particle moves with its position given by x= cos(2t) and y= sin (t), where positions are given in feet from the origin and time t is in seconds.
A. find the speed of the particle
speed =
B. Find the first positive time when the particle comes to a stop
t=
C. If n is any odd integer, write a formula (in terms of n) for all positive times t at which the particle comes to a stop
t=
Answers
Particle moves with its position given by x= cos(2t) and y= sin (t), where positions are given in feet from the origin and time t is in seconds. The speed of the particle at any time t is v = \(\sqrt\)(4sin²(2t) + cos²(t)).
For the speed of the particle, we can calculate the magnitude of its velocity vector.
The velocity vector can be obtained by differentiating the position vector with respect to time.
We have the position of the particle as x = cos(2t) and y = sin(t), we can differentiate these equations to find the corresponding velocity components:
vx = dx/dt = -2sin(2t)
vy = dy/dt = cos(t)
The magnitude of the velocity vector (v) is given by the square root of the sum of the squares of its components:
\(\sqrt\)(vx² + vy²) = \(\sqrt\)((-2sin(2t))² + (cos(t))²)
Simplifying this expression:
v = \(\sqrt\)(4sin²(2t) + cos²(t))
This is the speed of the particle at any given time t.
Note that the speed is not constant but varies with time due to the periodic nature of the sine and cosine functions.
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Related Questions
To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?
Answers
The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.
According to the statement
we have given that the to form a ellipse we use the base and angle of the cone, And we have to tell the relationship between them.
So, For this purpose, We know that the
An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
And to make a ellipse the relationship between the base of triangle and the angle of the cone is that the
The plane must be at a 45 degree angle to the base of the cone.
By this way we make a ellipse with the help of the cone.
So, The relationship between the base of the cone and the angle of the plane that intersects the cone is that the plane must be at a 45 degree angle to the base of the cone. Thus, Option D is correct.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
To form an ellipse, what is the relationship between the base of the cone and the angle of the plane that intersects the cone?
A. The plane is parallel to the base of the cone..
B. The plane may be perpendicular to the base of the cone..
C. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.
D. The plane must be at a angle to the base of the cone.
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Answer:
The plane is at an angle that is neither parallel nor perpendicular to the base of the cone.
Step-by-step explanation:
The plane doesn't need to be at an exact angle of 45 degrees. The most important thing is that the angle isn't parallel or perpendicular to the base of the cone, but it has to be non-zero without intersecting the base itself. It also only intersects one of the cones when looking at a double-cone.
diseases tend to spread according to the exponential growth model and the early days of AIDS in the growth factor was around 1.9 in 1983 about 1,500 people in the US died of AIDS if this trend had continued unchecked how many people would have died from Aids in 2005
Answers
Given the exponential model:
\(f(x)=A\cdot b^x^{}\)Where A is the initial condition, b is the growth factor and x is a time-like variable.
We know that the growth factor is 1.9 and that 1500 people died of AIDS in 1983. If we make x to be the years passed since 1983, then 1500 is our initial condition (because 0 years passed). In our model:
\(f(x)=1500\cdot1.9^x\)For 2005, x = 22:
\(f(22)=1500\cdot1.9^{22}=2035497063\)
the braille system of representing characters was developed early in the nineteenth century by louis braille. the charac- ters, used by the blind, consist of raised dots. the positions for the dots are selected from two vertical columns of three dots each. at least one raised dot must be present. how many distinct braille characters are possible?
Answers
The Braille system uses two vertical columns of three dots each to represent characters. There are 8 possible combinations for each column, giving a total of 64 distinct Braille characters.
The Braille system of representing characters was developed by Louis Braille in the early nineteenth century. This system is used by blind people and consists of raised dots that represent characters. The positions for the dots are selected from two vertical columns of three dots each. At least one raised dot must be present to represent a character.
To determine the number of distinct Braille characters possible, we need to consider the number of ways we can arrange the dots in the two vertical columns. Each column has three dots, and we need to choose which of these three dots to raise to represent a character. This gives us a total of 2^3 = 8 possible combinations for each column.
Since we have two columns, we can multiply the number of possible combinations for each column to get the total number of distinct Braille characters. This gives us 8 x 8 = 64 possible characters.
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the pew research center reported in 2017 that only 12% of americans supported cuts in federal spending on medicaid. is the percentage smaller this year? we tested the following hypotheses at the 5% level of significance. : this year the proportion of americans who support federal spending cuts to medicaid is 0.12 : this year the proportion of americans who support federal spending cuts to medicaid is less than 0.12 the p-value is 0.026, so we reject the null hypothesis and accept the alternative hypothesis. we conclude that this year the proportion of americans who support federal spending cuts to medicaid is less than 0.12 what type of error is possible here?
Answers
The possible error in this case is a Type I error, which occurs when we reject the null hypothesis when it is actually true, and conclude that the proportion is less than 0.12 when it is actually 0.12 or greater.
In hypothesis testing, a Type I error occurs when we reject the null hypothesis when it is actually true, while a Type II error occurs when we fail to reject the null hypothesis when it is actually false.
In this case, we rejected the null hypothesis that the proportion of Americans who support federal spending cuts to Medicaid is 0.12, in favor of the alternative hypothesis that the proportion is less than 0.12. The p-value was 0.026, which is less than the 5% level of significance.
Since we rejected the null hypothesis, there is a possibility of a Type I error. However, we cannot determine the probability of a Type II error without knowing the actual proportion of Americans who support federal spending cuts to Medicaid this year.
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Simplify x/4 + x/6 help please
Answers
Answer:
5/12x
Step-by-step explanation:
Suppose the linear regression line y = 2.1x + 130 predicts sales based on the
money spent on advertising. If x represents the dollars spent in advertising,
and y represents the company sales in dollars, about how much can the
company expect in sales if it spends $150 in advertising?
Answers
Answer:
$445
Step-by-step explanation:
Linear regression line y=2.1x+130 predicts sales based on the money spent on advertising.
Linear regression represents the relationship between two variables. the value of y depends on the value of x.
x represents the dollars spent in advertising and y represents the company sales in dollars.
We need to find out sales y when $150 spends on advertising.
Plug in 150 for x and find out y
y = 2.1 x + 130
y = 2.1 (150) + 130
y= 445
The company expects $445 in sales
The company expects $445 in sales.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Linear regression line y = 2.1x + 130 predicts sales based on the money spent on advertising.
Now, Linear regression represents the relationship between two variables. the value of y depends on the value of x.
Here, x represents the dollars spent in advertising and y represents the company sales in dollars.
We need to find out sales y when $150 spends on advertising.
Plug in 150 for x and find out y as;
y = 2.1 x + 130
y = 2.1 (150) + 130
y = 445
Thus, The company expects $445 in sales.
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missing socks imagine that after washing 5 distinct pairs of socks, you discover that two socks are missing. of course, you would like to have the largest number of complete pairs remaining. thus, you are left with 4 complete pairs in the best-case scenario and with 3 complete pairs in the worst case. assuming that the probability of disappearance for each 1 of the 10 socks is the same, find the probability of the best-case scenario; the probability of the worst-case scenario; the number of pairs you should expect in the average case. previousnext
Answers
5/45 = 1/9 represents the probability of the best-case scenario. 40/45 = 8/9 represents the probability of the worst-case scenario.
When two socks from the same pair are missing, the likelihood of the best-case scenario increases. As a result, all four pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. The probability of choosing one pair of socks from five pairs is equal to the number of ways to choose two socks from a pool of ten socks, and this is provided by the formula 5C1 = 5. given by 5 / 45 = 1 / 9. The worst case situation is when they are not from the same pair of socks. As a result, all three pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. 10C2 - 5C1 = 45 - 5 = 40 is the number of ways to choose two socks from a group of ten so that they are not from the same pair. given that by 40 / 45 = 8 / 9
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Simplify: -2s - 9+ 7 - 5r use s = 3 and r=-832-48None of these answers are correct.-83-1
Answers
Answer:
Step-by-step explanation:
We are given the following expression:
2s - 9 + 7 - 5r
Adding common terms, it becomes:
2s - 2 - 5r
Replacing s by 3 and r by -8, we get:
2*3 - 2 - 5*(-8) = 6 - 2 + 40 = 44
x-4y=-2
Determine if the given ordered pair, (2, 1), satisfies the given equation.
O YES
O NO
Answers
Answer:
Yes.
Step-by-step explanation:
Replace x with 2 and y with 1 and see if the equation is true
x - 4y = -2
2 - 4(1) = -2
2 - 4 = -2
-2 = -2
The statement is true so the point is on the line.
a company has given you the task to research the amount of snowfall in cleveland from december to february. would you be more interested in looking at the mean, median, or mode?
Answers
The number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.
The mean, median, and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February. The mean is calculated by adding up all of the snowfall measurements and dividing that by the number of measurements. For example, if there were 4 snowfall measurements of 10, 20, 30 and 40 inches, the mean would be 25 inches (10+20+30+40 / 4). The median is the middle value of the snowfall measurements when they are arranged from least to greatest. In this example, the median would be 25 inches as well. The mode is the most frequently occurring value among the snowfall measurements. In this example, the mode is also 25 inches.
The mean, median and mode are all useful measures of central tendency when researching the amount of snowfall in Cleveland from December to February, with the mean and median being calculated by adding up all of the snowfall measurements and dividing that by the number of measurements, and the mode being the most frequently occurring value among the snowfall measurements.
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Camila and Caleb are selling doughnuts at the school bake sale. Caleb sold twice as many doughnuts as Camila. Together, they sold 15 doughnuts at the bake sale. Could Camila have sold 5 doughnuts?
a
Yes, because 5 doughnuts is less than 15 doughnuts
b
No, because 2(5) doughnuts is less than 15 doughnuts
c
Yes, because 2(5) + 5 = 15
d
No, because 2(5) ≠ 15
Answers
Answer:
cC
Step-by-step explanation:
∑ Hey, jramirez0612 ⊃
Answer:
[C] Yes, because 2(5) + 5 = 15
Step-by-step explanation:
Given:
Camila and Caleb are selling doughnuts at the school bake sale. Caleb sold twice as many doughnuts as Camila. Together, they sold 15 doughnuts at the bake sale. Could Camila have sold 5 doughnuts?
(a) Yes, because 5 doughnuts is less than 15 doughnuts
(b) No, because 2(5) doughnuts is less than 15 doughnuts
(c) Yes, because 2(5) + 5 = 15
(d)No, because 2(5) ≠ 15
Solve:
According from the given:
Caleb sold twice as many doughnuts as Camila.
Together, they sold 15 doughnuts at the bake sale.
Hence,
the equation is
2(?) = 15
And then it asking if Camila could have sold 5 doughnuts.
Now we know that;
Camila = 5 doughnuts
Caleb = twice of Camila then 2(5)
Therefore, now let put it together:
Camila + 2 times Camila doughnut(Caleb)
2(5) + 5 = 15
Hence, the answer is
(C) Yes, because 2(5) + 5 = 15.
xcookiex12
8/24/2022
You want to buy a guitar that costs $425, but today there is a sale of 30% off. What is
the sale price of the guitar you want to buy? Would it be a mark up or a mark down and how do you know?
Answers
Answer:
297.50
Step-by-step explanation:
This would be considered a markdown because the guitar is on sale.
What will be the new position of the given point (–6, 8) after rotating 90 degrees clockwise about the origin? *
Answers
Answer:
The new position after 90 degrees clockwise rotation will be (8,6)
Step-by-step explanation:
Here, we are interested in knowing what the new position of a point will be when it is rotated 90 degrees clockwise about the origin.
Let’s say we have a point; n (x,y) as in the case above and we want to rotate clockwise 90 degrees about the origin.
Mathematically, this point will become n’ (y , -x)
Wondering what n and n’ is?
n represents the resultant of the coordinates while n’ represents the new image of the resultant after rotation.
Thus, by the expressions given above, after rotating (-6,8) , the new image taken after rotation will be (8, 6)
If point (–6, 8) is rotated 90 degrees clockwise about the origin, the new point is at (8, 6).
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is rotated 90 degrees clockwise about the origin, the new point is at A'(y, -x).
Hence if point (–6, 8) is rotated 90 degrees clockwise about the origin, the new point is at (8, 6).
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If,0 < 3x - 2 < 1, what is one possible value for x?
Answers
Answer:
one possible solution is 5/6
Step-by-step explanation:
Solving for x
0 < 3x - 2 < 1
Add 2 to each side
0+2 < 3x - 2+2 < 1+2
2 < 3x<3
Divide each side by 3
2/3 < 3x/3 < 3/3
2/3 < x < 1
X must be between 2/3 and 1
Getting a common denominator
4/6 < x < 6/6
So x can be 5/6
A store sells about 30 pants each week for Nu 800 each. The owner expects to lose one sale each week for every increase in price of Nu 40. a) Write an expression to represent the i) new price of a pant after n Nu 40 price increases. ii) expected number of pants that will be sold weekly after n price increases. b) Write a function to represent the expected weekly sales as a function of the number of price increases of Nu 40. c) Use the function to determine the price that will maximize totally sales.
Answers
The new price after the price increase of Nu 40 will be Nu 840.
How to calculate the price?The price of a pant after n Nu 40 price increases will be:
= 800 + 40
= 840
The expected weekly sales as a function of the number of price increases will be:
= n - 1) × 800
= (30 - 1) × 800
= 29 × 800
= 23200
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PLZZZZZ Find the difference between 74.8 and 35.10
NOOOO Scam
Answers
Answer:39.7
Step-by-step explanation:DUDE chilll I got you the answer is
what proportion of the variation in y can be explained by the variation in the values of x? report answer as a percentage accurate to one decimal plac
Answers
The relation R is not reflexive, but it is symmetric and transitive.
What is transitivity?A homogeneous relation R over the set A, which comprises the elements x, y, and z, is known as a transitive relation. If R relates x to y and y to z, then R likewise relates x to z.
For x, y ∈ Z, xRy if and only if (x+y)² ≡ ±1.
(a) Reflexivity: For x ∈ Z, we have (x + x)² = 4x² ≡ 0 (mod 1), which is not equal to ±1. Therefore, xRx does not hold for any x ∈ Z, and R is not reflexive.
(b) Symmetry: For x, y ∈ Z, if xRy, then (x + y)² ≡ ±1. This implies that (y + x)^2 ≡ (x + y)² ≡ ±1. Therefore, yRx also holds, and R is symmetric.
(c) Transitivity: For x, y, z ∈ Z, if xRy and yRz, then (x + y)² ≡ ±1 and (y + z)² ≡ ±1. Expanding these expressions, we get:
(x + y)² ≡ ±1 => x² + 2xy + y² ≡ ±1
(y + z)² ≡ ±1 => y² + 2yz + z² ≡ ±1
Adding these two equations, we get:
x² + 2xy + y² + y² + 2yz + z² ≡ ±2
Simplifying, we get:
x² + 2xy + 2yz + z² ≡ ±2 - 2y²
Now, we need to show that (x + z)² ≡ ±1. Expanding (x + z)², we get:
(x + z)² = x² + 2xz + z²
Substituting x² + 2xy + 2yz + z² ≡ ±2 - 2y², we get:
(x + z)² ≡ 2 - 2y² + 2xz
To complete the proof, we need to show that there exists some integer k such that 2 - 2y² + 2xz - k² ≡ ±1. We can rewrite this expression as:
2xz - k² ≡ 2y² - 3 (mod 4)
Since the left-hand side is even, the right-hand side must also be even. Therefore, y² ≡ 1 (mod 4), which implies that y is odd.
Now, we can substitute y = 2m + 1 for some integer m, and simplify:
2xz - k² ≡ 8m² + 8m - 1 (mod 4)
We can rewrite the right-hand side as 4(2m² + 2m) - 1, which is congruent to -1 (mod 4). Therefore, there exists some integer k such that 2xz - k² ≡ ±1, which implies that (x + z)² ≡ ±1. Hence, xRz holds, and R is transitive.
In summary, the relation R is not reflexive, but it is symmetric and transitive.
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///////////////lelelelelelelelel//////
Answers
Answer: I do not understand this question
Step-by-step explanation: Enjoy your day today
The left and right ends of the normal probability distribution extend indefinitely, never quite touching the horizontal axis. True False
Answers
It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.
The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.
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m + 7 ≥ 20, if m = 11
Answers
Answer:
False;18 ≥ 20
Step-by-step explanation:
Add 11 and 7
The left side 18 is less than the right side 20 , which means that the given statement is false.
surface area of a cuboid with dimensions of 9cm 5cm and 7cm
Answers
Which of the following describe 9.629? Select all that apply.
whole number
real number
rational number
irrational number
Answers
Answer:
Real number
Rational number
Step-by-step explanation:
Point P is the incenter of HKM.
Find JP
Answers
Given:
Point P is the incenter of triangle HKM.
To find:
The measure of JP.
Solution:
In triangle MNP, using Pythagoras theorem, we get
\(Hypotenuse^2=base^2+Perpendicular^2\)
\((MP)^2=(MN)^2+(NP)^2\)
\((25)^2=(24)^2+(NP)^2\)
\(625=576+(NP)^2\)
\(625-576=(NP)^2\)
\(49=(NP)^2\)
Taking square root on both sides, we get
\(\pm \sqrt{49}=NP\)
\(\pm 7=NP\)
Side cannot be negative. So,
\(NP=7\)
Point P is the incenter of triangle HKM.
\(JP=NP\) [Incenter is equidistant from each side of triangle]
\(JP=7\)
Therefore, the value of JP is 7 units.
Light sample A has a frequency of 4.30×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. What is the wavelength of light sample A in meters? Light sample A has a frequency of 4.30×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. What is the wavelength of light sample B in meters? Light sample A has a frequency of 4.30 ×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. Based on frequency, which set gives the most correct description of the types of light for samples A and B respectively? Light sample A has a frequency of 4.30 ×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. Based on frequency, which set gives the most correct description of the types of light for samples A and B respectively?
Answers
1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters
2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters
Since we know that the wavelength = speed of light / frequency
The speed of light is 3.00 × \(10^8\) meters per second.
For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;
wavelength of A = (3.00 × \(10^8\) m/s) / (4.30 × 10^15 Hz)
wavelength of A = 6.98 × \(10^{-8}\) meters
For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;
wavelength of B = (3.00 × \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)
wavelength of B = 3.45 × \(10^{-11}\) meters
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3. If the rent for two weeks is $500, how
much rent is paid for 5 weeks?
Answers
Answer:
rent for 5 weeks is $1,250
Step-by-step explanation:
2 weeks = 500
to find what one week is we must divide 500 by 2
500 ÷ 2 = 250
1 week = 250
now we can multiply 250 by the number of weeks
250 × 5 = $1,250
1,250 dollars
Find the surface area of the figure. Do NOT include units.
Answers
The surface area of the rectangular prism figure is S = 838 cm²
Given data ,
The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism
Surface Area of the prism = 2B + ph
So, the value of S is given by
The heights of the prism is represented as 7cm.
S = ( 11 x 20 ) + ( 7 x 20 ) + ( 4 x 20 ) + 2( 5 x 7 ) + 2( 6 x 4 ) + ( 6 x 20 ) + ( 5 x 20 ) + ( 3 x 20 )
On simplifying the equation , we get
S = 220 + 140 + 80 + 70 + 48 + 120 + 100 + 60
S = 838 cm²
Therefore , the value of S is 838 cm²
Hence , the surface area is S = 838 cm²
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Three boxes each contain a different number of marbles. Box A has 70 marbles, box B has 88 marbles, and box C has 80 marbles. Marbles are to be transferred from box B to box A. What is the least number of marbles that can be transferred so box C has the most marbles?
Answers
it A
Step-by-step explanation:
Yo could y’all help me with 6th grade math
Answers
Answer:
260
570
850
920
410
710
660
120
that all for now they out of order
Step-by-step explanation:
Answer:
2601204105705901908501003009205302004106309607108101000660810640Step-by-step explanation:
You better give brainliest for that also please refrain from these type of questions. I bet people would apprieate it
What is the equation of the line in point - slope form with slope 3/4and passes through the point (5, -8)?
Answers
Please Help ASAP
The table gives the value of Bianca's saving account at the end of each of the first four years. Which best describes the terms of this investment?
Answers
The term that best describes the investment is $1,250 invested at 4% compounded interest. The Option A is correct.
What is $1,250 invested at 4% compounded interest?We will use compound interest: A = P(1 + r/n)^(nt) formula to get the annual total investment. In this case, P = $1,250, r = 0.04, n = 1 and t = 1.
Plugging the values, we get:
A = 1250(1 + 0.04/1)^(1*1)
A = 1250(1.04)
A = $1,300
Therefore, term that best describes the investment is $1,250 invested at 4% compounded interest.
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