The position of a particle at time t is given by s. Find the velocity ds/dt. s^3 - 5st + 2t^4 - 5t = 0
ds/dt = ____
Answers
The velocity \(\frac{ds}{dt}\) is (5s - 8\(t^3\) + 5) / (3\(s^2\)).
The velocity of the particle at a given time t, we need to take the derivative of the position functions with respect to time t.
That is,
\(\frac{ds}{dt}\) = \(\frac{d}{dt}(s)\)
We are given the position function s(t) as:
\(s^3\) - 5st + 2\(t^4\) - 5t = 0
To find the derivative \(\frac{ds}{dt}\) , we need to take the derivative of each term in the equation with respect to time t using the rules of differentiation. We get:
3\(s^2\)(ds/dt) - 5s + 8\(t^3\) - 5 = 0
Now, we can solve for \(\frac{ds}{dt}\) by isolating it on one side of the equation:
3\(s^2\)(ds/dt) = 5s - 8\(t^3\) + 5
\(\frac{ds}{dt}\) = (5s - 8\(t^3\) + 5) / (3\(s^2\))
Therefore the velocity of the particle at a given time t is,
\(\frac{ds}{dt}\) = (5s - 8\(t^3\) + 5) / (3\(s^2\))
It's important to note that the velocity of the particle is not constant and depends on the position of the particle at any given time.
This means that the velocity will change as the particle moves along its path and we need to take into account the instantaneous position of the particle at any given time to determine its velocity.
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Related Questions
The following points represent a relation where x represents the independent variable and y represents the dependent variable.
three fourths comma negative 2, 1 comma 5, negative 2 comma negative 7, three comma negative one half, and 6 comma 6
Does the relation represent a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
Answers
Answer:
(c) Yes, because for each input there is exactly one output
Step-by-step explanation:
You want to know if this relation represents a function:
{(3/4, -2), (1, 5), (-2, -7), (3, -1/2), (6, 6)}
FunctionA function has exactly one output for any input. In a list of ordered pairs, this means no first-value is repeated.
Here, the first values of the pairs are 3/4, 1, -2, 3, 6. There are no repeats, so the relation is a function. The appropriate choice is ...
(c) Yes, because for each input there is exactly one output
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help me plzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
Step-by-step explanation:
f(-3)=-(-3)²+7(-3)-13
=-9-21-13
=-43
Answer:
Step-by-step explanation:
\(f(x)=-x^2+7x-13\\ \\ f(-3)=-(-3)^2+7(-3)-13\\ \\ f(-3)=-(9)-21-13\\ \\ f(-3)=-43\)
Calculate for the function f(x, y) = student submitted image, transcription available belowpartial derivatives with respect to the variable x on the path of the h(x, y), so solve student submitted image, transcription available below when a is a constant on the curve h(x,y)=y=a, h(x,y)=y+x=a, h(x,y)=x^2+y^2=a
Answers
∂f/∂x = (∂f/∂x), ∂f/∂x = (∂f/∂x) - (∂f/∂y), ∂f/∂x = (∂f/∂x) - (∂f/∂y)(2x/√(a - x^2)).
These are the partial derivative expressions for the function f(x, y) along the specified paths.
Calculate the partial derivatives of the function f(x, y) with respect to x on the paths h(x, y) = y, h(x, y) = y + x, and h(x, y) = x^2 + y^2.
To calculate the partial derivatives of the function f(x, y) with respect to the variable x on different paths, we will evaluate the derivatives along each path and solve the resulting equations.
Path: h(x, y) = y = aTo find the derivative of f(x, y) with respect to x along this path, we treat y as a constant:
∂f/∂x = ∂f(x, y)/∂x = ∂f(x, a)/∂x
We differentiate f(x, a) with respect to x using the chain rule:
∂f/∂x = ∂f(x, a)/∂x = (∂f/∂x)(∂x/∂x) + (∂f/∂y)(∂y/∂x) = (∂f/∂x) + (∂f/∂y)(0)
Since y = a is constant along this path, ∂y/∂x = 0.
Therefore, ∂f/∂x = (∂f/∂x).
Path: h(x, y) = y + x = aSimilarly, to find the derivative of f(x, y) with respect to x along this path, we treat y + x = a as a constant:
∂f/∂x = ∂f(x, y)/∂x = ∂f(x, a - x)/∂x
Using the chain rule again:
∂f/∂x = ∂f(x, a - x)/∂x = (∂f/∂x)(∂x/∂x) + (∂f/∂y)(∂y/∂x) = (∂f/∂x) + (∂f/∂y)(-1)
Since y + x = a, we have ∂y/∂x = -1.
Therefore, ∂f/∂x = (∂f/∂x) - (∂f/∂y).
Path: h(x, y) = x^2 + y^2 = aSimilarly, we differentiate f(x, y) with respect to x along this path:
∂f/∂x = ∂f(x, y)/∂x = ∂f(x, √(a - x^2))/∂x
Using the chain rule:
∂f/∂x = ∂f(x, √(a - x^2))/∂x = (∂f/∂x)(∂x/∂x) + (∂f/∂y)(∂y/∂x) = (∂f/∂x) + (∂f/∂y)(-2x/√(a - x^2))
Therefore, ∂f/∂x = (∂f/∂x) - (∂f/∂y)(2x/√(a - x^2)).
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Calculate the total cost of an item bought at a negotiated price of $13,290 with 5. 5 percent sales tax and a $125 registration fee.
Answers
Answer:
$14,145.95
Step-by-step explanation:
total = 125+(1+5.5%) *13290 =14145.95
Every morning Jack flips a fair coin ten times. He does this for an entire year. Let X be the number of days when all the flips come out the same way (all heads or all tails). (a) Give the exact expression for the probability P(X > 1).
Answers
The probability of P(X > 1) can be shown as the expression \(1 - \sum_{x = 0}^{1} 365Cx(\frac {1} {2^9})^x(1 - \frac {1} {2^9})^{365 - x}\), which has the value, P(X > 1) = 0.160199752.
The number of times Jack flips the coin = 10.
The number of outcome on each flip = 2 {viz. Heads and Tails}.
Thus, the number of outcomes after flipping the coin 10 times = 2¹⁰.
The number of outcomes of getting all heads or tails = 2.
Thus, the probability = 2/2¹⁰ = 1/2⁹.
This can make a binomial distribution when repeated for 365 days, with parameters, n = 365, and p = 1/2⁹, showing P(X = x) as,
P(X = x) = nCx.pˣ.qⁿ ⁻ ˣ, where q = 1 - p.
Thus, we can calculate the probability P(X > 1) as follows:
P(X > 1)
= 1 - P(X ≤ 1)
= \(1 - \sum_{x = 0}^{1} 365Cx(\frac {1} {2^9})^x(1 - \frac {1} {2^9})^{365 - x}\)
= 1 - {365C0.(1/2⁹)⁰.(1 - 1/2⁹)³⁶⁵ + 365C1.(1/2⁹)¹.(1 - 1/2⁹)³⁶⁴}
= 1 - {0.489883478 + 0.34991677}
= 0.160199752.
Thus, the probability of P(X > 1) can be shown as the expression \(1 - \sum_{x = 0}^{1} 365Cx(\frac {1} {2^9})^x(1 - \frac {1} {2^9})^{365 - x}\), which has the value, P(X > 1) = 0.160199752.
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8.4 divided by 0.006 ?
Answers
The answer would be 1400.
Three people selected a number. They could choose either 1 or 2. Their results were combined to give a 3-digit number. (For example, if they all chose 1, the 3-digit number was 111.) How many different 3-digit numbers were possible? a.3 b.8 c.4
Answers
111
112
122
121
211
212
222
221
Write the expanded form, for 34.75
Answers
Answer:
30
Step-by-step explanation:
Answer:
30+4+0.7+0.05
Step-by-step explanation:
Because expanded form is add the number.
3=30
4=4.
7=0.7
and 5=0.05 so all together is 30+4+0.7+0.05
organizations such as the u.s. centers for disease control (cdc) often use data collected from hospitals. what kind of data is the cdc using if it is collected by hospitals, then sold to the cdc for its own analysis? 1 point
Answers
Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of plotting data.
Data plotting: What is it?The most typical method of utilizing a chart to convey data is to graph the correlation of two additional variables. Diagrams created by hand or using a computer are also acceptable. From the origin, go three up, then 2 pieces to the right. On the reference system, it is important to display the digits for positions 2, 3, and 4. Be really explicit with your points. The pinkish squiggle with the letter P represents the value of 2.3. You must first generate a number line for each number in a collection of data to be able to create a chart.
Here,
Given :
Data gathered from hospitals is frequently used by institutions like the US Center of Disease Control (cdc).
In order to determine what data they use,
From the information provided, it is clear that they are using second-party data.
Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of charting the data.
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i really need help with this question id appreciate your time to help me:( please.
Answers
Answer:
12
Step-by-step explanation:
Please help due today
Answers
Answer:
Step-by-step explanation:
Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answers
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
what are the zeros of the function f(x)=x^2-3x?
Answers
Do you want me to explain why?
I help pls
I dum dum at math
Answers
Answer:
AB - XY ≅ 0
Step-by-step explanation:
since AB is identical to XY, AB - XY would be approximately 0
A sphere has a radius of 9in. the sphere is cut in half. what is the volume of each hemisphere. use 3.14 for pi and round to the hundredths if needed. Show work. PLEASE ANSWER IT
Answers
V = (4/3)πr³
where V is the volume of the sphere, r is the radius, and π is the constant pi (3.14).
To find the volume of each hemisphere, we need to find the volume of the entire sphere and then divide it by 2. The volume of the entire sphere is:
V = (4/3)πr³
V = (4/3)π(9in)³
V = (4/3)π(729in³)
V = 3053.63in³ (rounded to the hundredths)
Now, to find the volume of each hemisphere, we divide this value by 2:
V = 3053.63in³ ÷ 2
V = 1526.82in³ (rounded to the hundredths)
Therefore, the volume of each hemisphere is approximately 1526.82 cubic inches.
Give the domain and range of T.
Answers
Answer:
Domain = -2,4,0
Range = -8,-9,4,9
Step-by-step explanation:
Domain is the list of x-values in a relation(coordinate)
Range is the list of y-values in a relation
Make sure to not write any duplicates in the domain or range. See how I removed the duplicate -2 that way?
If my answer is incorrect, pls correct me!
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-Chetan K
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7. 20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8. 80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges.
Answers
In linear equation, { 2x + 3y = 7.20 , { 4x + 2y = 8.80 the price per pound for oranges.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Let be "x" the price per pound for grapefruit, "y" the price per pound for oranges.
We know that Steve buys 2 pounds of grapefruit and 3 of oranges for $7.20.
This means that the sum of the products of 2x and 3y is $7.20. Then, we can write this equation to represent it
2x + 3y = 7.20
Kennedy buys 4 pounds of grapefruit and 2 pounds of oranges for $8.80.
This means that the sum of the products of 4x and 2y is $8.80. Then, we can write this equation to represent this
4x + 2y = 8.80
Therefore, we get that the system of equations that models the situation is
{ 2x + 3y = 7.20
{ 4x + 2y = 8.80
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If you borrow $101 at 7% compounded annually for seven years, how much will you pay back by the end of the term?
Answers
The amount you will pay back by the end of the term is; 162.18 dollar.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
\(a = p(1 + r)^{t}\)
Given that you borrow $101 at 7% compounded annually for seven years, then we have;
P = 101 dollar
Rate = 7%
Times = 7 yr
Therefore,
\(a = p(1 + r)^{t}\)
\(a = 101(1 + 0.07)^{7}\\\\a = 101 (1.07)^7\\\\a = $162.18\)
Hence, The amount you will pay back by the end of the term is; 162.18 dollar.
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When multiplying an equation so that you can cancel one of the variables, be certain to multiply both sidesof the equation. For instance, multiplying the above equation incorrectly would yield
:--1.5x -1.5y = 40, which would give you very incorrect values when you tried to solve for x and y.
Part D Now, add the two equations and find the value of x.
Express your answer to three significant figures.
ANSWER
Answers
The two equations would be 1.5x + 2.5y = 30, 3x + 1.5y = 40, when we add both the equations we get, 4.5x + 4y = 70, and the value of x is 10.
How to solve the linear equation in two variables?To solve a system of linear equations in two variables using the substitution in two variables using the substitution method. First solve one of the equations for one variable. Substitute this in the other equation in terms of a single variable. Then solve it for the variable. Now, substitute it in any of the equations to get the value of another variable.
Given:
Add the two equations together:
1.5x + 2.5y = 30
3x + 1.5y = 40
(1.5x + 3x) + (2.5y + 1.5y) = (30 + 40)
4.5x + 4y = 70
Isolate the x-variable by subtracting 4y from both sides of the equation:
4.5x + 4y = 70
4.5x + 4y - 4y = 70 - 4y
4.5x = 70 - 4y
Divide both sides of the equation by 4.5 to solve for x:
4.5x = 70 - 4y
4.5x/ 4.5 = (70 - 4y)/4.5
x = (70 - 4y) / 4.5
Substitute the value of y from the first equation:
1.5x + 2.5y = 30
2.5y = 30 - 1.5x
y = (30 - 1.5x) / 2.5
Substitute the value of y into the equation for x and solve:
x = (70 - 4y) / 4.5
x = (70 - 4((30 - 1.5x) / 2.5)) / 4.5
x = 10
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describe the graph of the solution
Answers
First, we want to note two things:
We have a solid circle at -10, so -10 IS part of the solution.We have shading to the right of -10, meaning we also need to include numbers to the right of -10, or numbers greater than -10.
We can describe this with an inequality: x ≥ -10
Be sure you use ≥ and not >, since -10 is included.
We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.
You can also use set-builder notation: { x | x ≥ -10 }
Which is the equation of a line that is perpendicular to the line represented by ?
Answers
Answer:
It will be
.. y = -4/3x +c . . . . . for some value of c
_____
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 3/4.
Hw. 22.4
A high school has four soccer teams. The number of players on each team
is shown in the table. A soccer player is randomly chosen. What is the probability that the player is a
female student or a player on a varsity soccer team?
Answers
The probability that the player is a female student or a player on the varsity soccer team is 78. 8 %.
How to find the probability ?The probability that the player is a female student or a player on the varsity soccer team is :
= Probability that they are female + Probability that they are in varsity - Probability that the student is female and in varsity
Probability that they are female = ( 19 + 23 ) / ( 19 + 23 + 17 + 21 )
= 42 / 80
Probability that they are in varsity = ( 23 + 21 ) / ( 19 + 23 + 17 + 21 )
= 44 / 80
Probability that the student is female and in varsity = 23 / 80
The probability that the player is a female student or a player on the varsity soccer team is :
= 42 / 80 + 44 / 80 - 23 / 80
= 63 / 80
= 78. 8 %
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any musical recommendations?
Answers
Answer:
Hamilton, Dear Evan Hansen, Grease and S H R E K
Step-by-step explanation:
B)When ABCD is drawn to scale, would
the lines AD and BC be parallel or not?
You must justify your answer without
using a scale drawing.
Answers
Answer:
No.
Step-by-step explanation:
The angles A and B are not equal.
The angles C and D are not equal.
Therefore, it is impossible for lines AD and BC to be parallel.
Solve x4 – 2x2 – 24 = 0.
Answers
Answer: 7
Step-by-step explanation:
Replace each ___ with >,< , or = to make a true statement.
3/8 in. ______ 6/16 in.
Answers
The statement "3/8 in. ___ 6/16 in." is true when filled with the symbol "<" (less than).
To compare the fractions 3/8 and 6/16, we need to make the denominators the same. Both fractions can be converted to have a denominator of 16.
To convert 3/8 to an equivalent fraction with a denominator of 16, we multiply both the numerator and denominator by 2. This gives us 6/16.
Since 6/16 is equal to 6/16, we can conclude that 3/8 is less than 6/16. Therefore, the symbol "<" (less than) can be used to complete the statement "3/8 in. < 6/16 in."
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Eva earns $40 more than Neima and Sarah earns double the amount of Neima minus $20. Their total combined earnings are $500. How much do each of them earn?
Answers
Answer: Let's say Neima's earnings are x dollars.
Then, Eva's earnings would be x + 40 dollars.
And, Sarah's earnings would be 2x - 20 dollars.
The total combined earnings of the three would be:
x + (x + 40) + (2x - 20) = 500
Simplifying the above equation, we get:
4x + 20 = 500
4x = 480
x = 120
Therefore, Neima's earnings are $120, Eva's earnings are $160 ($120 + $40), and Sarah's earnings are $220 (2 x $120 - $20).
Step-by-step explanation:
What is the value of 4/15 divided by 2/3 as a fraction
Answers
Answer:
2/5Step-by-step explanation:
4/15 ÷ 2/3 = ?4/15 × 3/2 = ?12/30 = ?12 ÷ 6 ; 30 ÷ 6 = ?2/5\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)
Step-by-step explanation:
pls mark me as brainliest
Can someone please help me?
Answers
A furlong is a distance of 220 yards. A fortnight is a time period of two weeks. A race horse is running at a speed of 6.00 yards per second. What is his speed in furlongs per fortnight
Answers
To calculate the speed of a racehorse in furlongs per fortnight, we need to convert the given speed from yards per second to furlongs per fortnight/ The horse's speed would be 0.001694 furlongs per fortnight.
Given that the horse is running at a speed of 6.00 yards per second, we can convert this speed to furlongs per fortnight. First, we need to convert yards to furlongs by dividing by the conversion factor of 220 yards per furlong:
6.00 yards/s / 220 yards/furlong = 0.02727 furlongs per second
Next, we need to convert seconds to fortnights. Since there are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 14 days in a fortnight, we can perform the necessary conversions:
0.02727 furlongs/s * 60 s/min * 60 min/hour * 24 hours/day * 14 days/fortnight = 334.84 furlongs per fortnight
Rounding to the appropriate decimal places, the horse's speed is approximately 0.001694 furlongs per fortnight.
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