A particle moves on a circle of radius 9 cm, centered at the origin, in the xy-plane (x and y measured in centimeters). It starts at the point (0, 9) and moves counterclockwise, going once around the circle in 6 seconds. Write a parameterization for the particle's motion. x (t) = What is the particle's speed? Speed =
Answers
It moves at a 1.5 m/s speed .
What is the motion equation with parameters?Two parametric equations—x=(v0cos)t and y=(v0sin)t+h—determine the motion of a projectile. Initial velocity is denoted by the symbol v0. The angle at which the object is hurled is represented by, and the height to which it is propelled by h.Every function with a vector value offers a parameterization of a curve. A parameterization of a curve is a set of equations such as x = x (t) and y = y (t) that express the coordinates of a point on the curve in terms of a parameter.Particle velocity is the speed of an actual or hypothetical particle as it transmits a wave through a medium. A particle's speed is measured in SI in meters per second (m/s).Explanation:
Speed = d/t = 9/6 = 3/2 = 1.5m/s.
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It moves at a 1.5 m/s speed .
What is the motion equation with parameters?Two parametric equations—x=(v0cos)t and y=(v0sin)t+h—determine the motion of a projectile. Initial velocity is denoted by the symbol v0. The angle at which the object is hurled is represented by, and the height to which it is propelled by h.
Every function with a vector value offers a parameterization of a curve. A parameterization of a curve is a set of equations such as x = x (t) and y = y (t) that express the coordinates of a point on the curve in terms of a parameter.
Particle velocity is the speed of an actual or hypothetical particle as it transmits a wave through a medium. A particle's speed is measured in SI in meters per second (m/s).
Speed = d/t = 9/6 = 3/2 = 1.5m/s.
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Related Questions
I need help in this algebra problem plz
Answers
Answer:
X+2
Step-by-step explanation:
Find the surface area of the cone in terms of π.
180π cm2
108π cm2
144π cm2
90π cm2
Answers
Answer:
\(54\pi \: {cm}^{2} \)
Step-by-step explanation:
Given:
A cone
l = 15 cm
r (radius) = 3 cm
Find: A (surface area) - ?
\(a(surface) = \pi {r}^{2} + \pi \times r \times l\)
\(a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} \)
Cafeteria A has 7 packs of granola bars and 12 loose granola bars. Cafeteria B has 3 packs of granola bars and 84 loose granola bars. If the cafeterias have
the same number of granola bars, how many are in each package?
Answers
Each package has 18 granola bars.
Step-by-step explanation:This problem can be solved through a system of linear equations.
1. Form the equations.Let "x" be the total number of granola bars that each pack of granola has. Let "y" be the total amount of granola bars that each cafeteria has.
For cafeteria A: \(7x+12=y\)
For cafeteria B: \(3x+84=y\)
2. Equal the equations.
Since both equations are solved for y, we may take the argument at the left of the equal sign from both equations and equal them.
\(7x+12=3x+84\).
3. Solve for x.\(7x+12=3x+84\)
\(7x-3x=84-12\) --> Substract 3x and 12 from both sides.
\(4x=72\) --> Simplify by solving the substraction.
\(\frac{4x}{4} =\frac{72}{4}\)--> Divide both sides by 4.
\(x= 18\)
4. Substitute the vallue of x by x on any of the equations.\(y=7(18)+12\\ \\y=138.\)
5. Interpret the results.If a system of linear equations was created, where 2 equations that gave the number of granola bars that each cafeteria has, then the x value obtained when the system was solved, indicates the amount of granola bars that each cafeteria has in each package. Each package has 18 granola bars.
PLEASE HELP ASAP
Apostolis is making a beaded dress to enter in
a design competition. He must buy the beads to
fulfill the pattern, but he can spend no more than
$125 of this part of the project. Packages of blue
beads contain 10 beads per package and cost $0.85
whereas the packages of yellow beads contain
15 beads per package and cost $1.15 per package.
Apostolis needs at least 425 beads. If b represents
the number of blue beads and y represents the
number of yellow beads, which of the following
systems best describes these constraints?
I have been trying to solve and I just can’t figure it out yet, my answer is B or A bug I’m not quite to sure
Answers
Answer:
okok so the anwser is 1+1
Step-by-step explanation:
1 and add another is 2
boom.
:)
BK plays a game, which assigns a number (Z)that is the continuous random variable with the density function
(z) =1/5,0≤z≤5
0, otherwise.
If the game assigns a number less than or equal to, then he loses 10 dollars, on the other hand, if the game assigns a number larger than, then he will gain 10 dollars. (a) Find the expected profit of the game. (b) Find the variance of the profit. (c) If you were to play this game 10 times, what is the probability that you gain 20 dollars?
Answers
(a) The expected profit of the game is $0. (b) The variance of the profit is 0. (c) The probability of gaining $20 in 10 plays is 0.
Answers to the questionsTo solve the given problem, we'll calculate the expected profit, variance of the profit, and the probability of gaining $20 in 10 game plays.
(a) Expected Profit:
To calculate the expected profit, we need to multiply the potential profit or loss with its corresponding probability and sum them up.
Profit (X) = Gain - Loss = $10 - $10 = $0
Probability of gaining: P(X = $0) = P(Z > 5) = 0 (since Z is only defined up to 5)
Expected Profit (E(X)) = $0 * P(X = $0) = $0
(b) Variance of the Profit:
The variance can be calculated using the formula: Var(X) = E(X^2) - (E(X))^2.
In this case, since the profit is always zero, the variance will also be zero.
Variance of the Profit (Var(X)) = 0 - (0)^2 = 0
(c) Probability of Gaining $20 in 10 plays:
Since each play is independent, the probability of gaining $20 in a single play is 0. Since the probability of gaining is 0 for each play, the probability of gaining $20 in 10 plays will also be 0.
Probability of gaining $20 in 10 plays = 0
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Area and perimeter assignment. (9th Grade geometry)
Answers
Thus, the perimeter of the shown triangle using the distance formula is found as 13.45 units.
Explain about the perimeter:A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.
Given that:
coordinates of triangle: A(5,3) , B(1,5) and C(3,0)Perimeter = sum of all sides
Perimeter = AB + BC + CA
Estimate each distance using the distance formula:
d = √(x2 - x1)² + (y2 - y1)²
AB = √(1 - 5)² + (5 - 3)²
AB = √(-4)² + (-2)²
AB = √(16 + 4)
AB = √20
BC = √(3 - 1)² + (0 - 5)²
BC = √(2)² + (-5)²
BC = √(4 + 25)
BC = √29
CA = √(5 - 3)² + (3 - 0)²
CA = √(2)² + (3)²
CA = √(4 + 9)
CA = √13
Perimeter = AB + BC + CA
Perimeter = √20 + √29 + √13
Perimeter = 4.47 + 5.38 + 3.60
Perimeter = 13.45 units.
Thus, the perimeter of the shown triangle using the distance formula is found as 13.45 units.
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If 9 more than twice a number is 7 less than three times the same number, what is the number?
Answers
Answer:
12
Step-by-step explanation:
9+2x=3x-3
9+3=3x-2x
Answer:
16
Step-by-step explanation:
Let x be "a number"
9 + 2x = 3x - 7
Isolate variables to one side
9 + 7 = 3x - 2x
16 = x
A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?
Answers
Answer:
\(\frac{30meters}{second}\)
600meters
Step-by-step explanation:
Use conversion factors that represent 1. You can cross cancel wods just like numbers.
\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)
\(\frac{108000meters}{3600seconds}\)
\(\frac{30meters}{second}\)
\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)
600 meters
Helping in the name of Jesus.
Solve for x and graph the answer on a number line
2
Answers
The solution to the system of inequalities in interval notation is [-2, 1].
How to solve the system of inequalities?Based on the information provided in the image below, we have the following system of inequalities;
-12 < 3x - 6
-3 ≥ 3x - 6
By adding 6 to both sides of the equation (inequality), we have;
-12 < 3x - 6
-12 + 6 < 3x - 6 + 6
-6 < 3x
-2 < x
x > -2 (flip)
-3 ≥ 3x - 6
-3 + 6 ≥ 3x - 6 + 6
3 ≥ 3x
1 ≥ x
x ≤ 1
Therefore, the solution to the system of inequalities is given by:
-2 < x ≤ 1
In interval notation, we have [-2, 1].
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which of these is something you can pay for with the money in a savings account?
Answers
Which of the following finance options will have the lowest total financed
cost?
A. Balloon mortgage with balloon payment paid in full
B. 7/1 ARM
Ο Ο Ο
C. Balloon mortgage with balloon payment financed at lower rate
O D. 30-year fixed mortgage
Answers
Answer:
A is the answer
Step-by-step explanation:
did the test hope this helps
Balloon mortgage with balloon payment paid in full, will pay off the mortgage in the shortest time.
What is a mortgage?A mortgage is a loan that is used to purchase real estate (such as a house) with the property being used as collateral for the loan.
Here, we are given that balloon mortgage is a type of loan that requires a lump sum payment at the end of the loan term (the "balloon payment").
Option A involves paying off the entire mortgage balance at the end of the term, which will result in paying off the mortgage in the shortest amount of time.
A 30-year fixed mortgage and a 7/1 ARM will take 30 years and 7 years plus the adjustment period, to pay off the mortgage.
In a Balloon mortgage with a balloon payment refinanced at a lower rate, the mortgage would still be outstanding after the balloon payment, and the borrower will need to refinance to a new mortgage to continue making payments.
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A health club charges a one-time sign-up fee and a monthly membership fee. The
equation y = 28x + 50 represents what the health club charges. Find the rate of
change.
Answers
Answer:
The rate of change is 28.
Step-by-step explanation:
The equation is in slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept.
For which of the following displays of data is it not possible to find the mean histogram frequency, table, stem, and leaf plot doc plot
Answers
The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.
A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.
A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.
A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.
A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.
In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.
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x^3 - 2y^2 - 3x^3 + z^4
Answers
Answer:
-2x³ - 2y² + z⁴
Step-by-step explanation:
Step 1: Write out expression
x³ - 2y² - 3x³ + z⁴
Step 2: Combine like terms (x³)
-2x³ - 2y² + z⁴
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
100 meters
50 meters
48 meters
40 meters
Answers
The width of the cooling tower at the base of the structure is 40 meters.
Width of the cooling towerGiven equation
x²/400 -(y-90)²/1600=1
Solving for the width
Cooling tower width =2√400
Cooling tower width=2×20
Cooling tower width=40 meters
Therefore the correct option is D. 40 meters.
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Answer:
40
Step-by-step explanation:
Ae
A Man travels distance
84km in Ihr 20mins. Find
His speed average find-
Answers
Answer:
1.05km/min
Step-by-step explanation:
\(Distance = 84 km\\\\Time = 1hr 20 min= 80minuttes\\\\Average \: Speed = \frac{Distance}{Time} \\\\A.S =\frac{84}{80} \\\\A.S = 1.05km/min\)
we, know that
➺ Average Speed = Total Distance/Total Time taken
where,
Total Distance = 84km = 84000mTotal time = 1hr20mins = 4800sec♛ Substituting these values ♛
◗Average Speed = Distance/Time
◗Average Speed = 84000/4800
◗Average Speed = 840/48
◗Average Speed = 70/4
◗Average Speed = 17.5m/s
Hence, Average Speed of the man is 17.5m/sIf 3 boxes weigh 10 pounds, how much do 4 boxes weigh?
Answers
Answer:
About 13.32 Pounds
Step-by-step explanation:
First. take the total weight of the three boxes and divide it by the number of boxes.
10/3 = 3.33 and so on
Now we know each box ways 3.33 pounds.
Now multiply 4 boxes by 3.33 pounds.
4 x 3.33 = 13.32
So the answer should be about 13.32 pounds.
Answer:
13.3pounds
Step-by-step explanation:
if 3boxes = 10pounds
4boxes= ?
4×10= 40÷3
13.3pounds
What is the measurement of 1?
Answers
Answer:
6
Step-by-step explanation:
The angles of a triangle equal 180 degrees. It tells you 68 and 52. Add those, which gives you 120. Which then tells you your last angle is 60 degrees. That is a supplementary angle, therefore angle #1 equals 120
What is the binomial is a factor to this trinomial:
4x^2+20x-24
Answers
\(4x^2+20x-24 = 4x^2-4x+24x-24 = 4x(x-1)+24(x-1) = (4x + 24)(x-1)\\\)
\(= 4(x+6)(x-1)\)
poly has 7 different books. She is going to arrange 3 of them on the shelf above her desk. In how many different ways can she arrange three books?
Answers
PLEASE HELP ME WORTH ALOT OF POINTS
Answers
Am not sure though
social health is one component of the health tringal what are the other two components
Answers
Answer:
mental health and emotional health
In NTUV, the measure of N=90) UV = 8.7 feet, and VT = 3.6 feet. Find the measure of to the nearest degree.
Answers
Answer:
5
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
the triangles shown below must be congruent A. True B. false
Answers
Answer:
A. True
Step-by-step explanation:
Answer: B. False.
Step-by-step explanation:
Hope this helps!
please help i wanna pass
A wildlife society is taking a sampling of the lengths of bluegill fish at a local lake.
If the survey resulted in the data above, the distribution of fish lengths would be best described as...
A.
symmetrical with multiple modes.
B.
symmetrical with one mode.
C.
skewed to the right.
D.
skewed to the left.
Answers
Answer:
it was skewed to the right
Step-by-step explanation:
i just answered the quistion and D was not the answer
A small pebble has a mass of
about
20 L
b.
20 ml
20 g
20 kg
d.
Answers
Answer:
20g
since mass should be in kg or gram if small then g
What is the coefficient of 20x?
Answers
Answer:
20
Step-by-step explanation:
A coefficient is the number that is attached to the variable.
In this case, the number attached to the variable is 20.
Therefore, the coefficient is 20
hope this helps :)
Consider the steps to solve the equation. 2/5 ( 1/2 y + 20 ) − 4/5 = 9/20 (2y − 1) Distribute: 1/5 y + 8 − 4/5 = 9/ 10 y − 9/20 What is the next step after using the distributive property? Use the multiplication property of equality to isolate the variable term on one side of the equation. Use the multiplication property of equality to isolate the constant on one side of the equation. Combine the like terms on the right side of the equation. Combine the like terms on the left side of the equation. member to subscribe to my channel michadsen
Answers
The initial expression is:
\(\frac{2}{5}(\frac{1}{2}y+20)-\frac{4}{5}=\frac{9}{20}(2y-1)_{}\)First we use the distibution propertie so:
\(\frac{1}{5}y+8-\frac{4}{5}=\frac{9}{10}y-\frac{9}{10}\)Now we pass all term with y to the right and all constats to the left so:
\(\frac{8}{1}-\frac{4}{5}+\frac{9}{10}=\frac{9}{10}y-\frac{1}{5}y\)now we operate so:
\(\begin{gathered} \frac{80}{10}-\frac{8}{10}+\frac{9}{10}=\frac{9}{10}y-\frac{2}{10}y \\ \frac{81}{10}=\frac{7}{10}y \end{gathered}\)now we multiply by 10 and divide by 7 so:
\(\begin{gathered} \frac{10}{7}\cdot\frac{81}{10}=y \\ \frac{81}{7}=y \end{gathered}\)6.The heights of an adult female population are normally distributed
with mean 162 cm and standard deviation 7.5cm.
(a) Find the probability that a randomly chosen adult female is taller
than 150 cm.
(b) Sarah is a young girl. She visits her doctor and is told she is at the
60th percentile for height. Assuming that Sarah remains at the 60th
percentile, estimate her height as an adult. (use table V)
Answers
a) The probability that a randomly chosen adult female is taller than 150 cm, using the normal distribution, is of: 0.9452 = 94.52%.
b) Sarah's adult height will be estimated as: 164 cm.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the heights are given as follows:
\(\mu = 162, \sigma = 7.5\)
For item a, the probability that a randomly chosen adult female is taller than 150 cm is one subtracted by the p-value of Z when X = 150, hence:
\(Z = \frac{X - \mu}{\sigma}\)
Z = (150 - 162)/7.5
Z = -1.6
Z = -1.6 has a p-value of 0.0548.
1 - 0.0548 = 0.9452 = 94.52%.
The 60th percentile is X when Z = 0.253, hence:
0.253 = (X - 162)/7.5
X - 162 = 0.253 x 7.5
X = 164 cm.
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let f(x) = 1/x-3 and g(x) = square root of x+5
Answers
Answer:
Option B is correct. the required domain of the function will be expressed as[-5, 3) U (3, ∞)
Step-by-step explanation: