Answers
The width of the rectangle is [tex]4x^8y^6[/tex]inches.
Option A is correct.
What is the area of the rectangle?
A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:
A = l x w
To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:
Area = length x width
In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:
width = Area / length
Substituting the given values, we have:
width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]
Simplifying the expression, we get:
width = [tex]4x^{8}y^{6}[/tex]
Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.
Option A is correct.
To learn more about the area of the rectangle, visit:
https://brainly.com/question/25292087
#SPJ1
Related Questions
Select the correct answer. What is the simplified form of this expression? (-3x2 + x + 5) − (4x2 − 2x)
Answers
Answer:
-9+3x
Step-by-step explanation:
(-3x2 + x + 5) − (4x2 − 2x)
(-6+x+5)-(8-2x)
(-1+x)-8+2x
-1+x-8+2x
-9+3x
What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
Answers
The measure of each angle in the regular polygon is 154.3 degrees
How to determine the measure of each angle in a regular polygonFrom the question, we have the following parameters that can be used in our computation:
Number of sides, n = 14
The measure of each angle is calculated as
Angle = ( n − 2 ) × 180/n
substitute the known values in the above equation, so, we have the following representation
Angle = (14 − 2) × 180/14
Evaluate
Angle = 154.3
Hence, the angle is 154.3
Read more about angles at
https://brainly.com/question/25716982
#SPJ1
4. Reginald created a mosaic from 6" square tiles.
If the completed mosaic was 2 feet by 3 feet, how
many square tiles did he use?
Answers
Reginald used 2 square tiles to make the mosaic
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The area is the product of the length and width. Hence:
Area = length * width
Reginald created a mosaic from 6" square tiles. Therefore:
Area of tiles = 6 in * 6 in = 36 in²
If the completed mosaic was 2 feet by 3 feet, Hence:
Area of mosaic = 2 feet * 3 feet = 6 feet
1 feet = 12 in
6 feet = 6 feet * 12 in per feet = 72 in²
Number of tiles = Area of mosaic / area of tiles = 72 in² / 36 in² = 2
Reginald used 2 tiles
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
If f(x) = 2x² - x - 6 and g(x) = x² - 4, find f(x) = g(x).
OA.
B.
C.
2x+3
2
2x-3
#+2
2x+3
#+2
O D. 22-2
Jhayq
Answers
Answer:
Step-by-step explanation:
To find the value of x such that f(x) = g(x), we need to set the two functions equal to each other and solve for x.
First, let's define the variables:
f(x) = 2x² - x - 6 is a quadratic function with x as the variable.
g(x) = x² - 4 is also a quadratic function with x as the variable.
Now, to find the value of x such that f(x) = g(x), we set the two functions equal to each other:
2x² - x - 6 = x² - 4
Next, we simplify this equation by subtracting x² from both sides:
x² + x - 10 = 0
This is a quadratic equation, which we can solve for x using either the quadratic formula or by factoring.
Let's try factoring:
x² + x - 10 = (x + 5)(x - 2) = 0
So either x + 5 = 0 or x - 2 = 0. Solving for x, we find that:
x = -5 or x = 2
These are the two values of x such that f(x) = g(x).
Need assistance with this problem
Answers
We can see that the exponential model is better
What is the difference between a linear and an exponential function?The main difference between a linear and an exponential function is the way they change as their input variable (usually denoted as x) increases.
In summary, linear functions have a constant rate of change, while exponential functions have an increasing rate of change.
For the linear function;
f(x) = 946(6) + 3349
= 9025
For the exponential function;
g(x) = 3866e^0.138(6)
g(x) = 8848
Learn more about exponential:https://brainly.com/question/28596571
#SPJ1
Select the correct answer.
A fantasy board game makes use of four dice. The first is a standard 6-faced die, the second die has 4 faces, and the other two have 10 faces each. If all the dice are thrown together and their combination dictates a certain outcome of the game, how many possible outcomes exist?
A.
30
B.
240
C.
2,400
D.
3,000
Answers
Answer:
The total possible outcomes that exist are:
2400
Step-by-step explanation:
We are given four dices:
first is a standard 6-faced die.
The second die has 4 faces.
Third dice has 10 faces.
Fourth dice has 10 faces.
Now when all the dice are thrown together then the total number of possible outcomes are:
( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)
The answer is:
2400
128 Sa se afle suma dintre produsul numerelor 45 250 şi 98 numer 100 000 şi 89 756.
Answers
45250 • 98 = 4434500
100000 • 89756 = 8975600000
4434500 + 8975600000 = 901994500
What is 7/8 of sixteen times a half of 30
Answers
7/8 of sixteen times a half of 30 is 210.
What is a PEMDAS rule?
PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
Start with the expression inside the parentheses: half of 30 is 15.
Multiply 16 by 15: 16 times 15 is 240.
Find 7/8 of 240:
7/8 of 240 = (7/8) x 240
= 210
Hence, 7/8 of sixteen times a half of 30 is 210.
To learn more about the PEMDAS rule, visit:
https://brainly.com/question/23385237
#SPJ1
graph the function f (x) = 3 cos (x) -4
Answers
Answer: DESMOS
Step-by-step explanation:
Your OHVA teacher reminded you in class to use DESMOS to see the graph and then sketch it on your test...
Mary is driving at 60 mph. She decreases her speed by 5 mph every second. Which signed number
represents the change in her speed after 5 seconds?
Answers
Answer:
35 mph
Step-by-step explanation:
5×5=25
60-25=35.
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 . It goes through the point (5,189).
Answers
If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.
If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.
Based on the roots and multiplicity, we have:
P(x) = k · (x-2)^2 · (x-0) · (x - (-2))
P(x) = k · (x-2)^2 · (x-0) · (x+2)
We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).
To find "k", we plug in that point and solve for "k":
189 = k · (5-2)^2 · (5-0) · (5+2)
189 = k · (3)^2 · (5) · (7)
189 = k · 315
0.6 = k
So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)
A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the volume of 15 bags in cubic yards.
Answers
Answer:
285.76 kilograms 1.1 cubic yard
Step-by-step explanation:
Answer:
1.11121 cubic yards.
Step-by-step explanation:
First, let's convert the weight of 1 bag of garden soil from pounds to kilograms:
1 lb = 0.45359237 kg
42 lbs = 42 * 0.45359237 kg = 19.05 kg
So, the weight of 1 bag of garden soil is 19.05 kilograms.
Next, let's find the weight of 15 bags of garden soil:
15 bags * 19.05 kg/bag = 285.75 kg
So, 15 bags of garden soil weigh 285.75 kilograms.
Next, let's find the volume of 15 bags of garden soil in cubic yards:
1 cubic foot = 0.037037 cubic yards
2 cubic feet * 15 bags = 30 cubic feet
30 cubic feet = 30 * 0.037037 cubic yards = 1.11121 cubic yards
So, 15 bags of garden soil have a volume of 1.11121 cubic yards.
-10 -8 -6 -4 -2 0 2 4 6 8 10
Plot the integer -7 on the number line.
The distance between 0 and -7 is
The absolute value of -7 is
The magnitude of -7 is
Answers
Step-by-step explanation:
To plot the integer -7 on the number line, we can place it to the left of 0. The number line would look like this:
-10 -8 -7 -6 -4 -2 0 2 4 6 8 10
The distance between 0 and -7 is 7 units, since 0 is 7 units to the right of -7.
The absolute value of -7 is 7, since the absolute value of a number is its distance from 0 on the number line.
The magnitude of -7 is also 7, which is the same as its absolute value. The magnitude of a number refers to its size or absolute value, regardless of its sign. In this case, the magnitude of -7 is 7.
For each value of y , determine whether it is a solution to 10 < y
Answers
If a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
What is inequality?
In mathematics, an inequality is a statement that describes a relationship between two values, expressing that one value is greater than, less than, or equal to the other value. Inequalities are denoted by symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
The inequality 10 < y means that "y" is greater than 10. To determine whether a given value of "y" is a solution to this inequality, we simply need to check whether that value is indeed greater than 10.
For example:
If y = 11, then 10 < y is true, because 11 is greater than 10.
If y = 10, then 10 < y is false, because 10 is not greater than 10 (they are equal).
If y = 9, then 10 < y is false, because 9 is not greater than 10.
Hence, if a value of "y" is greater than 10, then it is a solution to the inequality 10 < y. If it is less than or equal to 10, then it is not a solution.
To learn more about the inequalities, visit:
https://brainly.com/question/25275758
#SPJ1
check all of the following that are possible units for measuring mass in the metric system. A. Pound B. Kilogram C. Anagram D. Gram
Answers
The following that are possible units for measuring mass in the metric system include the following below:
B. Kilogram
D. Gram.
What is Mass?This is a quantitative measure of inertia and it is referred to as the amount of matter which is present in a given body.
Options B and D both have the suffix "gram" which represents a metric system and are used in measuring mass unlike anagram which isn't a form of measurement which was why they were chosen as the correct set of options.
Read more about Mass here https://brainly.com/question/1838164
#SPJ1
Rylon Corporation manufactures Brute and Chanelle perfumes. The raw materials needed to manufacture each type of perfume can be purchased for $3 per pound. Processing 1 lb of raw material requires 1 hour of laboratory time. Each pound of processed raw material yields 3 oz of Regular Brute Perfume and 4 oz of Chanelle perfume. Regular Brute can be sold for $7/oz and Regular Chanelle for $6/oz. Rylon also has the option of further processing Regular Brute and Regular Chanelle to produce Luxury Brute, sold at $18/oz, and Luxury Chanelle, sold at $14/oz. Each ounce of Regular Brute processed further requires an additional 3 hours of laboratory time and $4 processing cost and yields 1 oz of Luxury Brute. Each ounce of Regular Chanelle processed further requires an additional 2 hours of laboratory time and $4 processing cost and yields 1 oz of Luxury Chanelle. Each year, Rylon has 6,000 hours of laboratory time available and can purchase up to 4,000 lb of raw material. Question : what is the simplex algorithm (manual table ) to find a solution to the linear programming problem given above
Answers
Convert the problem to standard form and write the initial tableau with slack variables:
Maximize
[tex]Z = 7*3 + 6*4 + 18*5 + 14*6 - 3*1 - 3*2 - 4*5 - 4*6[/tex]
Subject to:
[tex]x1 + x2 + s1 = 4000\\x3 - (1/3)*1 + (1/3)*5 = 0\\x4 - (1/3)*2 + (1/2)*6 = 0\\x3*1 + 3*2 + 3*3 + 3*4 + 3*5 + 2*6 + s2 = 6000[/tex]
All variables are non-negative.
Tableau
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
s1 1 1 0 0 0 0 1 0 4000
s2 3 3 3 3 3 2 0 1 6000
x5 0 0 1 0 1/3 0 0 0 0
x6 0 0 0 1 0 1/2 0 0 0
The basic variables are s1, s2, x5, and x6.
Step 1: Choose entering variable. The most positive coefficient in objective row is 18, corresponding to x5. x5 enters the basis.
Step 2: Choose the leaving variable. The minimum ratio of right-hand side to coefficient of x5 is 12000/(1/3) = 36000,
corresponding to s1. s1 leaves the basis.
Step 3: Perform, pivot operation to make x5 the basic variable for s1. Divide, pivot row by 1/3 and subtract appropriate multiples of the pivot row from other rows to make other entries in column 5 zero.
x1 x2 x3 x4 x5 x6 s1 s2 b
Z -3 -3 7 6 18 14 0 0 0
x5 0 0 1 0 1/3 0 0 0 0
s2 3 3 3 3 2 2/3 2/3 0 1/3 24000
x3 1 0 1/3 0 1/3 0 -1/3 0 0
x4 0 1 0 1/3 0 1/2 -1/6 0 0
The basic variables are x5, x3, x4, and s2.
Step 4: Choose the entering variable. The most positive coefficient in the objective row is 7, corresponding to x3. x3 enters the basis.
Step 5: Determine the leaving variable. The right-hand side's minimum ratio to the coefficient of x3 is 0, indicating that x3 can be increased without bound. This implies that the optimal solution is unbounded and that there is no finite optimal value for the problem.
As a result, the simplex algorithm demonstrates that the given linear programming problem lacks a feasible solution. This means that it is not possible to meet all of the constraints at the same time.
For more question on simplex algorithm click on
https://brainly.com/question/29554333
#SPJ4
How do I find the answer to this question?
Answers
Answer:
you see
Step-by-step explanation:
Here are the first four terms of a number sequence.
2 7 12 17
Here are the first five terms of another number sequence.
-4 -1 2 5 8
Find two numbers that are in both number sequences.
Answers
Two numbers that are in both sequences are the numbers 17 and 32.
What is a sequence?A sequence can be described as a set of numbers each with a defined interval between one another. For example, in the sequence 2, 4, 6, 8, 10, the interval is 2.
What numbers do these sequences have in common?To find two common numbers, let's expand the sequences as it is shown below:
First sequence: In this sequence, the interval is 5.
2 7 12 17 22 27 32
Second sequence: In this sequence, the interval is 3.
-4 -1 2 5 8 11 14 17 20 23 26 29 32
Learn more about sequences in https://brainly.com/question/30262438
#SPJ1
A bag of garden soil weighs 42 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the (((volume of 15 bags in cubic yards.)))
Answers
Answer:
he weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Step-by-step explanation:
To find the weight of 15 bags in kilograms, we can first convert the weight of one bag from pounds to kilograms and then multiply by the number of bags:
1 pound = 0.453592 kilograms
So the weight of one bag in kilograms is:
42 pounds * 0.453592 kilograms/pound = 19.05 kilograms
The weight of 15 bags in kilograms is:
15 bags * 19.05 kilograms/bag = 285.75 kilograms
To find the volume of 15 bags in cubic yards, we can first convert the volume of one bag from cubic feet to cubic yards and then multiply by the number of bags:
1 cubic yard = 27 cubic feet
So the volume of one bag in cubic yards is:
2 cubic feet / 27 cubic feet/cubic yard = 2 / 27 = 0.07407 cubic yards
The volume of 15 bags in cubic yards is:
15 bags * 0.07407 cubic yards/bag = 1.111 cubic yards
Therefore, the weight of 15 bags of garden soil in kilograms is 285.75 kilograms, and the volume of 15 bags in cubic yards is 1.111 cubic yards.
Allen’s hummingbird has been studied by zoologist Bill Alther (Reference: Hummingbirds, K. Long and W. Alther). A small group of 15 of Allen’s hummingbirds has been under study in Arizona. The average weight for these birds is = 3.15 grams. Based on previous studies, we can assume that the weights of Allen’s hummingbirds have a normal distribution, with = 0.33 gram.
Find an 80% confidence interval for the average weights of Allen’s hummingbirds in the
study region. What is the margin of error?3.02, 3.28).
Sample mean of :
Population standard deviation of:σ=0.32
Sample size of : n=10
The confidence interval is:
80% confidence level, hence, z is the value of Z that has a p-value of , so .
The margin of error is:Then
The 80% confidence interval for the average weights of Allen's hummingbirds in the study region is (3.02, 3.28).
The margin of error is of 0.13.
The lower limit is of 3.02.
The upper limit is of 3.28.
Give a brief interpretation of your results in the context of this problem The standard deviation σ is known.
•the standard deviation σis known
•normal distribution of weight
•n is large
Find the sample size necessary for an 80 % confidence level with a maximal error of estimate = 0.08 for the mean weights of the hummingbirds.
Answers
a) The required margin of error and lower and upper limits are:-
E =0.124
Lower limit =3.026
Upper limit = 3.274
b) sample size is n = 27.
What is a confidence interval?An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
The margin of error will be calculated as:-
a) Margin of error (E) :
[tex]E = Z_c\times \dfrac{\sigma}{\sqrt{n}}[/tex]
E =0.124
Margin of error = E =0.124
The lower and upper limits are calculated as:-
Lower limit = x-E
L= 3.15 - 0.124
L= 3.026
Lower limit =3.026
Upper limit = x + E
U= 3.15 + 0.124
U= 3.274
Upper limit = 3.274
b) The following equation may be used to calculate the right number of samples, n when is already known:
Margin of error = 0.13
Sample size (n):
[tex]n = (\dfrac{Z_c\sigma}{E})^2[/tex]
[tex]n = (\dfrac{1.28\times 0.36}{0.09})^2[/tex]
n = 26.21
To read more about confidence intervals follow
brainly.com/question/795909
#SPJ9
Identify the y- intercept of the graph below
b= -4
b=6
b=4
b= -10
Answers
Explanation
The y intercept is the point where the line crosses the y axis, it will be point ( 0, 4 ) here, 4 being the y value.
There is no x value as it only has a “rise” up or down, no “run” Left or right.
A woman has a total of $7,000 to invest. She invests part of the money in an account that pays 10% per year and the rest in an account that pays 11 per year. If the interest earned in the first year is $730 , how much did she invest in each account
Answers
The investments are $ 4000 and $ 3000 in the respective accounts
What is Algebra ?The mathematical field of algebra assists in the depiction of problems or conditions as mathematical statements. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
In the given question,
x = amount invested at 10 %
( 7000 - x ) = amount invested at 11 %
The total interest was $730 :
.10 (x) + .11 (7000-x) = 730
0.1 x + 770 - 0.11 x = 730
0.01 x = 40
x = 4000
Therefore, the amount invested in an account that pays 10 % per year is $ 4000.
Hence , the amount invested in an account that pays 11 % per year is
= ( 7000 - x ) = 7000 - 4000 = $ 3000.
Learn more about algebra, visit :
https://brainly.com/question/29131718
#SPJ1
Select all the expressions that have a value of 13.5 when s = 1.5
Answers
Answer:
Given that s = 1.5, the expressions that have a value of 13.5 are:
(1) 5s + 8 = 5 × 1.5 + 8 = 13.5
(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5
Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.
What is the x-coordinate of the image when M(4, −1) is reflected in y=3.
Answers
The image of the point M(4, -1) after reflection in the line y = 3 would have the x-coordinate of 4.
What is another way to say reflecting?When you reflect, you are giving something serious thought. [written] I continued my thoughtful stroll to the car while contemplating the unfortunate honeymooners. Synonyms: thoughtful, ponderous, contemplative, and pensive More reflective's opposites.
What other word for reflecting is there?Cogitate, deliberate, reason, conjecture, and think are a few words that frequently replace the word reflect. All of these terms indicate "to utilise one's faculties of imagination, reasoning, or inference," but reflect denotes thoughtful deliberation over a memory that has just come to mind.
To know more about Reflection visit:
https://brainly.com/question/28969632
#SPJ1
Convert the following quantities to the indicated units. 34 liters=to how many quarts
Answers
Answer:
Step-by-step explanation: 34 quarts
1 Liter = approximately 1.06 quarts
so 34 x 1.06 is about 36.04 quarts
How much time will it take to earn $760.00 in interest if you deposit $3,200.00 into a simple interest account earning 4.5% annum Simple interest
Answers
Using the formula of simple interest, the time it will take to accumulate to $3200 at a rate of 4.5% is 71.35 years
What is Simple InterestSimple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.
The formula for simple interest is:
I = P * r * t
where:
I is the interest amount
P is the principal amount
r is the interest rate (expressed as a decimal)
t is the time period (in years)
Substituting the values into the formula;
A = P(1 + rt)
3200 = 760(1 + 0.045(t))
3200 = 760 + 34.2t
34.2t = 3200 - 760
34.2t = 2440
t = 2440 / 34.2
t = 72.35 years
Learn more on simple interest here;
https://brainly.com/question/20690803
#SPJ1
Find the dimensions for which the enclosed area is 1600 square feet. (View image)
Answers
Answer:
perimeter of rectangle = 2(length +breadth)
=2(20+80) m
=200 m
∴perimeter of rectangle is 200 m
Qué fracción restada a 1/2 da como resultado 4/10?
Answers
-1/10 should be subtracted from 1/2 to get 4/10.
How can you represent a fraction? Are fractions and ratios same?A fraction is of the form → (x/y).
For example, we can write fractions as → 2/3.
Fractions and ratios represent the same aspect. We can write -
2 : 3 = 2/3
4 : 7 = 4/7
Given is to solve the expression -
(1/2) - ? = 4/10
We can write the expression as -
(1/2) - (x) = (4/10)
(x) = 4/10 - 1/2
(x) = 4/10 - 5/10
(x) = -1/10
Therefore, -1/10 should be subtracted from 1/2 to get 4/10.
To solve more questions on subtracting fractions, visit the link below
https://brainly.com/question/30489902
#SPJ9
{Question in English -
What fraction subtracted from 1/2 equals 4/10?}
Is 8 a solution to 3/4x=6?
Answers
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
YES, x = 8
Step-by-step explanation:
plug in 8 for x and see if both sides are equal
3/4 times 8 = 24/4 or 6
Answer:
Yes, 8 a solution to 3/4 x=6 !Step-by-step explanation:
If we solve it as....
[tex]\mathrm{\cfrac{3}{4}x=6}[/tex]
[tex]\mathrm{4\times\cfrac{3}{4}x=6\times\:4}[/tex]
[tex]\mathrm{3x=24}[/tex]
[tex]\mathrm{\cfrac{3x}{3}=\cfrac{24}{3}}[/tex]
[tex]\mathrm{x=8}[/tex]
Yes, 8 would be the solution!
___________________
Hope this helps!
A Ferris wheel at a carnival has a diameter of 72 feet. Suppose a passenger is traveling at 100 revolutions per hour. (A) Find the angular speed of the wheel in radians per minute.(B) Find the linear speed of a passenger in miles per hour. (use the fact that 1 mile = 5280 feet)
Answers
(A) The angular speed of the wheel in radians per minute is 3.78 radians per minute.
(B) The linear speed of a passenger in miles per hour is 4.09 miles per hour.
Angular speed is the rate at which an object rotates, measured in radians per unit of time. The unit of radians is commonly used in circular motion problems because it allows us to express angles and rotational motion in a consistent way. Linear speed, on the other hand, is the rate at which an object moves in a straight line, measured in units of distance per unit of time.
(A) To find the angular speed of the Ferris wheel in radians per minute, we first need to convert the given rate of revolutions per hour to revolutions per minute. We can do this by dividing the rate by 60 since there are 60 minutes in an hour. Therefore, the wheel completes
=> 100/60 = 5/3 revolutions per minute.
Next, we need to find the angle that the wheel turns in one minute, which we can do by dividing a full rotation (360 degrees) by the number of revolutions per minute. In this case, the angle turned in one minute is
=> (360 degrees)/(5/3 revolutions per minute) = 216 degrees per minute.
To convert this angle to radians, we multiply by (π/180) since there are π/180 radians in one degree. This gives us an angular speed of
=> (216 * π/180) = 3.78 radians per minute.
(B) Using these values, we can calculate the linear speed of the passenger as follows:
Linear speed = (distance traveled)/(time taken) = (π * 72 feet)/(1/5 minutes) = (π * 72 * 5 feet/minute) = (360 * π feet/minute)
To convert this speed to miles per hour, we divide by the number of feet per mile (5280) and multiply by the number of minutes per hour (60), giving us:
Linear speed = (360 * π feet/minute)/(5280 feet/mile) * (60 minutes/hour) = 4.09 miles per hour (rounded to two decimal places).
Therefore, the linear speed of the passenger on the Ferris wheel is approximately 4.09 miles per hour.
To know more about linear here.
https://brainly.com/question/15830007
#SPJ4
