The temperature of the mixture when it cools is; -10.7°C
What is the change in temperature?A change in temperature is defined as the difference in the initial and final temperatures.
Now, we are told that the chemist has a mixture with a temperature of 3.5°C.
We are also told that the temperature changes by -14.2 °C
Let the initial temperature be T₁ and the final temperature be T₂ and as such, the change in temperature will be;
ΔT = T₂ - T₁
Plugging in the relevant values gives;
-14.2 = T₂ - 3.5
T₂ = -14.2 + 3.5
T₂ = - 10.7°C
This is the temperature of the mixture after it cools.
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50 POINTS! PLEASE HURRY!
Answer:
question 1: T
question 2: F
question 3: C
Step-by-step explanation:
Answer:
1. True
2. False
3. D. {2,4,9,16}
Step-by-step explanation:
⭐What is a function?
a type of relation between an independent variable (x, domain) and a dependent variable (y, range) such that there is one x-value for every y-value.however, there can be the same y-value for multiple x-values.Therefore, #1 is a function because for every x-value, there is 1 y-value.
Therefore, #2 is NOT a function because 6 has 2 y-values, and 12 has 2 y-values.
⭐What is the range of a function?
the list of the y-values of the functionthe range of the function must be in ascending order (smallest to largest)Therefore, {2,4,9,16} is the range of #3 because it lists all of the y-values in ascending order.
find the missing length indicated multiple choice
Answer:
? = 6
Step-by-step explanation:
given a line parallel to a side of a triangle and intersecting the other 2 sides , then it divides those sides proportionally , that is
[tex]\frac{?}{15}[/tex] = [tex]\frac{4}{14-4}[/tex] = [tex]\frac{4}{10}[/tex] ( cross- multiply )
10? = 15 × 4 = 60 ( divide both sides by 10 )
? = 6
a manager for an insurance company believes that customers have the following preferences for life insurance products: 50% prefer whole life, 20% prefer universal life, and 30% prefer life annuities. the results of a survey of 300 customers were tabulated. is it possible to refute the sales manager's claimed proportions of customers who prefer each product using the data?product number whole150universal60annuities90 step 1 of 10: state the null and alternative hypothesis.
There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.
H0:p1=0.5,p2=0.3,p3=0.2
Ha:At least one proportion is different from the stated proportions.
Null hypothesis indicate that proportions are same as stated.
Product observed(fo) pi Expected(fe) (fo-fe)^2/fe
Whole 74 0.5 154.50 41.943
Universal 71 0.3 92.70 5.080
Annuities 164 0.2 61.80 169.010
Total 309 1 309 216.033
Expected value for the number of customers who prefer Whole Life=309*0.5=154.50
Expected value for the number of customers who prefer Universal Life=309*0.3=92.70
Test statistic:
Chi square=216.033
df=3-1=2
critical Chi square value=CHIINV(0.01,2)=9.210
Reject the null hypothesis
Therefore, There is sufficient evidence to to refute the sales manager's claimed proportions of customers who prefer each product using the data.
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A line passes through (0,2) and has a slope of 1/3 what is the equation of the line in slope intercept form
Y = 1/3x + 2
Y = 1/3x - 2
Y = -1/3x+2
Answer:
The equation of the line in slope-intercept form is: y = 1/3x + 2
To derive this equation, we first need to identify the slope of the line, which is given as 1/3. We then use the point (0,2) to find the y-intercept, which is 2. Finally, we substitute these values into the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we have m = 1/3 and b = 2, so the equation of the line is y = 1/3x + 2.
Alternatively, we could use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, we have (x1, y1) = (0,2) and m = 1/3, so the equation of the line is y - 2 = 1/3(x - 0), which simplifies to y = 1/3x + 2. This is the same result as before, but using a different method to derive the equation.
Step-by-step explanation:
Which of the following is not a test of congruence of triangle a SAS B SAA C SSS D AAA?
after how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old iddm women, if the incidence rate remains constant over time? (round your answer to one decimal place.) years
After 13 years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old iddm women, if the incidence rate remains constant over time.
In this question we have been given the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.
We need to find the number of years after which we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time.
Let n be the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females.
The probability of becoming blind over n years is 0.10
Given that the annual incidence rate of blindness per year was 0.74% IDDM females.
This means the rate r = 0.0074
For n years the annual incidence rate of blindness 0.0074n
We need to find the value of n,
0.0074n = 0.10
n = 13.51
n ≈ 13 years
Therefore, the number of years to expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females = 13
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The complete question is:
A study [12] of incidence rates of blindness among insulin-dependent diabetics reported that the annual incidence rate of blindness per year was 0.67% among 30- to 39-year-old male insulin-dependent diabetics (IDDM) and 0.74% among 30- to 39-year-old female insulin-dependent diabetics.
After how many years of follow-up would we expect the cumulative incidence of blindness to be 10% among 30-year-old IDDM females, if the incidence rate remains constant over time?
which graph represents f(x)=log3x 1?
The correct option A: graph A, shows the logarithmic function;
f(x) = log₃x + 1
Explain the term logarithmic function?The opposite of such an exponential function is a logarithmic function. A log function and then an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function be expressed. The formula again for logarithmic function is f(x) = log base b of x.f(x) = log₃x + 1
When x = 1f(1) = log₃1 + 1
f(1) = 0 + 1
f(1) = 1
(1, 1)
When x = 3f(3) = log₃3 + 1
f(3) = 1 + 1
f(3) = 2
(3, 2)
Thus, the graph must contain the points (1, 1), (3, 2).
Therefore, graph A define the given logarithmic function;
f(x) = log₃x + 1.
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. The angle measures of an isosceles triangle are (4x + 5)°, (4x + 5)°, 10⁰.
What is the measure (in degrees) of an exterior angle supplementary to one
of the base angles?
The measure of the supplementary angle for one of the base angles is 95°.
What are supplementary angles?The supplementary angles are the angles whose sum is given as 180°. The sum of all angles on one side of straight line is also 180°
The measures of angles are given as (4x + 5)°, (4x + 5)°and 10⁰ respectively.
Since, the sum of the angles of a triangle is 180⁰. The following equation can be written as,
(4x + 5)° + (4x + 5)° + 10⁰ = 180⁰
⇒ 8x = 160°
⇒ x = 20°
Thus, the angles can be written as 4 × 20 + 5 = 85° and 10° respectively.
Now, the measure of the exterior angle can be written as below,
⇒ 180° - 85° = 95°.
Hence, the measure of the exterior angle is given as 95°.
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T/F: a large p-value in a test will favor a rejection of the null hypothesis.
A test's large p-value does not necessarily mean that the null hypothesis should be accepted.
In a test, a low P-value will favor rejecting the null hypothesis.
The P-value approach evaluates whether something is "likely" or "unlikely," assuming that the null hypothesis is correct, by calculating the probability of observing a test statistic that is more extreme in the direction of the alternative hypothesis than the one actually seen. If the P-value is low, such as less than, it is "unlikely" (or equal to) α.
The null hypothesis is disregarded in favor of the alternative hypothesis if the P-value is less than (or equal to) α. Additionally, the null hypothesis is not disproved if the P-value is higher than α.
As a result, the right response is false.
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simplify.4x3−12x24x2 7x−22x2−6x5x2 11x 2
The answer for this Simplifiction 4x3−12x24x2 7x−22x2−6x5x2 11x 2 using BODMASS rule is -19316
What is BODMASS?=4*3-12*24*27*-22*2-6*5*211*2
=-19316
To simplify a phrase, use various techniques to make it shorter and simpler. The actions needed to simplify things are carried out in a predetermined sequence known as BODMASBracket = B0 = ofDivide by DM is for multiplicationA = AdditionS=SumS=SubtractMaking something simpler makes it easier to understand, grasp, or use it. It could entail simplifying complicated concepts, eliminating superfluous details, or drawing diagrams or models.an explanation that leaves out extraneous information and condenses complexity.Statement simplification is rewriting the same algebraic expression in a compact form and without any like terms. Making something less complex means simplifying it.To learn more about BODMASS refer to:
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Erin makes the following statements. The scale factor from ∆ABC to ∆XYZ is 31. The area of ∆XYZ is 13 the area of ∆ABC.
The statement made by Erin about the triangles is false
How to determine the true statements?From the question, we have the following parameters that can be used in our computation:
The scale factor from ∆ABC to ∆XYZ is 31. The area of ∆XYZ is 13 the area of ∆ABC.As a general rule of dilation (i.e. scale factors),
The area of the image of the dilation is the square of the scale factor multiplied by the area of the pre-image shape
Mathematically, this is represented as
Area of the image of the dilation = scale factor² * Area of the pre-image shape
Using familiar terms, we have
Area of ∆XYZ = (31)² * the area of ∆ABC.
The above statement is true and it is not the same as Erin's statement
Hence, Erin is incorrect
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Find the slope
It has to be in a fraction form pls help
The slope of the line is 4/3
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.
In the slope marked,
vertical length = change in y values = number of unit squares = 4
Horizontal length = change in x values = number of unit squares = 3
Slope= ( change in y values )/ ( change in x values ) = 4/3
Thus, the slope = 4/3
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write 312 as a product of prime factors
Answer: 312=(2)(2)(2)(3)(13)
Step-by-step explanation:
312 | 2
156 | 2
78 | 2
39 | 3
13 | 13
Hence, 312=(2)(2)(2)(3)(13)
Find the value of a for which v = [6 -10 4 a] is in the set H = span
The value of a for which v is a linear combination is given as follows:
a = -8.
How to obtain the value of a?v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.
From the vectors, the system is defined as follows:
-x = -1.2x - y = 4.5x + 4y - 3z = -6.-x + 3y - z = a.From the first equation, the value of x is obtained as follows:
-x = -1
x = 1.
From the second equation, the value of y is obtained as follows:
2x - y = 4
2 - y = 4
y = 2 - 4
y = -2.
From the third equation, the value of z is obtained as follows:
5x + 4y - 3z = -6.
5 - 8 - 3z = -6
3z = 3
z = 1.
Then the value of a needed for the linear combination is of:
a = -x + 3y - z
a = -1 - 6 - 1
a = -8.
Missing InformationThe problem is given by the image shown at the end of the answer.
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three more than twice the sum of a number and half the number equals 105. which equation models this relationship?2 (x one-half x) 3 = 1052 x one-half x 3 = 1052 x 3 = one-half x 105
(x+x/2)*3=105 is the equation for "three times the sum of a number and half the number equals 105."
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. 4 + 6 = 10 is an example of an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
Three more than twice the sum of a number and half the number equals 105,
The equation will be,
(x+x/2)*3=105
The equation for "Three more than twice the sum of a number and half the number equals 105" will be (x+x/2)*3=105.
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radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute. what is the rate of change of the surface area when the radius is 6 inches and the height is 18 inches?
The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.
Given:
radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.
we are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.
we have dr/dt = 6 in/min and dh/dt = -4 in/min
Volume, V = πr²h
Differentiate the above expression to get:
dV/dt = 2πrh dr/dt + πr² dh/dt
SUbstitute the value we get:
dV/dt = 2π(6)(18)(6) + π(6)²(-4)
= 4069.44 - 452.16
= 3617.28 in³ per minute.
The volume is increasing at a rate of 3617.28 in³ per minute.
Area = 2πr(h+r)
Differentiate the above expression:
dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}
dA/dt = 2π {(18+6)(6) + 6(-4+6)}
= 2π(144 + 12)
= 312π
= 979.68 in² per minute.
The area is increasing at a rate of 979.68 in² per minute.
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The rate of change of the surface area when the radius is 6 inches and the height is 18 inches is 979.68 in² per minute.
Given:
The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute.
We are asked to find the rate of change of the surface area when the radius is 6 inches and the height is 18 inches.
We have dr/dt = 6 in/min and dh/dt = -4 in/min
In geometry, it is defined as a three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
Volume, V = πr²h
Differentiate the above expression to get:
dV/dt = 2πrh dr/dt + πr² dh/dt
Substitute the value we get:
dV/dt = 2π*6*18*6 + π*6² * -4
= 4069.44 - 452.16
= 3617.28 in³ per minute.
The volume is increasing at a rate of 3617.28 in³ per minute.
Area = 2πr(h+r)
Differentiate the above expression:
dA/dt = 2π {(h+r) dr/dt + r (dh/dt + dr/dt)}
dA/dt = 2π {(18+6)(6) + 6(-4+6)}
= 2π(144 + 12)
= 312π
= 979.68 in² per minute.
The area is increasing at a rate of 979.68 in² per minute.
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Nth Term of a Geometric Sequence
Dec 05, 4:44:35 PM
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Find the 12th term of the geometric sequence 9, -18, 36, ..
Answer:
Submit Answer
Answer:
Step-by-step explanation:
Help with question 11
Answer:
The lowest common denominator is 12
Step-by-step explanation:
Finding the lowest common denominator
Multiples of 6: 6,12,18,24
Multiples of 4: 4,8,12,16,20
The lowest common multiple is 12
The lowest common denominator is 12
How do you write 16/25 as a percent?
16/25 as a percentage is 64%.
The number in the denominator is the one below the fraction line, while the number in the numerator is the one above the fraction line.
When we talk about percentages, we really mean that it's a subset of 100. Since the word "percent" refers to a hundred, 50% is equivalent to expressing 50/100 or 5/10 in fractional form.
Therefore, since 25 is the denominator in 16/25, we might change the fraction so that 100 is the denominator.
To do that, we divide 100 by the denominator:
100/25 = 4
Once we have that, we can multiply both the numerator and denominator by this multiple:
[tex]\frac{16}{25}[/tex] × [tex]\frac{4}{4}[/tex] = [tex]\frac{64}{100}[/tex]
Now we can see that our fraction is 64/100.
Thus, 16/25 as a percentage is 64%.
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when does a parametric equations describe a physical situation where a standard relationship between two variables does not suffice
Parametric equations describe a physical situation only when we have to draw the coordinates of the figure which actually didn't have any such coordinates.
There are many reasons. The best way to answer any “why?” question in math is to work, at least a little, with the subject to see what it can do.
With parametric equations you will find that they simplify many problems that are a complex jumble of variables if viewed in rectangular coordinates.
To illustrate a very simple case:
Define a certain circle as: x^2 + y^2 = 25 in rectangular coordinates.
Switching to polar coordinates we have: x = 5*cos(theta) and y = 5*sin(theta).
We have parameterized an equation in two variables into two simpler equations in the one variable theta. We did this by finding a single variable (the parameter theta) that will show the behavior of x and y independently.
This can be a very powerful tool if we have an equation in many variables and can reduce it to many equations but in fewer variables.
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a care has wheels of radius 16 inches. the wheels are spinning at 800 rotations per minute. what is the speed of the vehicle in miles per hour
Answer:
8.98 miles/hour
Step-by-step explanation:
To find the speed of the vehicle in miles per hour, you can first convert the number of rotations per minute to the number of rotations per hour by multiplying it by 60. So, the number of rotations per hour is 800 rotations/minute * 60 minutes/hour = <<800*60=48000>>48000 rotations/hour.
Then, you can use the formula for the circumference of a circle to find the distance traveled by one of the wheels in one rotation: C = 2 * pi * r, where C is the circumference, pi is approximately 3.14, and r is the radius of the wheel. So, the circumference of each wheel is 2 * 3.14 * 16 inches = <<23.1416=100.48>>100.48 inches.
Then, you can use the formula for speed: distance traveled / time traveled. Since the distance traveled by one of the wheels in one rotation is 100.48 inches, and there are 48000 rotations per hour, the distance traveled by one of the wheels in one hour is 48000 rotations/hour * 100.48 inches/rotation = 4.81E5 inches.
To convert this distance to miles, you can divide it by the number of inches per mile: 4.81E5 inches / (12 inches/foot * 5280 feet/mile) = 8.98 miles/hour. This is the speed of the vehicle.
Brent is a member of the school's basketball team. Brent is 74 inches tall, the mean height of the
players on the team is 76 inches. Brent's height translates to a z-score of -0. 85 in the team's height
distribution. What is the standard deviation of the team members' heights?
Round to 2 decimal places
The standard deviation of the team members' heights is 2.35.
A z-score is a number that indicates how far an observation deviates from the mean and in which direction.
A z-score is a common name for a standardized number.
The standardized value of x is: If x is an observation from a distribution with known mean and standard deviation :
z = (x - mean) / Standard Deviation
Given in question,
z = -0.85
x = 74
mean = 76
Let the Standard deviation be s.
By putting the values in the equation,
-0.85 = (74 - 76)/s
s = -2/-0.85
= 2/0.85
= 2.35
Hence, the standard deviation of the team members' heights is 2.35.
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What is the length of AB
The length of AB will be 32
Given that,
AC=32
AD=8
∠ABC=90 degree
From the diagram, we can see that it is a right-angle triangle so we can use that trigonometry to find the value of AB.
We know that,
sinФ=[tex]\frac{perpendicular}{hypotenuse }[/tex]
Now using this formula we can find the value of AB. And we know that the value of sin90= is 1.
sin90=AB/AC
⇒1=AB/32
⇒32=AB
⇒AB=32
So the length of AB mean x is 32
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Fill in the blanks with two rational numbers (other than 1 and -1). -5.6 ?
A triangle has one side that measures 12, another side that measures x, and a third side that measures 4 less than x. The perimeter is 26.
Which equation would we use to find the value of x?
Answer:
Triangle perimeter = 12 + x + (x - 4) = 26 which is the equation you can use to find out the value of x.
Step-by-step explanation:
la grange a rectangular box without lid is to be constructed from 100 square inches of material. find the dimensions that will yield the box with largest volume.
The dimensions of the rectangular box is 2.
Find the solution ?The base will be 4×4 and the height will be 2 (all numbers in feet)
Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is
base+height×perimeter
=b2+4bh=48
From which we can determine:
h=48−b24b
The Volume of the box:
V(b)=b2h=b2⋅(48−b24b)
=12b−3b34
b=±4
Plugging this back into the formula
h=48−b24b
we get
h=2
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Triangle ABC is similar to triangle XYZ. What is the length of YZ?
28 in.
32 in.
AA
C
20 in.
B
А
26 in.
15 in.
30 in.
24 in.
The length of the YZ for the two similar triangles will be 9 inches.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Given that triangle, ABC is similar to triangle XYZ. The value of the side YZ will be calculated by the similarity property,
YZ / BC = XZ / AC
x / 3 = 15 / 5
x = ( 15 x 3 ) / 5
x = 3 x 3
x = 9 inch
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HELPPPPP!
What is the value of x when g(h(x)) = 4?
Ο Α. Ο
OB. 2
O C. 4
OD. 5
The value of the x in g(h(x)) = 4 is 4 if the g⁻¹(4) = 2 and at x = 4 h(x) = 2 option (C) is correct.
The correct value of x when g(h(x)) = 4 is,
⇒ x = 4
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;
The relation is,
g (h (x)) = 4
Now, Substitute x = 4;
LHS;
g (h (x)) = g (h (4))
= g (2)
= 4
Thus, The correct value of x when g(h(x)) = 4 is,
⇒ x = 4
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Which graph is best for trend analysis?
A line chart is the best chart to show trends over time. It shows trends and data variables clearly.
What is a graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
Types of GraphsBar chart.Line graph.Area graph.Scatter plot.Pie chart.Pictograph.Column chart.Bubble chart.We can deduce that a line chart is the best chart to show trends over time as it shows trends and data variables clearly and also assists readers with making predictions for the future. However, for a data set comparison being useful, you must use the same scale on both axes.
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a thin, 120 g disk with a diameter of 8.00 cm rotates about an axis through its center with 0.18 j of kinetic energy.
The speed of a point on the rim is 2.44 m/s.
What is a quick answer for diameter?
The diameter is the distance along the circle's center that must travel in order to touch two points on its edge.
First convert diameter into radius
r = d/2 = 0.08/2 = 0.04 m
The moment of inertia of disc is given by
I = 0.5mr²
Where m is the mass and r is the radius of the disk
I = 0.5(0.1)(0.04)²
I = 0.00008 kg.m²
and since we are dealing with rotational motion then rotational kinetic energy is given by
E = 0.5 I ω²
we have to separate ω
ω² = E/0.5 I
ω = √E/0.5 I
ω = √0.15/0.5(0.00008)
ω = 61.23 rad/sec
Finally we know that speed is given as
v = ω r
v = 61.23 (0.04)
v = 2.44 m/s
Therefore, the speed of a point on the rim is 2.44 m/s.
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The complete question is -
A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim