Given an acceleration vector, initial velocity ⟨u0,v0,w0⟩, and initial position ⟨x0,y0z0⟩, find the velocity and position vectors for t≥0
a(t)=⟨7t,e−t,11⟩,⟨u0,v0,w0⟩=⟨0,0,2⟩,⟨x0,y0z0⟩=⟨3,0,0⟩
What is the velocity vector?
v(t)=
What is the position vector?
r(t)=
Answers
The velocity vector is given by v(t)=⟨7/2t² + C1, -e⁻ᵗ + C2, 11t + C3⟩ and the position vector is given by r(t) = ⟨7/6t³ + C1t + C4, e⁻ᵗ + C2t + C5, 11/2t² + C3t + C6⟩
The given information is: a(t)=⟨7t,e−t,11⟩⟨u0,v0,w0⟩=⟨0,0,2⟩⟨x0,y0z0⟩=⟨3,0,0⟩From the given acceleration vector a(t), we need to find the velocity vector and position vector for t ≥ 0. The velocity vector is the integral of acceleration, and the position vector is the integral of the velocity vector. We can get the velocity vector v(t) by integrating a(t) as follows: v(t) = ∫a(t)dt = ⟨(7/2)t² + C1, -e⁻ᵗ + C2, (11)t + C3⟩, where C1, C2 and C3 are constants of integration that we need to find by using the initial conditions. Using the given initial velocity ⟨u0,v0,w0⟩=⟨0,0,2⟩, we get: C1 = u0 = 0C2 = v0 = 0C3 = w0 = 2Therefore, the velocity vector is:v(t) = ⟨(7/2)t², -e⁻ᵗ, (11)t + 2⟩The position vector r(t) can be obtained by integrating the velocity vector v(t) as follows: r(t) = ∫v(t)dt = ⟨(7/6)t³ + C1t + C4, e⁻ᵗ + C2t + C5, (11/2)t² + C3t + C6⟩, where C4, C5 and C6 are constants of integration that we need to find by using the initial conditions. Using the given initial position ⟨x0,y0z0⟩=⟨3,0,0⟩, we get:C4 = x0 = 3C5 = y0 = 0C6 = z0 = 0Therefore, the position vector is:r(t) = ⟨(7/6)t³ + C1t + 3, e⁻ᵗ + C2t, (11/2)t² + 2t⟩Hence, the velocity vector is given by v(t) = ⟨7/2t², -e⁻ᵗ, 11t + 2⟩ and the position vector is given by r(t) = ⟨7/6t³ + C1t + 3, e⁻ᵗ + C2t, 11/2t² + 2t⟩, where C1, C2 are constants of integration.
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Related Questions
Two trains leave towns 492 miles apart at the same time and travel toward each other. One train travels 16 miles per hour slower than the other. If they meet in 3 hours, what is the rate of each train?
Answers
Answer:
The rate of each train is 74 miles per hour and 90 miles per hour respectively.
Step-by-step explanation:
Given;
distance between the two trains, d = 492 miles
total time traveled by each train before meeting the other, t = 3 hours
Let the speed for the first train = p
Let the speed for the second train = q
Assuming the first train is 16 mph slower than the second train, then;
q = p + 16
Distance = speed x time
492 miles = (p + q) x 3
492 = 3p + 3q
but, q = p + 16
492 = 3p + 3(p + 16)
492 = 3p + 3p + 48
492 - 48 = 6p
444 = 6p
p = 444 / 6
p = 74 miles per hour
q = 74 + 16
q = 90 miles per hour
Therefore, the rate of each train is 74 miles per hour and 90 miles per hour respectively.
HELP imdjhehdhshshssksjish
Answers
Answer:
40
Step-by-step explanation:
\( \dfrac{ab^2 - 5}{10} \)
a = 5; b = 9
First, substitute 5 for a and 9 for b.
\( \dfrac{ab^2 - 5}{10} = \)
\( = \dfrac{(5)(9)^2 - 5}{10} \)
\( = \dfrac{(5)(81) - 5}{10} \)
\( = \dfrac{405 - 5}{10} \)
\( = \dfrac{400}{10} \)
\( = 40 \)
Can someone help me with this
Answers
Answer:
Step-by-step explanation:
It pretty simple, you need to read the sentence and match the number.
Ex:
Seven more than one half = 7 more than 1/2
= 7+ 1/2
Because ‘more’ shows that you’re adding
While difference shows you’re subtracting
Quotient shows you’re dividing
And product shows you’re multiplying
And when it refers to ‘a number’ it means your variable which in this case is ‘n’.
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space Randomly choosing an even number between 1 and 10, inclusive
The sample space is______. (Use a comma to separate answers as needed. Use ascending order) There are________outcome(s) in the sample space.
Answers
Answer:
Step-by-step explanation:
Sample Space
off even numbers
= {2,4,6,8,10}.
There are 5 outcomes in the sample space,
PLEASE HELP ME!
Question in image. Thank you
Answers
The correct options for the given polynomial are:
NEG/EVENas x goes to ∞, f(x) goes to -∞as x goes to -∞, f(x) goes to -∞How to identify the end behavior of the polynomial?To analyze the end behavior of a polynomial we need to look at the degree and the sign of the leading coefficient.
Remember that the degree is the largest exponent of the polynomial.
Here we can see that the degree is 12, so it is even.
And the leading coefficient (the coefficient in the term with the largest exponent) is -10, so it is negative.
Then the first correct option is:
NEG/EVEN
That means that in both ends the polynomial tends to negative infinity, so:
as x goes to ∞, f(x) goes to -∞as x goes to -∞, f(x) goes to -∞Learn more about end behavior at:
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Need help ASAP need to turn this in
Answers
Answer:
click the turn in button
theres a button you can click to turn in
the study of statistics rests on what two major​ concepts?
Answers
The study of statistics rests on two major​ concepts probability which is the branch of mathematics that deals with the likelihood of events occurring and Data Analysis is the process of examining and interpreting data in order to gain insights and make better decisions
Probability theory is based on the idea that, given enough data, the frequency of an event can be predicted and allows for the formulation of mathematical models that can quantify the likelihood of particular outcomes. Probability is the foundation of statistics and helps to explain the behavior of chance events.It involves the collection, organization, and analysis of data from a variety of sources, such as survey responses, observations, experiments, or existing databases.
Data analysis is used to identify patterns and relationships in data, draw conclusions, and make decisions. It is an important part of statistics, as it helps to uncover insights that would otherwise remain hidden. Data analysis tools, such as statistical models, can be used to gain greater insight into the data.
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Greg's home is 1.8 miles from his school.
There is a music store halfway between school and his home. Today, Greg wants to stop at
the store after school. Right now, he is 0.36 miles away from school.
a. How far is the music store from Greg's school?
b. How much farther does Greg need to walk to get to the store?
c. How many miles does he have left to walk home?
Answers
Answer:
a. 0.9 miles
b. 0.54 miles
c. 1.44 miles
Step-by-step explanation:
Ten runners join in a race. In how many ways can they ba arranged as first, second, and third placers?
Answers
The answer is that the ten runners can be arranged in 720 ways as first, second, and third placers. We can do this by using the concept of permutations.
Ten runners are participating in a race, and we need to know in how many ways they can be arranged as first, second, and third placers.In this case, we have to find the number of arrangements in which the top three runners can be chosen out of ten runners. We can do this by using the concept of permutations.Permutations are the ordered arrangements of a set of objects. There are different types of permutations based on the arrangement of the set of objects. These are:- Permutations with repetition- Permutations without repetition- Circular permutations.In this case, we need to calculate the permutations without repetition as the runners cannot be repeated in the top three places.As the runners are being arranged in order, we can use the formula for permutations:
nPr = n! / (n - r)!Here, n = 10 (as there are ten runners), and r = 3 (as we need to find the top three runners).Therefore, the total number of permutations possible for ten runners as first, second, and third placers is:
10P3 = 10! / (10 - 3)!10P3 = 10! / 7!10P3 = (10 x 9 x 8) / 3 x 2 x 1 = 720
Hence, the answer is that the ten runners can be arranged in 720 ways as first, second, and third placers.
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I want to know how to divide fractions can any one help P.S this is my first time on brainly
Answers
Answer:
Simple rules
KCF
keep your denominator
change your numerator
flip one of your fractions
Step-by-step explanation:
:)
Answer:
Problem: 1/4 divided by 1/2
Step 1 : Put it in multiplication format
1/4 * 1/2
Step 2 : Flip the denominator with the numerator of only the second fraction
1/4 * 2/1
Step 3 : Answer
2/4 or 1/2
Step-by-step explanation:
I know
One-third of a number yields twelve. Which equation could be used to find the number?
1/3 n= -12
1/3 n = 12
3 n = 12
3 n = -12
Answers
Answer:
1/3n=12
Step-by-step explanation:
The reason why it is 1/3n=12, is because you know that the number in front of n is 1/3. By figuring that out, you have already ruled out 3n=12 and 3n=-12. Finally, you know that 12 is a positive number leaving you with 1/3n=12.
this is the answer
if we assume that the horses constitute a random sample of all horses in the state, then we estimate the probability that a randomly selected horse is a stallion to be
Answers
the sample is truly representative of all horses in the state, and that there are no biases or confounding factors that might affect the proportion of stallions in the sample.
If we assume that the horses constitute a random sample of all horses in the state, then we can estimate the probability that a randomly selected horse is a stallion by calculating the proportion of horses in the sample that are stallions. Let's assume that we have a sample of n horses, and that x of these horses are stallions. Then the estimated probability of selecting a stallion is:
x/n
For example, if we had a sample of 100 horses and 25 of them were stallions, the estimated probability of selecting a stallion would be:
25/100 = 0.25 or 25%
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Mario had 40 shares of stock that each lost $75 during the half of the year. He also had 24 shares of a different stock that gained $50 each. What was his net change during this time period on these stocks?
Answers
The net change in the stock is $1800
How to calculate the net change ?Mario has 40 shares of stick that each lost $75 during half of the year
He also had 24 shares of a different stock that gained $50
The net change can be calculated as follows
-40 × 75
= -3000
= 24 × 50
= 1200
Net change
-3000 + 1200
= -1800
Hence the net change in the stocks is $1800
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Given: GH || KL, J is the midpoint of HK
Prove: AGHJ ALKJ
STATEMENT
REASON
1. GH | KL
Given
2. J is the midpoint of HK
Given
3
4
5
6.GHJ=LKJ
Answers
Answer:
Step-by-step explanation:
From the picture attached,
Given:
GH║KL and J is the midpoint of HK.
To Prove:
ΔGHJ ≅ ΔLKJ
Statements Reasons
1. GH║KL 1. Given
2. J is the midpoint of HK 2. Given
3. JH ≅ JK 3. Definition of the midpoint of a segment
4. ∠JKL ≅ ∠JHG 4. Alternate interior angles
5. ∠GJH ≅ ∠KJL 5. Vertically opposite angles
6. ΔGHJ ≅ ΔLKJ 6. By ASA theorem of congruence
Statements Reasons
1. GH║KL 1. Given
2. J is the midpoint of HK 2. Given
3. JH ≅ JK 3. Definition of the midpoint of a segment
4. ∠JKL ≅ ∠JHG 4. Alternate interior angles
5. ∠GJH ≅ ∠KJL 5. Vertically opposite angles
6. ΔGHJ ≅ ΔLKJ 6. By ASA theorem of congruence
We have to prove the statement, ∠GHJ = ∠LKJ
Given; GH || KL, J is the midpoint of HK.
To prove; ∠GHJ = ∠LKJ
Given; J is the midpoint of HK,
By definition midpoint of a segment,
The midpoint is the middle part of the line segment J, it is equidistant from both endpoints it is the centroid of the segment of the endpoints.
JH ≅ HK
Then, by the property of alternate interior angles,
∠JKL≅ ∠JKH
Therefore, by the property of vertically opposite angles,
When two lines intersect they form four angles. Vertical angles are the angles that are opposite to each other. Any two intersecting lines form two pairs of vertical angles that are opposite to each other.
∠GJH ≅ KJL
By ASA congruence theorem,
When two triangles are congruent to each other - If two angles and the involved side of one triangle is equivalent to the two angles and the included side of the other triangle.
ΔGHJ ≅ ΔLKJ
Hence Proved.
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The extreme water slide forms a 20 angle with the tower it leans against 80 feet above the ground find the length of the slide x
Answers
Answer:
85.1 ft
Step-by-step explanation:
The extreme water slide forms a 20 angle with the tower it leans against 80 feet above the ground find the length of the slide x
We solve using the Trigonometric function of Cosine
cos y = adjacent/hypotenuse
y = angle = 20°
Adjacent = 80 ft
Hypotenuse = ?
cos 20 = 80/Hypotenuse
Hypotenuse = 80/cos 20
x = 85.134221798 ft
Approximately = 85.1 ft
Length of the slide = 85.1 ft
Henry bought 5/6 pound of roasted almonds for $5. He wants to know the price per pound. What is the price per pound?
Answers
Given
He bought 5/6 pound for $5
The price per pound can be calculated using the formula:
\(price\text{ per pound = }\frac{Amount\text{ he spent}}{Weight\text{ in pounds of roasted almonds}}\)Hence, the price per pound is:
\(\begin{gathered} price\text{ per pound = }\frac{\text{ \$}5}{\frac{5}{6}\text{ pounds}} \\ =\text{ \$6 /pound} \end{gathered}\)Answer:
price per pound : $6/ pound
BASED ON THESE NUMBERS, AND YOUR KNOWLEDGE OF FIBONACCI NUMBERS, IS THE STATEMENT THAT FOLLOWS TRUE OR FALSE? F(N+2) IS EXACTLY EQUAL TO THE SUM OF THE FIRST N TERMS OF THE FIBONACCI SEQUENCE.
A. TRUE
B. FALSE
Answers
Answer:
false
Step-by-step explanation:
what is the probability that a randomly chosen person 25 years of age or older is in the labor force? show your work.
Answers
The probability that a randomly chosen person 25 years of age or older is in the labor force 67.035%.
The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.
The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.
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20 POINTS NEED HELP DUE TODAY HELP!!!!!!
2. Is the point (-0.5, sin(4π/3)) on the unit circle? Explain your reasoning.
3. Is the point (-0.5, sin(5π/6)) on the unit circle? Explain your reasoning.
4. Suppose that sin(Θ) = -0.5 and that Θ is in quadrant 4. What is the exact value of cos(Θ)? Explain your reasoning.
Answers
1) The point is on the unit circle.
2) The point is not on the unit circle
3) cos(Θ) = 0.866
Is the point on the unit circle?We know that all the points on the unit circle have a magnitude of 1, then we can write:
√[ (-0.5)² + (sin(4π/3)²) = 1
This means that the point is on the unit circle.
b) Now the point is (-0.5, sin(5π/6))
We need to do the same thing, this time we will get:
√[ (-0.5)² + (sin(5π/6)²) = 0.71
So this point is not on the number line.
c) Here we know that sin(Θ) = -0.5 and the angle is in the quadrant 4.
Then Θ = Asin(-0.5) = -30°
Remember that -30° is on the fourth quadrant, so this is correct, now the cosine of that is:
cos(-30°) = 0.866
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The lengths of the four sides of a quadrilateral (in meters) are consecutive integers. If the perimeter is 50 meters, find the value of the shortest of the four side lengths.
(also, what do those numbers mean that are next to the subject when i'm asking a question?)
Answers
Mark me Brainly
Can you please answer this question
Answers
Answer:
9/14
Step-by-step explanation:
add them
Suppose I want to investigate whether babies can tell the difference between a collection of 12 and a collection of 18 objects. What would you advise me to choose a dependent measure in my experiment
Answers
One possible dependent measure for your experiment could be the looking time of the babies towards each collection of objects. You can use a visual preference method where you present the babies with both collections of objects side-by-side and measure the amount of time they spend looking at each one.
Another possible dependent measure is habituation or dishabituation. In this method, you repeatedly present one collection of objects to the babies until they become habituated, i.e., they stop paying attention to it. Then, you introduce the other collection of objects and measure if the babies show a renewed interest, indicating that they perceive a difference between the two collections.
Other measures could include physiological measures such as heart rate or brain activity using non-invasive techniques like electroencephalography (EEG) or functional near-infrared spectroscopy (fNIRS). However, these measures may require more specialized equipment and expertise.
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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (0, ∞).
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (0, ∞).
The function is increasing on the interval (–∞, 0).
Answers
Using translation concepts, it is found that the correct statement about h(x) is:
The function is decreasing on the interval (0, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
\(f(x) = \sqrt{x}\)
Which is increasing on (0, ∞).
After the translation, the function is:
\(h(x) = -2\sqrt{x}\)
It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).
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Difference Between Bar Chart and Histogram
Answers
Answer:
Histograms visualize quantitative data or numerical data, whereas bar charts display categorical variables
Given three perspective views, draw each solid.
1. Front view:
Top view:
Side view:
Solid:
2. Front view:
Top view:
Side view:
Solid:
PIN
abse bilost
Answers
The drawing of each solid in three dimension is sketched and attached
What are perspective views in drawing?Perspective views in drawing are a way of representing a three-dimensional object or scene on a two-dimensional surface. By using perspective, the artist can create the illusion of depth and spatial relationships between objects in the scene.
There are several types of perspective views in drawing, including:
One-point perspective: This type of perspective is used when the subject is viewed straight-on, and all lines converge to a single point on the horizon line.
Two-point perspective: This type of perspective is used when the subject is viewed from an angle, and two vanishing points are used to create the illusion of depth.
Three-point perspective: This type of perspective is used when the subject is viewed from a very high or very low angle, and three vanishing points are used to create the illusion of depth.
Perspective views are an essential tool for artists in many fields, including architecture, product design, and illustration. Understanding perspective is crucial for creating realistic and compelling images that accurately represent three-dimensional space on a two-dimensional surface.
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what is the sum of all the even numbers between 30 and 36?
Answers
Answer:
30 + 32 + 34 + 36 = 132
Hope this helps!!
2.
A
is straight and extends in both directions forever.
a) point
b) line
c) line segment
d) ray
Answers
Marco has two bags of candy. One bag contains three red lollipops and
2 green lollipops. The other bag contains four purple lollipops and five blue
lollipops. One piece of candy is drawn from each bag. What is the probability
of choosing a green lollipop and a purple lollipop?
Answers
The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45
We have to given that;
One bag contains 3 red lollipops and 2 green lollipops.
And, The other bag contains four purple lollipops and five blue lollipops.
Hence, The probability of choosing a green lollipop is,
P₁ = 2 / 5
And, The probability of choosing a purple lollipop is,
P₂ = 4 / 9
Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,
P = P₁ × P₂
P = 2/5 × 4/9
P = 8/45
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For what values of a and b does √a+√b=√a+b?
Answers
The equation is satisfied for all values of a and b.
The values of a and b can be any non-negative real numbers as long as the product ab is non-negative.
The equation √a + √b = √(a + b) is a special case of a more general rule called the Square Root Property.
According to this property, if both sides of an equation are equal and non-negative, then the square roots of the two sides must also be equal.
To find the values of a and b that satisfy the given equation, let's square both sides of the equation:
(√a + √b)² = (√a + √b)²
Expanding the left side of the equation:
a + 2√ab + b = a + 2√ab + b
Notice that the a terms and b terms cancel each other out, leaving us with:
2√ab = 2√ab
This equation is true for any non-negative values of a and b, as long as the product ab is also non-negative.
In other words, for any non-negative real numbers a and b, the equation √a + √b = √(a + b) holds.
For example:
- If a = 4 and b = 9, we have √4 + √9 = √13, which satisfies the equation.
- If a = 0 and b = 16, we have √0 + √16 = √16, which also satisfies the equation.
So, the values of a and b can be any non-negative real numbers as long as the product ab is non-negative.
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If Cara continues to run at this rate, predict how far she will run in 4 hours.