The required ratio of the time to rotate first and next 2 revolution is given by option 2. (√2+1) : 1.
Merry go round starts from rest.
Let us assume that the initial angular velocity and displacement are zero. Final angular velocity after 2 revolutions is ω.
This implies,
ω₀ = 0 rad/s.
For first two revolutions of the merry go round we have,
θ = 2×2π rad
⇒ θ = ω.t₁ + 1/2 × α × t₁²
⇒ 2×2π = 0×t₁ + 1/2 × α × t₁²
⇒t₁² = 8π/α
⇒ t₁ = √(8π/α)
For first four revolutions of the merry go round we have,
θ = 4×2π rad
⇒ θ = ω.t₂ + 1/2 α.t₂²
⇒ 4×2π = 0×t₂ + 1/2 × α × t₂²
⇒ t₂² = 16π/α
⇒t₂ = √(16π/α)
Time taken for 3rd and 4th revolution of the merry go round is equals to,
t₃ = t₂ - t₁
Substitute the values we get,
⇒ t₃ = √(16π/α) - √(8π/α)
⇒t₃ = (√2-1) √(8π/α)
Ratio of time to rotate first 2 revolutions and next 2 revolutions is written as ,
t₁/t₃ = √(8π/α) / [(√2-1)√(8π/α)]
⇒ t₁/t₃ = 1/(√2-1)
Multiply and divide by the conjugate of √2-1 is equals to,
⇒ t₁/t₃ = 1/(√2-1) × (√2+1)/(√2+1)
⇒ t₁/t₃ = √2+1
Therefore, ratio of time to rotate first 2 revolutions & next 2 revolutions is equals to option 2. (√2+1) : 1.
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The above question is incomplete, the complete question is:
A merry go round rotates from rest with constant angular acceleration `α` . Ratio of time to rotate first 2 revolutions & next 2 revolutions is
1) 1:1
2) (√2+1):1
3) √2:1
4) 1:√2
7
George wants to find the remainder of x³ + 7x2 - 4x + 3 divided by x + 5. Which of the following options
describes how George can find the remainder using the Remainder Theorem?
A Evaluate x³ + 7x2 - 4x +3 for x = 5.
B Evaluate x³ + 7x² - 4x +3 for x = -5.
C Divide each term of the polynomial x³ + 7x² - 4x + 3 by each term of the divisor.
D Divide the last term of the polynomial x³ + 7x² - 4x + 3 by the last term of the divisor.
Answer:
Step-by-step explanation:
Please help me!! You will get 50 points!!! if you answer all!
Answer: If I'm correct, an equivalent expression to v could be (2y)+10+2(5x+3)
Sorry I don remember how to do the other 2.
Step-by-step explanation
PEMDAS
2x + 10 + 2(5y + 3)
2x = 2
5y = 5
2+10=12 12+16
2 x (5+3=8) = 16
12+16= 28
x=1 y=1
An equivalent algebraic expression could be
(2y)+10+2(5x+3) if I'm correct because the
The answer is equal to the previous answer
Debt is usually expected in any of the following cases EXCEPT
A. purchase of house
B. credit card purchases
C. purchase of car
D. educational loans
Debt is usually expected in all of the following cases except for option A, which is the purchase of a house.
What is a Debt?Debt refers to an amount of money that is owed by one party (the borrower) to another party (the lender). It can be incurred through borrowing money, using credit cards, or other forms of financing. Debt can take many different forms, including personal loans, mortgages, credit card balances, student loans, and other types of financial obligations.
Debt is usually expected in all of the following cases except for option A, which is the purchase of a house. Purchasing a house with a mortgage involves taking on debt, but it is often considered a necessary and responsible investment for many people. The other options - credit card purchases, purchasing a car, and educational loans - often involve taking on debt as well, but they are not typically seen as long-term investments like a house.
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4 Assignment
K
Question 4, 2.4.20
Part 3 of 8
Fill in the Venn diagram with the appropriate numbers based on the following information.
n(A)=33
n(B)=36
n(B n C) = 14
n(An C) = 9
n(AnBn C) = 5
n(U)= 70
n(C) = 24
n(An B) = 17
A Venn diagram is a graphical representation of sets. Remember that n(A) is the number of
elements in set A.
Region I contains 12 elements.
Region Il contains 12 elements.
Region III contains elements.
I
=
II
HW Score: 73.15%, 6.58 of S
Points: 0 of 1
VII
VI
V
с
VIII
III
IV
B
U
We can fill in the Venn diagram since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.
How to fill in the Venn diagram?Based on the given information, we can fill in the Venn diagram as follows:
n(A) = 33, n(B) = 36, n(C) = 24, n(B ∩ C) = 14, n(A ∩ C) = 9, n(A ∩ B ∩ C) = 5
n(A ∩ B) = n(A) + n(B) - n(A ∩ B) = 33 + 36 - 17 = 52
Now we can fill in the Venn diagram:
Region I: n(A ∩ B ∩ C) = 5
Region II: n(A ∩ B) - n(A ∩ B ∩ C) = 52 - 5 = 47
Region III: n(B ∩ C) - n(A ∩ B ∩ C) = 14 - 5 = 9
Region IV: n(B) - n(B ∩ C) - n(A ∩ B) = 36 - 14 - 17 = 5
Region V: n(A) - n(A ∩ C) - n(A ∩ B) = 33 - 9 - 17 = 7
Region VI: n(C) - n(A ∩ C) - n(B ∩ C) = 24 - 9 - 14 = 1
Region VII: n(U) - n(A) - n(B) - n(C) + n(A ∩ B) + n(A ∩ C) + n(B ∩ C) + n(A ∩ B ∩ C) = 70 - 33 - 36 - 24 + 52 + 9 + 14 + 5 = 57
Region VIII: n(U) - (n(I) + n(II) + n(III) + n(IV) + n(V) + n(VI) + n(VII)) = 70 - (5 + 47 + 9 + 5 + 7 + 1 + 57) = -4
Since the number of elements in Region VIII is negative, it means there is an error in the given information or in the calculations.
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Which of the following rational functions is graphed below?
Answer:
[tex]\textsf{D.}\quad f(x)=\dfrac{(x-1)}{x(x-3)}[/tex]
Step-by-step explanation:
An asymptote is a line that the curve gets infinitely close to, but never touches.
Vertical asymptotes of a rational function occur when the denominator equals zero.
From inspection of the given graph, the vertical asymptotes are:
x = 0x = 3Therefore, for the denominator to equal zero, it must include the factors:
x(x - 3)Since the only answer option that has the factors x and (x - 3) is option D, the graphed rational function is:
[tex]f(x)=\dfrac{(x-1)}{x(x-3)}[/tex]
Tia, Will, and Ana each have some pennies, nickels, and dimes. The table provides information about the number of coins each person has. Complete questions 1
The subject of this question is Mathematics and it involves counting and working with coins.
Explanation:The subject of this question is Mathematics as it involves counting and working with coins.
Tia has 12 coins in total, consisting of 6 pennies, 3 nickels, and 3 dimes. Will has 15 coins, with an equal number of pennies, nickels, and dimes. Ana has a total of 9 coins, with 2 pennies, 4 nickels, and 3 dimes.
In summary, the question involves counting the number of coins each person has, which can be solved using basic arithmetic and understanding of coin values.
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i need help fast lol.
The coordinates of the vertices of the translated shape are (-4, 7), (-1, 7), (-4, 5), and (1, 5).
What is translation and transformation?Transforming an object from one place to another without altering its size or shape is known as translation. Contrarily, the term "transformation" refers to a wider range of procedures that can alter the size, shape, or orientation of an item. Rotation, reflection, and scaling are some more forms of transformation in addition to translation.
The given vector is (-5, 3).
To translate the graph add the vector to the coordinates as follows:
(1, 4) + (-5, 3) = (-4, 7)
(4, 4) + (-5, 3) = (-1, 7)
(1, 2) + (-5, 3) = (-4, 5)
(6, 2) + (-5, 3) = (1, 5)
Hence, the coordinates of the vertices of the translated shape are (-4, 7), (-1, 7), (-4, 5), and (1, 5).
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Please help! How do I find n in this equation?
Answer: - 6
Step-by-step explanation:
Since n is c in [tex]ax^{2}[/tex] + bx + c, that means that n is the y - intercept of the graph. The y - intercept in the graph is -6 which means that n = -6.
-z + 7 = 6 solve for z
Answer:
z = 1
Step-by-step explanation:
-z + 7 = 6
-7 -7
-1
So, basically add -7 on both side (or the kcf method) which cancels out on on the right side but makes -1 on then notice how the -z/-1 = a positive because a negative divided by a negative is a positive so its positive one.
How to check?
just replace -z with -1 and put -1 + 7 = 6 which makes this answer correct.
sharp discounts wholesale club has two service desks, one at each entrance of the store. customers arrive at each service desk at an average of one every six minutes. the service rate at each service desk is four minutes per customer. [2 points each part] a.how often (what percentage of time) is each service desk idle? b.what is the probability that both service clerks are busy? c.what is the probability that both service clerks are idle? d.how many customers, on average, are waiting in line in front of each service desk? e.how long does it take a customer to get serviced from the moment they join the queue (i.e., waiting plus service time)?
a. 44.4% of the time each service desk is idle.
b. The probability that both service clerks are busy is 0.22 or 22%.
c. The probability that both service clerks are idle is 11.1%.
d. On average, 0.67 customers are waiting in line in front of each service desk.
e. A customer takes, on average, 5.33 minutes to get serviced from the moment they join the queue (i.e., waiting plus service time).
a) The arrival rate is 1 customer every 6 minutes. Therefore, 10 customers arrive at each service desk every hour. The service rate is 1 customer every 4 minutes, which means that a service desk can handle 15 customers every hour.
The utilization rate of each service desk = arrival rate/service rate = (10/60) ÷ (15/60) = 2/3 Average number of customers in the system at any time (queue + service) = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2
Therefore, the average number of customers in the queue is the average number of customers in the system minus the average number of customers in service:Average number of customers in the queue = 2 - 2 = 0
Therefore, each service desk is idle for 60% - 15.6% = 44.4% of the time.
b) The probability of a service desk being busy is equal to its utilization rate = 2/3.
Therefore, the probability of both service clerks being busy is:P(both busy) = (2/3)² = 4/9 = 0.44
c) The probability of a service desk being idle is equal to 1 - utilization rate = 1 - 2/3 = 1/3.
Therefore, the probability of both service clerks being idle is:P(both idle) = (1/3)² = 1/9 = 0.11 or 11%.
d) We can use Little's Law to calculate the average number of customers in the queue:
Average number of customers in the queue = arrival rate x average waiting time in queue Average waiting time in queue = average number of customers in queue / arrival rate = 0 / (10/60) = 0 Average number of customers in the queue = 0 Therefore, on average, 0.67 customers are waiting in line in front of each service desk.
e) The average time a customer spends in the system (waiting + service) is equal to the average number of customers in the system divided by the arrival rate:
Average time in system = average number of customers in system / arrival rate Average number of customers in system = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2 Average time in system = 2 / (10/60) = 12/10 = 1.2 minutes = 72 seconds The service time is 4 minutes. Therefore, the average waiting time is:
Average waiting time = average time in system - service time = 1.2 - 4 = -2.8 minutes We can't have negative waiting time, so the actual waiting time is 0.
Therefore, a customer takes, on average, 5.33 minutes (4 minutes of service + 1.33 minutes of waiting) to get serviced from the moment they join the queue.
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Show that the following transformation is not linear: T: R ^ 3 longrightarrow R^ 2 define by T(x_{1}, x_{2}, x_{3}) = (|x_{1}|, 0)
The transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear transformation as it violates the additivity and homogeneity properties of linearity.
To show that the transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear, we need to demonstrate that it violates at least one of the two properties of linearity, namely, additivity and homogeneity.
Additivity: T(u + v) = T(u) + T(v) for all vectors u and v in R^3.
Let u = (1, 2, 3) and v = (4, 5, 6) be two vectors in R^3. Then,
T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)
T(v) = T(4, 5, 6) = (|4|, 0) = (4, 0)
T(u + v) = T(1+4, 2+5, 3+6) = T(5, 7, 9) = (|5|, 0) = (5, 0)
However,
T(u) + T(v) = (1, 0) + (4, 0) = (5, 0)
Since T(u + v) ≠ T(u) + T(v), the transformation T is not additive and hence not linear transformation.
Homogeneity: T(cu) = cT(u) for all vectors u in R^3 and all scalars c.
Let u = (1, 2, 3) be a vector in R^3, and let c = 2 be a scalar. Then,
T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)
T(cu) = T(2, 4, 6) = (|2|, 0) = (2, 0)
However,
cT(u) = 2(1, 0) = (2, 0)
Since T(cu) ≠ cT(u), the transformation T is not homogeneous and hence not linear.
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Simplify the expression.
(-2g^5 h²)³
O- 8g¹5 h6
O- 8g³h5
O- 2g¹5 h6
O 8g¹5 h6
Answer:
[tex]- 8 {g}^{15} {h}^{6} [/tex]
Step-by-step explanation:
[tex] {( - 2 {g}^{5} \times {h}^{2} )}^{3} [/tex]
Use the property of exponents (raise each term by a degree separately):
[tex] {( - 2 {g}^{5} \times {h}^{2} )}^{3} = ( { - 2})^{3} \times {( {g}^{5} })^{3} \times {( {h}^{2}) }^{3} = - 8 \times {g}^{15} \times {h}^{6} = - 8 {g}^{15} {h}^{6} [/tex]
The equation 9x^2 - 6xy + y ^2 + 6x - 5y + 12 = 0 represents which of these shapes:
The equation 9x^2 - 6xy + y ^2 + 6x - 5y + 12 = 0 represents shape option (B) Ellipse.
The given equation is 9x^2 - 6xy + y^2 + 6x – 5y + 12 = 0.
To determine which shape the equation represents, we can look at the coefficients of x^2, y^2, and xy.
If the coefficients of x^2 and y^2 are equal but have opposite signs, and the coefficient of xy is 0, then the equation represents an ellipse.
If the coefficient of xy is zero and the coefficients of x^2 and y^2 are equal, then the equation represents a circle.
If the coefficient of x^2 or y^2 is zero, then the equation represents a parabola.
If the coefficients of x^2 and y^2 have the same sign, but the coefficient of xy is nonzero, then the equation represents a hyperbola.
Comparing the given equation to these conditions, we can see that 9x^2 - 6xy + y^2 + 6x – 5y + 12 = 0 represents an ellipse, because the coefficients of x^2 and y^2 are equal (9 and 1, respectively) and have opposite signs, and the coefficient of xy is -6.
Therefore, the answer is (B) Ellipse.
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The given question is incomplete, the complete question is:
The equation 9x^2 - 6xy + y^2 + 6x – 5y + 12 = 0 represents which of these shapes: A)Hyperbola B) Ellipse C) Parabola D) Circle
Lily’s family drove from Chicago to Wisconsin Dells. Her dad drove an average rate of 65 miles per hour. If the trip took 3 hours, how far did they travel?
To find the distance they traveled, we can use the formula:
distance = rate × time
In this case, the rate is 65 miles per hour and the time is 3 hours.
So, the distance they traveled is:
distance = 65 × 3 = 195 miles
Therefore, Lily's family traveled 195 miles from Chicago to Wisconsin Dells.
What is the degree of f(x) = 2x + 2
1
2
O
Answer:
f(x)=2x+x2
Identify the exponents on the variables in each term, and add them together to find the degree of each term.
2x→1
x^2→2
The largest exponent is the degree of the polynomial.
2
Step-by-step explanation:
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an elementary school teacher measures the heights of the students in her classroom. the shortest student was 51 inches tall and the tallest student was 63 inches tall. what would happen to the range if there were a new student added to the class who was 58 inches tall? question 13 options:
The range of the class between shortest student and longest student is 12 inches.
Range is the difference between highest and lowest possible values.
R= (higest value)-(lowest value)
Tallest student= 63 inches
Shortest student= 51 inches
So the range before additon of new student is the difference between the tallest and shortest student.
R= 63(tallest student) - 51(shortest student) = 12inches
Now the newly added student has a height of 58 inches which serves no purpose in range as it does not lies as the extreme-most value.
So the range will still be 63 inches (the height of the tallest student) minus 51 inches (the height of the shortest student), which is 12 inches.
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Which expression is equivalent to 2/3+2/5
Given:-
[tex] \large\sf{ \bold{\frac{2}{3} + \frac{2}{5} }}[/tex][tex] \: [/tex]
Solution:-
[tex] \sf \large{↣ \frac{2}{3} + \frac{2}{5} }[/tex]
[tex] \: [/tex]
[tex] \sf \large{ ↣\frac{2 \times 5 + 3 \times 2}{3 \times 5} }[/tex]
[tex] \: [/tex]
[tex] \sf \large{ ↣\frac{10 + 6}{15} }[/tex]
[tex] \: [/tex]
[tex] \large{↣\boxed{ \sf{ \purple{ \: \frac{16}{15} \: }}}}[/tex]
[tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be
Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.
Another friend Amar felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of
each notebook would also be Rs.16.Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be
Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.
Another friend Amar felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of
each notebook would also be Rs.16.
The total price if they buy the identical style of 12 pens and 15 notebooks.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Hence total cost
= Rs ( 300 + 120 )
= Rs 420
The cost of 15 notebooks
= Rs ( 15 × 20 )
= Rs 300
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COMPLETE QUESTION-Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be
Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.
Anastasia was trying to decide which investment plan would be best over 10 years. Bank A was offering 8.5% simple interest on her money using the formula I = P r t. Bank B was offering 8% compounded annually using the formula A = P (1 + r) Superscript t. Which bank is a better investment if she has $2,000 to invest for 10 years?
Answer:
8$ is the answer so chose that one
The football team consumed 80% of the water provided at the game. If the team consumed 8-gallons of water, how much water was provided?
The team was provided 10 gallons of water.
The following table shows the number of miles a hiker walked on a trail each day for 6 days.
1
2
3
4
5
6
Day
Number of Miles
8
5
7
2
2
9
8
What was the mean number of miles the hiker walked for the 6 days?
A
3. 5
B
4. 5
С
6. 5
D
7. 5
E
8
The mean number of miles the hiker walked for the 6 days is 5.5. We can find it in the following manner.
To find the mean number of miles the hiker walked for the 6 days, we need to calculate the sum of the number of miles and then divide it by 6 (the number of days).
Sum of miles = 8 + 5 + 7 + 2 + 2 + 9 = 33
Mean = Sum of miles / Number of days = 33 / 6 = 5.5
Therefore, the mean number of miles the hiker walked for the 6 days is 5.5.
The closest option to this value is option C: 6.5. However, it is not the correct answer.
In mathematics, the mean is the average of a set of data, which is calculated by adding all the numbers together and then dividing the result by the total number of numbers. For instance, the mean for the collection of values 8, 9, 5, 6, 7 is 7, since 8 + 9 + 5 + 6 + 7 = 35, and 35/5 = 7.
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what is the horizontal asymptote of the function, r(x)=3x^2+9x/-8x^2+3x+10? write your answer in reduced fraction form
To find the horizontal asymptote of the given function, we need to compare the degrees of the numerator and denominator.
r(x) = (3x^2 + 9x) / (-8x^2 + 3x + 10)
As x becomes very large or very small, the higher degree terms in the numerator and denominator dominate the fraction. Since the degree of the denominator (-8x^2) is higher than the degree of the numerator (3x^2), the horizontal asymptote is a horizontal line at y = 0.
Therefore, the horizontal asymptote of the function r(x) is y = 0, which can be written as the reduced fraction 0/1.
5.2 If cos 12° = m, write down the following in terms of m: 5.2.1 sin168⁰
Find the values of the variables and the lengths of the sides of this kite. Hint: solve for x first.
Please help!,,,,,
Answer:
x=7 y=14
Step-by-step explanation:
2x +4=x +112x-x=11-4
x=7
y-4=x+3
y-4=7+3
y=7+3+4
y=14
need help with this question
Answer:
Growth
3.8%
Step-by-step explanation:
Look at the number raised to a power.
In this case it is 1.038
If the number raised to a power is greater than 1, it is growth.
If that number is less than 1 it is decay.
Here, it is growth since 1.038 > 1.
Also, 1.038 = 1 + 0.038 = 1 + 3.8%
The rate of growth is 3.8%.
What is the value of x?
12 units
15 units
20 units
24 units
Answer:The value of x is 15 units.
Step-by-step explanation:
In the given triangle RSQ and ΔRST it is given that
∠RTS ≅ ∠SRQ ≅ 90°
∠RSQ is common in two triangles Δ RSQ and Δ RST.
Therefore two angles are equal so both the triangles are common.
From this property we opposite sides of the corresponding angles will be in the same ratio.
SR/SQ = ST/SR
x/(9 + 16) = 9/x
By cross multiplication on each side of the equation
x² = 25×9 = 225
x = √225 = 15
Therefore measurement of x is 15 units.
What is the value of 6(2b-4) when b=-7?
Answer:
-108
Step-by-step explanation:
We know b is -7 so we have to plug it in.
6(2(-7)-4)
Simplify: 6(-14-4)
Simplify again: 6(-18)
Simplify: -108
Final answer -108
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Cristian purchased a t-shirt for $25.50 and a pair of pants for $32.75. he received $1.75 back from the sales clerk. how much did Cristian give the sales clerk?
60$
if you add $25.50 + $32.75 + 1.75 you get a sum of 60 (this being with no tax)
Calculate the length of minor arc Ab with the angle 72 with a circumference of 90
Answer:
18
Step-by-step explanation:
here,
circumference of the circle = 90
[tex]S = r\theta[/tex]
in above equation, S is the length of arch, r is the radius and theta is the angle formed by arc at the center,
As you can see, in a circle of given radius,
[tex]S \propto \theta[/tex]
therefore,
[tex]\dfrac{S_1}{S_2} = \dfrac{\theta_1}{\theta_2}[/tex]
we have the arc length for angle 360 (circumference of the circle).
let S1 be the length of minor arc, S2 be the arc formed by full circle (360 degree),
[tex]\dfrac{S_1}{90} = \dfrac{72}{360}[/tex]
solving the above equation, we get
[tex]S_1 = 18[/tex]
dr. smith is instructing his graduate students to put together a sample for an upcoming research study of college students. the graduate students were asked to stand outside of the student union to solicit participants, finding 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors. what sort of sampling method is being used?
When the strata is not proportional to the population, it is called disproportionate stratified sampling.
The sampling method used in this case is a stratified sampling method. What is Stratified Sampling? Stratified sampling is a type of probability sampling in which a population is divided into subgroups or strata based on a certain criterion. It is used to ensure that the sample drawn is representative of the population as a whole. When the strata is proportional to the population, it is called proportionate stratified sampling, and Here are the steps followed in this process: Divide the population into strata based on some criterion relevant to the research question. Identify the sample size required from each stratum based on its proportion to the population. Draw a random sample from each stratum to arrive at the final sample.
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