equations are dependent or if there is no solution, state this.
12a+35b= 19
24a+8c= 1
28b+8c= 5
A) There is one solution. The solution is (__,__,__)
B) The system is dependent
C) There is no solution
Answers
Answer:
the answer is c .no solution
A manufacturer knows that their items have a lengths that are skewed right, with a mean of 10 inches, and standard deviation of 1.6 inches. If 39 items are chosen at random, what is the probability that their mean length is greater than 10.5 inches
Answers
Solution :
Given :
Mean, μ = 10 inches
Standard deviation, σ = 1.6 inches
Sample size is n = 39
Therefore,
[tex]$\mu_{\overline x}=\mu = 10$[/tex]
[tex]$\sigma_{\overline x}=\frac{\sigma}{\sqrt n } = \frac{1.6}{\sqrt{39}}$[/tex]
= 0.25
[tex]$P (\overline X > 10.5 ) = P\left( \frac{\overline X - \mu_{\overline x}}{\sigma_{\overline x}} > \frac{10.5 - 10}{0.25} \right)$[/tex]
= P( Z >2)
= 1 - P(Z < 2)
= 1 - 0.97225 (from standard normal table)
= 0.0277
Pythagorean triples are super important to know. If the hypotenuse of a triangle is 15, what are its legs ( hint - use the three, four, five triple)
Answers
Answer:
9, 12
Step-by-step explanation:
Just multiply the 3,4,5 triple by 3 and u get 9, 12, 15
2(x+3)=x-4
please help me <3
Answers
distribute
2x + 6 = x - 4
either subtract 6 from both sides or add 4. i will be subtracting 6.
2x = x - 10
subtract x from both sides
x = -10
Can someone help me with this question please..
Answers
Answer:
The ordered pair would be (2,3)
2 in the first Box
3 in the second
Suppose, as a rough estimate, we say that there are 20 distinct geons used for object recognition; and each geon can come in 5 classifiable qualitative sizes (tiny, small, moderate, large, huge); and a pair of geons can be placed in 10 distinct qualitative relations (geon A on top of geon B; geon A to upper left of geon B; geon A to the left of geon B; and so forth).How many distinct two-geon objects do we have in the space described above?
Answers
Answer:
49500
Step-by-step explanation:
According to the Question,
Given That, Suppose, as a rough estimate, we say that there are 20 distinct geons used for object recognition, and each geon can come in 5 classifiable qualitative sizes (tiny, small, moderate, large, huge). and a pair of geons can be placed in 10 distinct qualitative relations.We have, District geons = 20 , District Size = 5
So, The Number Of Ways A geon can be selected 20 x 5 = 100Now, We choose 2 geons From 100 Geons and arrange them in 10 district relations.
So, The number of district two-geon object= [tex]\left[\begin{array}{ccc}100\\2\end{array}\right] * 10[/tex]
= (100 × 99)/2 × 10
= 49.5×100×10 ⇒ 49500
does anyone know the answer to this question
Answers
r = R/100
r = 4/100
r = 0.04 rate per year,
A = P(1 + r/n)nt
A = 1,000.00(1 + 0.04/1)(1)(6)
A = 1,000.00(1 + 0.04)(6)
A = $1,265.32
1,265.32-1,000=265.32
Consider the following hypothesis test. : : The following results are for two independent samples taken from two populations. Excel File: data10-03.xlsx Enter negative values as negative numbers. a. What is the value of the test statistic? (to 2 decimals) b. What is the -value? (to 4 decimals) c. With , what is your hypothesis testing conclusion? - Select your answer -
Answers
Answer:
[tex]z = -1.53[/tex] --- test statistic
[tex]p = 0.1260[/tex] --- p value
Conclusion: Fail to reject the null hypothesis.
Step-by-step explanation:
Given
[tex]n_1 = 80[/tex] [tex]\bar x_1= 104[/tex] [tex]\sigma_1 = 8.4[/tex]
[tex]n_2 = 70[/tex] [tex]\bar x_2 = 106[/tex] [tex]\sigma_2 = 7.6[/tex]
[tex]H_o: \mu_1 - \mu_2 = 0[/tex] --- Null hypothesis
[tex]H_a: \mu_1 - \mu_2 \ne 0[/tex] ---- Alternate hypothesis
[tex]\alpha = 0.05[/tex]
Solving (a): The test statistic
This is calculated as:
[tex]z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} }}[/tex]
So, we have:
[tex]z = \frac{104 - 106}{\sqrt{\frac{8.4^2}{80} + \frac{7.6^2}{70} }}[/tex]
[tex]z = \frac{104 - 106}{\sqrt{\frac{70.56}{80} + \frac{57.76}{70}}}[/tex]
[tex]z = \frac{-2}{\sqrt{0.8820 + 0.8251}}[/tex]
[tex]z = \frac{-2}{\sqrt{1.7071}}[/tex]
[tex]z = \frac{-2}{1.3066}[/tex]
[tex]z = -1.53[/tex]
Solving (b): The p value
This is calculated as:
[tex]p = 2 * P(Z < z)[/tex]
So, we have:
[tex]p = 2 * P(Z < -1.53)[/tex]
Look up the z probability in the z score table. So, the expression becomes
[tex]p = 2 * 0.0630[/tex]
[tex]p = 0.1260[/tex]
Solving (c): With [tex]\alpha = 0.05[/tex], what is the conclusion based on the p value
We have:
[tex]\alpha = 0.05[/tex]
In (b), we have:
[tex]p = 0.1260[/tex]
By comparison:
[tex]p > \alpha[/tex]
i.e.
[tex]0.1260 > 0.05[/tex]
So, we fail to reject the null hypothesis.
Kayla wants to fence in a rectangular dog pen that is 30 ft by 40 ft How would you use wha
you know about geometry to help her ensure that she has truly built a rectangular pen?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the dimension of the dog pen = 30 ft by 40 ft.
Using the knowledge of geometry, that know that a rectangle has been built, the area of the pen should be :
Area of rectangle = Length * width
Area = 40 * 30
Area = 1200 ft²
Perimeter of rectangle = 2(Length + width)
Perimeter = 2(40 + 30)
Perimeter = 2(70)
Perimeter = 140 feets
Hence, area of the pen should be 1200 ft² and its perimeter or fencing should measure 140 feets
6(x + 2) in the simplest form
Answers
Using the Distributive Property we can put this in its simplest form.
6(x+2)
(6)(x)+(6)(2)
6x+12
Answer:
6x + 12
Step-by-step explanation:
Use the distributive property to multiply the 6 to the x and 2 to get 6x + 12.
i need help finding m<1 please :)
Answers
Answer
c,116°
Step-by-step explanation:
i don't know how to draw a diagram?
Join ends of chord with the center making angles ∠2,∠3 and angle at the center.
angle at the center=128°
∠1=∠2+90°
∠2=∠3
∠2+∠3+128=180
∠2+∠2+128=180
2∠2=180-128=52
∠2=52/2=26
∠1=26+90=116°
sorry i can't explain properly without picure.
f(x) = 3x + 10
х
f(x)
-3
-2
-1
-4
Answers
Miss Smith save 5% on her recent Starbucks order because she is a Starbucks Rewards member if the cost of per purchase before the discount was $5.20 how much did Miss smith save
Answers
Answer:
$4.94
Step-by-step explanation:
O 5.20 100%
P - 5
N 95%
0.95 x 5.20 = 4.94
Ms. Smith saved $4..94.
At Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice
cream alternating with layers of cake. If there are 8 flavors of ice cream, and we count
different cakes based on the order of ice cream layers from top to bottom:
a) how many different cakes can be made if flavors can be repeated?
Answers
Answer:
4096 different cakes can be made if flavors can be repeated.
Step-by-step explanation:
Since at Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice cream alternating with layers of cake, if there are 8 flavors of ice cream, and we count different cakes based on the order of ice cream Layers from top to bottom, to determine how many different cakes can be made if flavors can be repeated, the following calculation must be performed:
8 x 8 x 8 x 8 = X
64 x 64 = X
4.096 = X
Therefore, 4096 different cakes can be made if flavors can be repeated.
Find an equation for the line that passes through the points (-2,-6) and (6,4).
Answers
Step-by-step explanation:
Line P passes through POINTS (-2,6) and (6,4). Using y=mx + b where m is the SLOPE(rise divided by the run), and b is the Y-INTERCEPT. Pick the POINT (6,4) and plug into the Y-INTERCEPT EQUATION above to determine the Y-INTERCEPT
Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5 (and your wager) for rolling a 5 or a 2, nothing otherwise. What are your expected net winnings, to the nearest cent?
Answers
You would have a 2/6 chance or 1/3
You paid $3 so if you rolled both number you would make $10. Then you would have to subtract the cost of $3 from that. So you could win $7. Not sure if you were using on one or 2 dice to roll. You would just count all the numbers on both dice 12. Then you would have a 4 in 12 chance. 4/12 or 1/3 chance.
What is the solution set for the quadratic inequality x2 – 5 ≤ 0?
Answers
Answer: -4...?
Step-by-step explanation:
Your cell phone plan costs 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan.
Answers
Answer: Umm lemme try this
Step-by-step explanation:
55+35=x
31vw+41uvw+9uvw–11uvw
Combine any like terms in the expression. If there are no like terms, rewrite the expression.
Answers
Answer:
31vw+39uvw . yes we will rewrite the expression
Step-by-step explanation:
41uvw+9uvw=50uvw-11uvw=39uvw
