One revolution is completed when a fixed point on the wheel travels a distance equal to the circumference of the wheel, which is 2π (13 cm) = 26π cm.
So we have
1 rev = 26π cm
1 rev = 2π rad
1 min = 60 s
(a) The angular velocity of the wheel is
(35 rev/min) * (2π rad/rev) * (1/60 min/s) = 7π/6 rad/s
or approximately 3.665 rad/s.
(b) The linear velocity is
(35 rev/min) * (26π cm/rev) * (1/60 min/s) = 91π/6 cm/s
or roughly 47.648 cm/s.
The angular velocity of the wheel is 3.665 radians/sec.
The linear velocity is the hamster running is 47.648 cm/sec.
GivenA hamster running in a wheel of radius 13 cm spins the wheel at 35 revolutions per minute.
What is angular velocity?Angular Velocity It is defined as the rate of change in angular displacement of a particle in a circular motion.
The angular velocity of the wheel is given by;
[tex]\rm 1 \revolution = 2\pi \ radians\\\\Angular \ velocity = 35 \times 2\pi \ radians \ per \ minute\\\\Angular\ velocity = 70\pi \ radians \ per\ minute\\\\1 \ min = 60\ second\\\\Angular \ velocity = 70\pi \times \dfrac{1}{60} \\\rm \\Angular \ velocity = \dfrac{7}{6} \times 3.14 \ radians \ per \ second\\\\Angular \ velocity = 3.65\ radians \ per \ second\\\\[/tex]
The angular velocity of the wheel is 3.665 radians/sec.
What is linear velocity?Linear velocity definition deals with the measurement of an object’s velocity when it moves along a specific direction.
The linear velocity is the hamster running is given by;
[tex]\rm Linear \ velocity = 35 \times 26\pi \times \dfrac{1}{60}\\\\Linear \ velocity = 35 \times 26 \times 3.14 \times \dfrac{1}{60}\\\\ Linear \ velocity =47.648 \ cm \ per \ second[/tex]
The linear velocity is the hamster running is 47.648 cm/sec.
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4. GROCERIES A local grocery store sells grapes for $1.99 per pound. Determine whether the function that models the
cost of grapes is discrete, continuous, or neither discrete nor continuous. Then state the domain and range of the
function.
Answer:
Ok, we know that the price, per pond of grapes, is $1.99.
Now the function that models the cost of grapes is:
C(x) = $1.99*x
Where x is the number of pounds that you buy.
Here we can assume two things:
1) The grapes are already in bags, so x can be only whole numbers, as x can take only whole numbers, the cost c(x) will be discrete because there are a lot of possible costs that are not accessible.
Then the domain is:
D: {0, 1, 2, 3, 4.....}
And the range is :
R: {0*$1.99. 1*$1.99, 2*$1.99, ...}
2)You can choose any amount of grapes that you want, and then the grapes are weighted when yo pay. (This has not really sense, but it is fun to analyze the problem in different ways)
Here the weight can take almost any value, because with individual grapes you can have almost any number of pounds.
But the unit that defines the total weight is the weight of a single grape.
Then if you have N grapes (and all of them weight almost the same, let's say M)
The total weight will e N*M
If you add one more grape, the weight is: (N + 1)*M
Then it is still discrete!
As we do not know the mean weight of a grape, we can not find the domain nor the range in this situation, so the one above is the one that we should consider the correct one.
Please Help due tonight really need help It's a grade
Joey gets an allowance of $17 per week. He wants to buy a new basketball that costs $43.67. When will Jose be able to buy the basketball if he has already saved $22.22, but also has to pay $13.45 each week for snacks and school supplies? make an equation or inequality and solve. Show your work
Answer:
7 weeks
Step-by-step explanation:
Joey gets 17 per week
[tex]17x[/tex] with x the number of weeks
he wants to buy a basketball cap that 43.67
[tex]equation\geq 43.67[/tex]
he has already saved 22.22
[tex]+22.22[/tex]
has to pay 13.45 each week
[tex]-13.45x[/tex]
[tex]17x+22.22-13.45x\geq 43.67\\\\(17x-13.45x)+22.22\geq 43.67\\\\3.55x+22.22\geq 43.67\\\\3.55x\geq 43.67-22.22\\\\3.55x\geq 21.45\\\\x\geq \frac{21.45}{3.55} \\\\x\geq 6.04...[/tex]
but we don't wake a 0.4 of a week so we need the next whole number 7
so it will take 7
PLEASE SOLVE IF YOU CAN! Use order of operations to solve!! 6x3-^2-3^4x9+4^0
I NEED HELP IMMEDIATELY PLZ!
Answer:
f ( x ) = [tex]x^{3}[/tex] − 2 [tex]x^{2}[/tex] + x + C
Solve for x: 2x + 7 = -9 - 6x
(PLEASE HELP THIS IS FOR ALGEBRA AND ITS DUE AT IN 9 MINUETS)
Answer:
x=-2
Step-by-step explanation:
2x+7=-9-6x
add 6x on both sides
8x+7=-9
subtract 7 on both sides
8x=-16
x=-2
Answer:
x=-2
Step-by-step explanation:
Let me know if I need to explain but here is the answer cause i know you are in a rush.
Solve for x and y: 10x=5y+5 y=2x-1
Answer:
So there are infinite solutions along the line y = 2x-1
Step-by-step explanation:
10x=5y+5
y=2x-1
Substitute y into the first equation
10x = 5(2x-1) +5
10x = 10x-5+5
10x = 10x
This is always true
So there are infinite solutions along the line y = 2x-1
Alfred and his 4 friends bought 13 1/4 pounds of gummy bears at $1.20 pound . If the cost is divided between alfred and his four friends what would each person pay
the sum of 3 consecutive integers is -69. Find the largest
x = the first integer
x + 1 = the second integer
x + 2 = the third integer.
Let's set each of our variables equal to -69
x + x + 1 + x + 2 = -69
Combine like terms
3x + 3 = -69
Subtract 3 from both sides.
3x = -72
Divide both sides by 3
x = -24
The first integer = x = -24
The second integer = x + 1 = -24 + 1 = -23
The third Integer = x + 2 = -24 + 2 = -22
Selena purchased some gifts for her nieces and nephews online. She bought 3 dolls each priced at $19.99 each and 4 remote control cars priced at $21.99 each. Selena was able to get an online coupon for $3 off on each remote control car that she purchased. There was no sales tax, but the shipping charge was $10.50. What was the total amount Selena paid for her online purchase? a. $135.93 b. $144.93 c. $146.43 d. $155.43
Answer:
C
Step-by-step explanation:
Answer:
C: $146.43
Step-by-step explanation:
I just did the test. NOTICE: Edge loves moving stuff around so make sure its actually C... Look for $146.43
A bacterial population is modeled by the function P (t) = 10,000/1+499e^-0.6t, where t is elapsed time in days. What was the initial population of bacteria?
1
20
36
499
Answer:
It's B. 20
Step-by-step explanation:
edge 2020
Answer:
B
Step-by-step explanation:
Edg2020
simplify 3(x+2)-5x
1. 6-2x
2. 8x+2
3.-2x+2
4.2x+6
Answer:
-2x + 6
Step-by-step explanation:
Step 1: Write expression
3(x + 2) - 5x
Step 2: Distribute
3x + 6 - 5x
Step 3: Combine like terms
-2x + 6
Answer:
-2x+6
Step-by-step explanation:
first multiply the 3(x+2)
that equals 3x+6-5x
Add like terms
-2x+6
Which statement is true about the value of |6|?
Answer:
C
Step-by-step explanation:
I got it right on a quiz
Which equation represents a function? Select all that apply.
Find the ratio of 3 Km 300 m
Answer:
3km : 300m
3000 : 300
10 : 1
The length of a rctangle is to more than the
width. The perimeter of the rectangle is 72 meters
What is the length of the rectangle?
Answer:
19 m
Step-by-step explanation:
The width is 2 less than the length, so the perimeter is ...
P = 2(L +W)
72 = 2(L +(L -2))
76 = 4L . . . . . . . . add 4
19 = L
The length of the rectangle is 19 meters.
Which operation gives a result of 1.39?
Write the expression in radical form. [tex](36x)\frac{1}{2}[/tex]
12. Venu and Tanuj are running along a circular track. They take 48 seconds and 56 seconds to
complete a lap respectively. They begin from the starting point at the same time
6) How long does it take for them to meet at the starting point again?
How many laps will each boy have run by then?
Answer:
The meet at first time at starting point after 336 seconds,
Vanu have completed 7 laps while Tanuj has completed 6 laps.
Step-by-step explanation:
Given that Venu and Tanuj take 48 seconds and 56 seconds to
complete a lap respectively.
To meet them again at the startiong point, the time taken must be multiple of 56 and 48.
So, the minimum time required to meet them again at the startiong point is time taken for first time meet.
Time taken to first time meet is the smallest number which can be divided by 56 and 48, i.e the lowest common factor (LCM) of 56 and 48 which is 336 seconds or 5 minutes 36 seconds.
Number of laps by Venu
[tex]=\frac{336}{48}=7[/tex]
Number of laps by Tanuj
[tex]=\frac{336}{56}=6[/tex]
Write 0.12 as a fraction.
Let x = ?
100x = ?
100x - x = ? - ?
99x = ?
X = ?
Answer:
Let 0.12 be x.
Here, x is recurring in two decimal places so we'll multiply it by 10-
10x = 1.22Now, by subtracting them-
[tex] \\ \implies \sf \: 10x - x = 1.22 - 0.12 \\ \\ \\ \implies \sf \: 9x = 1.1 \\ [/tex]
Now, we'll divide both sides by 9 to get x as a fraction -
[tex] \\ \implies \sf \: x = \frac{1.1}{9} \\ \\ \\ \star \: \large{ \boxed{ \sf{x = \frac{11}{90} }}} \\ [/tex]
You have $85 in your bank account. Each week you plan to deposit $9 from your allowance and $20 from your paycheck. The equation $$b=55+(20+9)w$$ gives the amount b in your bank account after w weeks. How many weeks from now will you have $250 in your bank account?
Answer:
85+29x = 250
-85 -85
29x = 290
x = 10
10 weeks
Step-by-step explanation:
The verticies of triangle XYZare X(-3, -6), Y(21,-6) and Z(21, 4). What is the perimeter of the triangle?
Answer:
-3,-6
Step-by-step explanation:
What does b equal???
Answer:
17
Step-by-step explanation:
anddo the work you cheater
The required measure of the indicated angle b is 101°.
Use the concept of a triangle is defined as:
A triangle is a three-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
In the given figure,
Interior angle = 79°
And the corresponding exterior angle = b
If we combine both angles,
Then it becomes a complete angle of the line.
Since we know that,
The complete angle of a line = 180 degrees.
Therefore,
79° + b = 180°
Subtract 79° on both sides,
b = 101°
Hence,
The measure of angle b is 101°.
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Petite the indicated operation 10/14 + 11/14
Answer:
1 1/2
Step-by-step explanation:
10/14 + 11/14
Since we have a common denominator, we can add the numerators
21/14
Changing from an improper fraction to a mixed number
14/14 + 7/14
1 + 1/2
1 1/2
The sum of the measures of a triangle is 180 degrees.a triangle has angle measures of 5x+2,6x and 134.find the measures of x
Answer:
4
Step-by-step explanation:
6x + 5x+2 + 134 = 180 All triangles have 3 angles = 180. Combine
11x + 136 = 180 Subtract 136
11x = 180 - 136
11x = 44 Divide by 11
x = 44/11
x = 4
=======================
Angles are
5x + 2 = 22
6x = 24
<3 = 134
Total = 180
A factory produced 150 tons of steel in one year. The next year, the output increased to 180 tons. What is the percentage increase in the output?
A.
17%
B.
20%
C.
30%
D.
50%
E.
75%
Answer:
It would be 17%
Step-by-step explanation:
Answer:
B: 20%
Step-by-step explanation:
3h-2(4h-5)=10-5h A-0 B-4 C-infinity many solutions D-no solutions
Answer:
Step-by-step explanation:
3h - 8h + 10 = 10 - 5h
-5h + 10 = 10 -5h
10 = 10
infinitely many solutions
answer is C
help I tried finding answers nothing showed so now I’m here asking y’all :)
Which would NOT be found in the set of rational numbers? A. 5 B. 1/2 C. -12.5 D. 1.61803398874989484820
Answer:
D
Step-by-step explanation:
This is because rational numbers don't continue as a decimal infinitely
The height of Dougal is 1.84 metres. The height of Seb is 1.7 metres. Write the height of Dougal as a fraction of the height of Seb. Give your answer in its simplest form. Write your fraction in the form a / b eg * 19/16 would be 19/16
Answer:
No se bro suerte con eso V:
Step-by-step explanation:
Solve the equation
-3x + 1 + 10x = x + 4
0 x = 1/2
х
=
x = 12
X = 18
Answer:
x = 1/2Step-by-step explanation:
-3x + 1 + 10x = x + 4
-1 -1
7x = x + 3
-x -x
6x = 3
÷6 ÷6
x = 1/2