The coefficient of kinetic friction is 0.58
To determine the coefficient of kinetic friction [tex](\(\mu_k\))[/tex], we can use the following approach:
1. Identify the horizontal component of the pulling force [tex](\(F_{\text{pull, horizontal}}\))[/tex] and set it equal to the force of kinetic friction [tex](\(f_k\))[/tex].
2. The equation for the horizontal component of the pulling force is:
[tex]\[ F_{\text{pull, horizontal}} = F_{\text{pull}} \cdot \cos(30^\circ) \][/tex]
3. The equation for the force of kinetic friction is:
[tex]\[ f_k = \mu_k \cdot N \][/tex]
4. Since the sled is on a horizontal surface, the normal force [tex](\(N\))[/tex] is equal to the weight of the sled [tex](\(m \cdot g\))[/tex], where m is the mass of the sled and g is the acceleration due to gravity.
Putting these equations together and setting them equal to each other because the sled is moving at constant velocity, we get:
[tex]\[ F_{\text{pull}} \cdot \cos(30^\circ) = \mu_k \cdot m \cdot g \][/tex]
Now, substitute the given values:
[tex]\[ 80 \cdot \cos(30^\circ) = \mu_k \cdot 20 \cdot 9.8 \][/tex]
Solve for [tex]\(\mu_k\)[/tex]:
[tex]\[ \mu_k = \frac{80 \cdot \cos(30^\circ)}{20 \cdot 9.8} \][/tex]
Calculating this expression yields:
[tex]\[ \mu_k \approx 0.58 \][/tex]
So, the calculated coefficient of kinetic friction is approximately 0.58, which matches the provided answer.
Complete question:
A 20 kg sled is being pulled across a horizontal force at a constant velocity the pulling force has a magnitude of 80 N and it's directed at an angle of 30° above the horizontal determine the coefficient of kinetic friction.
Is it possible for two linear functions whose graph are parallel to have the same y-intercept
PLEASE HELP OVER 50 POINTS ONE QUESTION
8. Fill in the missing reasons for the algebraic proof below.
A:
B:
C:
The temperature was 8 degrees below zero. What does the 0 represent?
Factor the expression:
30x^3-5x^2-18x+3
PLZ SHOW YOUR WORK
If a = -4, and b = 3 what is |a-b|
What is the average of 12 1/2, 13, and 13?
solve 7d + d - 4d - 7 - 5d
A hummingbird can travel up to 15 meters per second. What is the hummingbird's speed in miles per hour? 1 mile ≈ 1609 meters Enter your answer, as a decimal to the nearest tenth, in the box.
there are 3600 seconds per hour
15 * 3600 = 54000 meters per hour
54000/ 1609 = 33.56
round to 33.6 miles per hour
The speed of Hummingbird's in miles per hour is 8,153.6463 mph.
What is speed-distance formula?Speed = Distance/Time – This tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance. Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,Distance = Speed X Time, and
Time = Distance / Speed, as the speed increases the time taken will decrease and vice versa.Given:
A hummingbird can travel up to 15 meters per second.
As,
1 m/s= 2.23694 mph
So, 15 m/s= 15 * 2.23694
= 8,153.6463 mph
Hence, the speed in mph is 8,153.6463.
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Find the values of x and y.
a. x=44, y=66
b. x=46, y=44
c. x=90, y=44
d. x=90, y=46
The function f(x) = ax^3 -x^2 + bx -24 has three factors. Two of these factors are x-2 and x+4. Determine the values of a and b, then determine the other factor. (My Nelson Advanced Functions Grade 12 book chapter 3)
Please help :)
The roots of any equation, always satisfies that equation.
Values of , a = - 2 and b = 22
Other factor of given function is (x - 3/2)
The given function [tex]f(x) = ax^3 -x^2 + bx -24[/tex]
Since, (x - 2) and (x + 4) are factors of given function
Therefore, x = 2 and x = -4 satisfies the given function.
[tex]f(2)=8a-4+2b-24=0\\8a+2b=28\\\\f(-4)=-64a-16-4b-24=0\\-64a-4b=40\\-16a-b=10[/tex]
Now , solving above two equation by elimination method
We get, a = -2 and b = 22
So, [tex]f(x) = -2x^3 -x^2 + 22x -24[/tex]
To find other factors , we divide above function by multiplication of (x - 2)(x+4).
So we get other factors, (x - 3/2)
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There are 8 pencils in package.how many packages will be needed for 28 children if each child get 4 pencils
The sum of two numbers is 39 . the smaller number is 13 less than the larger number. what are the numbers
The required numbers are given as 26 and 13.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
let the number be x and y,
According to the question,
x + y = 39 - - - - (1)
x = y + 13 - - - - - (2)
Put value from equation 2, in equation 1
y + y + 13 = 39
2y = 39 - 13
y = 26/y
y = 13
Now,
x = 13 + 13
x = 26
Thus, the required numbers are given as 26 and 13.
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What’s he hypotenuse, x, if ( 20, 21,x) is a Pythagorean triple?
Answer:
B) - 29
Step-by-step explanation:
What is the measure of each interior angle for a regular polygon with 30 sides?
First four terms of f(n)=3n-1
The first four terms of the function f(x) = 3n - 1 are 2, 5, 8, and 11.
Given,
f(n) = 3n - 1
We need to find the first four terms.
What is a function?A function has an input and an output.
Example:
f(x) = x + 1
x = 1,2,3 are inputs.
f(1) = 1 + 4 = 5
f(2) = 2 + 4 = 6
f(3) = 3 + 4 = 7
5, 6, and 7 are the outputs.
We have,
f(n) = 3n - 1
We can assume that the first four terms can be found with n= 1,2,3,4.
f(1) = 3 x 1 - 1 = 3 - 1 = 2
f(2) = 3 x 2 - 1 = 6 - 1 = 5
f(3) = 3 x 3 - 1 = 9 - 1 = 8
f(4) = 3 x 4 - 1 = 12 - 1 = 11
Thus the first four terms of the function f(x) = 3n - 1 are 2, 5, 8, and 11.
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A red kangaroo can cover 40 feet in 1 jump. How many feet can the red kangaroo cover in 12 jumps.
the height of a triangle is 4 times its base. if he are of a triangle is 200cm, what is the height
Geometry help please
2 attachments, 1 question
What is the value for X?
- 24
-9
-21
-14
what is the measure of <1?
- 45
- 60
- 120
-125
The value of X is -14 and the measure of <1 is 60 degrees.
Explanation:The value of X is -14. This can be determined by checking each option and finding the one that satisfies the given condition. Similarly, the measure of <1 is 60 degrees. This can also be determined by checking each option and finding the one that matches the given criteria.
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If a six sided die is tossed two times and '3' shows up both times, the probability of a '3' on the third trial is
If a six sided die is tossed two times and '3' shows up both times, the probability of a '3' on the third trial is [tex]\frac{1}{6}[/tex]
Given :
A six sided die is tossed two times and '3' shows up both times
'3' shows up both the times .
When the dice is rolled third time. there are 6 possibilities comes up
In the third trial , we have six possibilities 1,2,3,4,5,6
Out of six possibilities , the chance of getting '3' is only once
So, the probability of a '3' on the third trial is [tex]\frac{1}{6}[/tex]
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Which number is a solution of the inequality? 6 ≥ 6k?
1. solve the proprotion k/5=5/125.
a) 1/25
b) 25
c) 5
d) 1/5
2. round the answer of 0.4x-0.2=2.5 to two decimal places.
a) -2.70
b) -6.75
c) -5.75
d) -3.25
3. what is the y-intercept of 4x-3y=-12?
a) -4
b) 3
c) -3
d) 4
Raul is selling coupon books. He started with 50 coupon books and has already won a prize for selling at least 10 coupon books. The total amount of money Raul will make from selling x coupon books is represented by a function.
f(x)=20xf(x)=20x
What is the practical domain of the function if Raul sells 50 coupon books?
In how many ways can the letters in the word 'alaska' be arranged?
[2/(n+2)] - (3/n+2) = 5
Solve by u-substitution
4. Making financial decisions is fairly rare; most people make only a few during their lifetime. True False
solve for x
5.1 x = 1.02
What is the median of the data set: 15, -2, 0, 15, 2, 12
Which statement is true about regular exercise? 1.It decreases your resting heart rate.
2.It decreases your lung capacity.
3.It decreases your intelligence.
4.It increases your blood pressure.
Answer:
got correct on edmentum mastery test, hope this helps
You are playing a video game. For each diamond you collect, you earn 80 points. You also earn 100 bonus points by completing the level in less than 2 minutes. You need to earn more than 1220 points to continue on to the next level. Write and solve an inequality that represents the numbers dd of diamonds you must collect in less than 2 minutes to advance to the next level.
Given
For each diamond you collect, you earn 80 point
earn 100 bonus points by completing the level in less than 2 minutes.
earn more than 1220 points to continue on to the next level
Find the inequality that represents the numbers dd of diamonds you must collect in less than 2 minutes to advance to the next level.
To proof
As given in the question
For each diamond earn point = 80
bonus points by completing the level in less than 2 minutes = 100
earn more than 1220 points to continue on to the next level
Let us assume that the number of diamond = d
The inequality written in the form
we get
[tex]80d + 100 \geq 1220[/tex]
now solving the above equation
[tex]80d \geq1120[/tex]
[tex]d \geq14[/tex]
Thus the numbers of diamonds you must collect in less than 2 minutes to advance to the next level be 14.
Hence proved