The value of distance between two points on graph is,
⇒ d = √32 units
We have to given that;
The coordinates of two points are,
⇒ (9, - 4) and (5, -8)
We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The value of distance between two points on graph is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √ (5 - 9)² + (- 8 - (-4))²
⇒ d = √ 16 + 16
⇒ d = √32
Thus, The value of distance between two points on graph is,
⇒ d = √32 units
Learn more about the coordinate visit:
https://brainly.com/question/24394007
#SPJ1
Please help me I need help
The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' is given as follows:
A rotation followed by a translation.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.For this problem, we have that the inclination of the figure changed, and the figure moved from the second quadrant to the first/fourth, hence the figure underwent a rotation of 90º counterclockwise about the origin.
The figure also had the vertices changed from the rotation, hence a translation was also applied.
More can be learned about transformations in a figure at https://brainly.com/question/28687396
#SPJ1
In a class of 50 students, they had a chance to read novel,comics and textbook 21 read novel,24 read comics and 18 read textbook 3 read only novel 9 read only comics and 2 read only textbook 5 read all the 3. illustrate your information on a venn diagram. use your diagram to find the number of students who read a. comics and novel only b. textbook and novel only c. none of the 3
a. 3 students read comics and novel only.
b. 1 student read textbook and novel only.
c. 31 students read none of the three categories.
Here's a Venn diagram that shows the information given:
_________
/ \
/ \
/ \
/ \
/ A \
/ \
/__________\
| | |
| | |
| C | B |
| | |
|__________|__________|
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
|
|
|
D
The three circles represent the three categories: novel, comics, and textbook.
The overlap between the circles represents the number of students who read more than one category.
The letters A, B, C, and D represent the following regions:
A: Only comics and novel (not textbook)
B: Only textbook and novel (not comics)
C: Only textbook and comics (not novel)
D: All three categories
To answer the questions:
a. To find the number of students who read comics and novel only (region A), we need to add up the number of students who read both comics and novel (5) and subtract from it the number of students who also read textbook (2).
So, the number of students who read comics and novel only is 5 - 2 = 3.
b. To find the number of students who read textbook and novel only (region B), we follow the same process.
We add up the number of students who read both textbook and novel (3) and subtract from it the number of students who also read comics (2).
So, the number of students who read textbook and novel only is 3 - 2 = 1.
c. To find the number of students who read none of the three categories, we start with the total number of students (50) and subtract from it the number of students who read at least one category.
To find the latter number, we add up the number of students who read only novel (3), only comics (9), only textbook (2), and all three (5), which gives us 19. So, the number of students who read none of the three categories is 50 - 19 = 31.
For similar question on Venn diagram.
https://brainly.com/question/24713052
#SPJ11
1. If 2x + 3y = 14 and 3x + 2y = 12, then x + y = ?
A) 5
B) 6
C) 7
D) 8
Answer:
x + y = 5.2-----------------
Given system:
2x + 3y = 14 and3x + 2y = 12Add up the two equations to get same coefficient on both variables:
2x + 3x + 3y + 2y = 14 + 125x + 5y = 265(x + y) = 26x + y = 26/5x + y = 5.2As we see none of the choices match the answer. It means either question or answer choices are inaccurate.
Nicole made 10 dozen cupcakes. She made 20% with chocolate icing, 30% with vanilla icing, and 50% with powdered sugar. How many of each kind of cupcake did she make?
Answer:
2 Dozen Chocolate, 3 Dozen Vanilla, 5 Dozen Sugar.
Explanation:
0.5 x 10 = 5.
0.3 x 10 = 3.
0.2 x 10 = 2.
solve for x x/3=? please help me image attached
The value of x is 5.48 units
Let us assume that the left right triangle be ABC and the right triangle on the right side be ABD.
So, the larger right triangle would be DAC.
Consider thr outer right triangle DAC.
The length of the hypotenuse DC would be,
DC = CB + BD
DC = 3 + 7
DC = 10 units
Also right triangle ABC and DAC are similar triangles.
We know that the sides of the smilar triangles are in proportion.
Using the definition of similar triangles for DAC and ABC,
DA/AB = AC/BC = DC/AC
Consider, AC/BC = DC/AC
x/3 = 10/x
this is the required proportion.
x² = 3 × 10
x² = 30
x = 5.48 units
Thus the value of x = 5.48 units
Learn more about the proportion here:
https://brainly.com/question/26974513
#SPJ1
26. Tyler has been saving his winning lottery tickets. He has 23 tickets that are worth a total of $175. If each ticket is worth either $5 or $10, how many of each does he have?
Which fraction has the same value as 0.28
Answer:
7/25
Step-by-step explanation:
0.28 = 28/100 = 7/25
Verify that the given segments are parallel.
The verification of given segments in a triangle are parallel is as follow,
In triangle ABE, AC/ CE = BD/DE are in proportion ⇒ CD || AB.
In triangle RVS, VT/TR = VU/US are in proportion ⇒ UT || SR.
In the triangle ABE,
CD is the line segment divides AE and BE into equal parts.
AC = 1.5
CE = 1.5
BD = 1.5
DE = 1.5
AC/ CE = BD/DE
Line divides the two adjacent sides of a triangle are in proportion.
This implies ,
CD is parallel to AB.
In triangle RVS,
VT /TR = 90 /72
⇒VT /TR = 1.25
VU/US = 67.5/54
⇒VU/US = 1.25
This implies ,
VT/TR = VU/US are in proportion.
Hence , triangle proportionality theorem UT is parallel to RS.
Therefore, using triangle proportionality theorem in both the triangle that is,,
In triangle ABE , CD is parallel to AB and in triangle RVS , UT || RS.
learn more about parallel here
brainly.com/question/31529536
#SPJ1
Find the rank of the matrix [
2 − 1 − 3 − 1
1 2 3 − 1
1 0 1 1
0 1 1 − 1
]
The rank of the matrix is 3, since there are three linearly independent rows.
The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It is denoted by the symbol "rank(A)" for a matrix A.
To find the rank of the matrix:
[-2, -1, -3, -1] [ 1, 2, -3, -1] [ 1, 0, 1, 1] [ 0, 1, 1, -1]
We can perform row operations to reduce the matrix to row echelon form, which will help us determine the rank.
[tex]R_2 = R_2 + 2R_1 R_3 = R_3 + 2R_1 R_4 = R_4 + R_2[/tex]
This gives us the following matrix:
[-2, -1, -3, -1] [ 0, 0, -9, -3] [ 0, -1, -1, 1] [ 0, 0, -4, -4]
We can see that the third row is not a linear combination of the first two rows, and the fourth row is not a linear combination of the first three rows. Therefore, the rank of the matrix is 3, since there are three linearly independent rows.
Learn more about Rank of matrix at:
https://brainly.com/question/29857274
#SPJ1
Help please! Show all your work.
Answer:
If y and x have a proportional relationship, then we can write an equation of the form y = kx, where k is a constant of proportionality.
To find the value of k, we can use the given values of y and x:
y = kx
24 = k(12)
k = 2
Now that we know k, we can use the equation to find the value of y when x=16:
y = kx
y = 2(16)
y = 32
Therefore, when x=16, y=32.
Help me… it’s so hard!
The solution of the each given equations:
(1) x = 9
(2) x = -2
(3) x = -2
(4) x = 26
(5) x = 3/5
(6) x = 13/12
(7) x = 15
(8) x = 26
(9) x = 7/3
(10) x = 5/8
We have to solve this given equation in on variable.
(1) Given equation is,
x - 7 = 2
x = 2 + 7 = 9
Hence, the solution is, x = 9
(2) Given equation is,
3x + 4 = -2
3x = -2 -4
3x = -6
x = -6/3 = -2
Hence, the solution is, x = -2
(3) Given equation is,
2x + 7 = x + 5
2x - x = 5 - 7
x = -2
Hence, the solution is, x = -2
(4) Given equation is,
x/2 = 13
x = 2*13 = 26
Hence, the solution is, x = 26
(5) Given equation is,
5(2 + x) = 13
10 + 5x = 13
5x = 13 - 10
5x = 3
x = 3/5
Hence, the solution is, x = 3/5
(6) Given equation is,
6(2x - 1) = 7
12x - 6 = 7
12x = 7 + 6 = 13
x = 13/12
Hence, the solution is, x = 13/12
(7) Given equation is,
2x/5 = 6
2x = 6*5 = 30
x = 30/2 = 15
Hence, the solution is, x = 15
(8) Given equation is,
x/2 = 13
x = 2*13 = 26
Hence, the solution is, x = 26
(9) Given equation is,
(x - 1)3 = 4
3x - 3 = 4
3x = 4 + 3 = 7
x = 7/3
Hence, the solution is, x = 7/3
(10) Given equation is,
(2x - 1)4 = 1
8x - 4 = 1
8x = 1 + 4
8x = 5
x = 5/8
Hence, the solution is, x = 5/8
To know more about equations here
https://brainly.com/question/22688504
#SPJ1
10. i’d the area of a circle is 201.06 cm^2, find its diameter and circumference.
11. if m < MPL =63 degrees, find each measure
The diameter of the circle is 16.04 cm.
The circumference is 50.39 cm
How to solve for the diameterA = πr²
where A is the area of the circle and r is its radius.
square both sides
r = √(A/π) = √(201.06/π) = 8.02 cm
The diameter of the circle is twice the radius, so we can find it by multiplying the radius by 2:
d = 2r = 2(8.02) = 16.04 cm
Therefore, the diameter of the circle is 16.04 cm.
To find the circumference of the circle, we can use the formula:
C = 2πr
where C is the circumference and r is the radius. We already know the value of the radius, so we can substitute it into the formula:
C = 2π(8.02) = 50.39 cm
Therefore, the circumference of the circle is 50.39 cm.
Read more on diameter herehttps://brainly.com/question/23220731
#SPJ1
a cylinder has a radius of 6 cm and height 7 cm. Calculate the volume of the cylinder. (pie=22/7) and (v=pie^r 2 h)
Answer: The volume of the cylinder is 924 cubic centimeters.
Step-by-step explanation:
The formula to calculate the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.
Given, radius (r) = 6 cm and height (h) = 7 cm.
Using the formula, we have V = (22/7) x 6^2 x 7 = 924 cubic centimeters.
Therefore, the volume of the cylinder is 924 cubic centimeters.
pls helppp this is so confusinggg
Answer: .025
Step-by-step explanation: we first have to find the distance between each term we divide 12/5 by 6 you have to change it into multiplication so you invert is to 12/5 times 1/6 you then get 12/30 you reduce that to become 2/5 if you want to test this to make sure it is right then you can. you then use a formula but I can't remember it so then you can just multiply it several times to find the answer. you get the answer by round from the thousandths
Can anyone help me answer this question?
Find G(x) = sin^2(x) + 3cos(x), when x=
[tex]g(x)=\sin^2(x)+3\cos(x) \\\\[-0.35em] ~\dotfill\\\\ g(\pi )=\sin^2(\pi )+3\cos(\pi )\implies g(\pi )=[\sin(\pi )]^2+3\cos(\pi ) \\\\\\ g(\pi )=(0)^2+3(-1)\implies g(\pi )=-3[/tex]
Given that cos(x) =
A.
B.
2/3 113
D.
C. 1
13
2/3
3'
Mark this and return
find sin (90-x).
Please select the best answer from the choices provided
Save and Exit
Next
Su
Answer:
C
Step-by-step explanation:
cos x and sin(90 - x) are cofunctions and are equal , then
cos x = [tex]\frac{1}{3}[/tex] , then sin(90 - x) = [tex]\frac{1}{3}[/tex]
The United States has minted one-dollar silver coins called the American Eagle Silver Bullion Coin since 1986 . Each coin has a diameter of 40.6 millimeters and is 2.98 millimeters thick. The density of silver is 10.5 grams per cubic centimeter. Find the mass of an American Eagle Silver Bullion Coin to the nearest gram.
The mass of an American Eagle Silver Bullion Coin is about ( )
grams.
Answer:
41 grams
Step-by-step explanation:
trust i jus took it
The mass of an American Eagle Silver Bullion Coin is about 41 grams.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Each coin has a diameter of 40.6 millimeters and is 2.98 millimeters thick. The density of silver is 10.5 grams per cubic centimeter.
Hence, Volume is,
V = 3.14 x (40.6/2)² x 2.98
V = 3857.96 mm³
Since, 1000 mm³ = 1 cm³
Hence, The mass of an American Eagle Silver Bullion Coin is,
⇒ 33857.9 / 1000 x 10.5
⇒ 41 grams
Thus, The mass of an American Eagle Silver Bullion Coin is, 41 grams
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ2
solve the diagram for x
Answer:
Step-by-step explanation:
b. the length of the adjacent side :11
c. you want to know the x which is hypotenuse
d. SOH CAH TOA, you know a and wants to know h, so should use cos function
simplify the expression 4√ 2 + 2√ 32? 12/2 6/32 12/32 36/2
The solution is, simplification of the expression 4√ 2 + 2√ 32 is 12√2 .
We know that,
An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Here, given expression is,
4√ 2 + 2√ 32
=4√ 2 + 2√ 16 × 2
we know that,
√16 = 4
so, we get,
=4√ 2 + 2√2 × 4
=4√ 2 + 8√2
=12√2
Hence, The solution is, simplification of the expression 4√ 2 + 2√ 32 is 12√2 .
To learn more on Expression click:
brainly.com/question/14083225
#SPJ1
A train running between two stations 50 Km apart arrives on time if it travels at an
average speed of 60 km/h. How late will it be if travels at an average speed of 50 Km/h?
If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.
How late will the train be if it travels at an average speed of 50 Km/h?Speed is simply referred to as distance traveled per unit time.
It is expressed as:
Speed = distance / time
Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.
The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:
Speed = distance / time
time = distance / speed
time = 50 km / 60 km/h
time = 5/6 hour
Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:
Speed = distance / time
time = distance / speed
time = 50 km / 50 km/h
time = 1 hour
Now, the difference in time between the two scenarios would be:
time difference = 1 hour - 5/6 hour
time = 1/6 hour
Convert to minutes
time = 1/6 × 60
time = 10 minutes
Therefore, the train would be late by 10 minutes.
Learn more about speed here: https://brainly.com/question/27571996
#SPJ1
Martin, wyatt , and adeyla were having a contest to see who could throw a softball the farthest. Martin threw the ball 9 feet. Wyatt threw the ball three times as far as Martin. Adeyla threw the softball 3 feet farther than Wyatt. How far did Adeyla throw the softball?
Answer: 30 Feet
Step-by-step explanation: Martin threw the ball 9 feet so we have Martins distance, next we know that Wyatt throws the ball 3 times as far which is 9x3 which is 27, Adeyla threw it 3 feet farther then Wyatt who threw it 27. 27+3=30
So the answer is 30 feet
Gable Supplies Ltd will commence trading in July 2018 with Share Capital of £55,000. The company will spend £80,000 on equipment.
They have arranged a loan of £110,000 repayable over five years. Repayments of capital and interest are £2,450 each month. The loan interest for the first three months included in the repayments is £2,367.
Sales are expected to be as follows:
July £120,000
August £130,000
September £150,000
40% of sales are for cash, and attract a discount of 5%.
The remainder of sales is on credit terms and collected 1 month later.
Opening inventory of £50,000 is paid for in July, further inventory is purchased at 45% of sales each month. Suppliers are paid one month in arrears.
Closing inventory should be £60,000.
Wages are forecasted to be £12,000 per month, payable in the month they are incurred. Overheads excluding depreciation are forecast to be £15,000 per month and paid in the month they are incurred.
Rent is £36,000 per year payable annually in advance.
Equipment will be depreciated at 10% of cost per year.
Required:
a) Forecast Monthly Cash Flow Statement for the 3 months to 30th September 2018.
(15 marks)
b) Forecast Income Statement for the period ending 30th September 2018.
(7 marks)
c) Forecast Statement of Financial Position as at the 30th September 2018.
(8 marks)
It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.
How to solveMonthly Cash Flow Statement for Gable Supplies Ltd for the three months ending on 30th September 2018:
Month: July August September
Opening Cash: £0 £3,550 £16,700
Cash Inflows:
Share Capital: £55,000
Loan: £110,000
Cash Sales: £45,600 £49,400 £57,000
Credit Sales: £0 £72,000 £78,000
Total Inflows: £160,600 £125,950 £135,000
Cash Outflows:
Loan Repayment: -£2,450 -£2,450 -£2,450
Equipment: -£80,000
Inventory: -£50,000 -£54,000 -£67,500
Wages: -£12,000 -£12,000 -£12,000
Overheads: -£15,000 -£15,000 -£15,000
Rent: -£36,000
Total Outflows: -£157,050 -£109,250 -£118,450
Closing Cash: £3,550 £16,700 £33,250
It is assumed that the purchase of equipment and loan receipt occur in July. Although cash sales are evaluated with a 5% reduction, they make up 40% of totality.
Additionally, credit sales to be accrued in the subsequent month from when the product was sold.
Inventory acquisition constitutes approximately 45% of revenue each month, whereas payments to suppliers get delayed by one month.
Rent, on the other hand, needs to be paid annually but paid beforehand instead of scheduled billing periods.
To note, the non-cash category of expenditures does not encompass depreciation according to the cash flow statement rules.
Read more about cash flow here:
https://brainly.com/question/735261
#SPJ1
Huang buys 3 shirts that each cost the same amount, a pair of pants that cost $12, and he pays with a $100 bill. Which expression represents the amount of change Huang should receive? Select three options.
100 – (12(3x))
100 – (3x+12)
(100 – 12) – 3x
(100 – 12)(x+x+x)
100 – (x+x+x) – 12
Mark this and return
An expression that represents the amount of Huang's change include the following: A. 100 – (12(3x)).
How to write and determine an expression that represents the amount of Huang's change?In this scenario and exercise, you are required to write and determine an expression that represents the amount of change which Huang should receive from the seller.
This ultimately implies that, an expression that models or represents the amount of Huang's change would have the form;
Huang's change = Money presented - Total cost of 3 shirts
Huang's change = 100 - (12(3x))
By simplifying further, we have the following expressions;
Huang's change = 100 - 36x
Read more on expression here: https://brainly.com/question/16729936
#SPJ1
Triangle Angles
Yes or No
The sum of 150, 20 , and 20 is more than 180 degrees, therefore, it is not possible to draw a triangle.
How to Determine if a Set of Angles will Form a Triangle?A triangle is simply a three sided polygon that has three sides and three interior angles. When all three interior angles are added together, the sum is equal to 180 degrees according to the triangle sum theorem.
If we have a set of angles with the measure of 150, 20, and 20 degrees, respectively, the sum of these is more than 180 degrees.
150 + 20 + 20 = 190 degrees.
Therefore, it is not possible to draw a triangle with those set of angles.
Learn more about the equation of a line on:
https://brainly.com/question/24907633
#SPJ1
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
3,6,12,...
Find the 9th term.
Answer:
We can see that the sequence is formed by multiplying each term by 2 to obtain the next term. Therefore, the fourth term is 12 x 2 = 24, the fifth term is 24 x 2 = 48, and so on.
To find the ninth term, we can multiply the third term by 2 six times:
3 x 2^6 = 3 x 64 = 192
Therefore, the ninth term of the sequence is 192.
Jenny has recently begun keeping her spending under better control, but she
still can't fully pay off her credit card. She maintains an average monthly
balance of about $1100, and her card charges a 24% annual interest rate,
which it bills at a rate of 2% per month.
How much is she spending on credit card interest per year?
Jenny is paying $334.82 per year on credit card interest.
How much is she spending on credit card interest?We need to find his annual interest payment which is:
= $1100 * 2% * 12 month
= $264
So, we have an annual interest payment of $264
We must account for interest that accumulates on the interest itself. To calculate this, we can use the formula: A = P (1 + r/n)^(nt) when P is $264, r is 24%, n is 12 and t is 1.
A = $264 * (1 + 0.24/12)^(12*1)
A = $264 * 1.26824179456
A = $334.815833764
A = $334.82.
Read more about annual interest
brainly.com/question/25793394
#SPJ1
7
Select the correct answer from the drop-down menu.
Which term best fits the sentence?
After you make a decision, the next step in the decision-making process is to
whether you made the right choice.
Reset
Next
This step will help you det
Answer:
Step-by-step explanation: bot
A pharmaceutical company develops a new generation of blood pressure medication that may also help with cholesterol. The research and development department advertises in the local papers and online seeking volunteers who already take blood pressure medication to participate in a study for the new medication. Two hundred people volunteer, and their current blood pressure along with their cholesterol levels are measured. They are randomly assigned to two groups, one that takes the new generation of blood pressure medication and one that takes the original medication. At the end of the study, the subjects’ blood pressure and cholesterol levels are measured. The group with the new medication is found to have a significantly lower overall blood pressure than the original medication group. It was also determined that the new medication did not significantly lower cholesterol levels. Which of the following is a valid conclusion? Inferences can be made about all blood pressure patients, and the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication. Inferences can be made about all blood pressure patients, but the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication. Inferences cannot be made about all blood pressure patients, and the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication. Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
The valid inference based on the information provided is:
Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.
What's the information about?The study involved only 200 volunteers who were already taking blood pressure medication. This is a relatively small sample size and may not be representative of all blood pressure patients. Inferences about all blood pressure patients cannot be made from this limited sample.
While the group taking the new medication showed a significantly lower overall blood pressure than the group taking the original medication, it was also mentioned that the new medication did not significantly lower cholesterol levels.
Learn more about inference
https://brainly.com/question/25913650
#SPJ1
From the pharmaceutical company's test, we can conclude that the new medication is more effective than the original in lowering blood pressure for patients already taking blood pressure medication. However, this conclusion doesn't apply to all blood pressure patients.
Explanation:A valid conclusion from the scenario about the pharmaceutical company's testing of its new medication would be the following: Inferences cannot be made about all blood pressure patients, though the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients who are already taking blood pressure medication. The study has a specific sample population: people who are already taking blood pressure medication. We can't extrapolate this to all blood pressure patients, because the study didn't include those who don't take any medication. However, it was observed that the new medication was more effective in lowering blood pressure than the original one within this specific group.
Learn more about Clinical Trial Conclusion here:https://brainly.com/question/31718152
#SPJ1
A tire is 22 inches in diameter and rests on a platform that is 4 inches above the ground. The six o’clock position on the tire is level with the platform. A piece of gum stuck to the three o’clock position of the tire completed 1 full revolution in 12 seconds. The function h(t) gives the height of the piece of gum in inches above the ground t seconds after the tire begins to turn. Find a formula for the height function h(t)
Answer:
h(t) = 11 * sin(π/6 * t) + 15
Step-by-step explanation:
To find the height function h(t) for the piece of gum, we'll use a sinusoidal function since the height of the gum changes in a periodic manner as the tire rotates. The general formula for a sinusoidal function is:
h(t) = A * sin(B * (t - C)) + D
where A is the amplitude, B is the angular frequency, C is the horizontal shift, and D is the vertical shift.
1. Amplitude (A): The amplitude is half the distance between the highest and lowest points of the gum. Since the diameter of the tire is 22 inches, the radius is 11 inches. Thus, the amplitude is 11 inches.
2. Angular frequency (B): Since the gum completes 1 full revolution in 12 seconds, the period of the function is 12 seconds. The angular frequency, B, is found by dividing 2π by the period: B = 2π / 12 = π/6.
3. Horizontal shift (C): Since the gum starts at the three o'clock position, and we want the height to be at its maximum at t = 0, there is no horizontal shift. So, C = 0.
4. Vertical shift (D): The platform is 4 inches above the ground, and the radius of the tire is 11 inches. Therefore, the midpoint of the gum's motion is 4 + 11 = 15 inches above the ground. So, D = 15.
Now we can write the height function h(t):
h(t) = 11 * sin(π/6 * t) + 15
CAN SOMEONE HELP WITH THIS QUESTION?
The displacement of the particle at time t is 11t - t², and the total distance traveled by the particle in 2 seconds is 9 meters.
The displacement of a particle moving along a straight line can be calculated by finding the area under the velocity-time graph. In this case, the velocity function is v(t) = 11 - 2t for 0 ≤ t ≤ 2.
To find the displacement at time t, we need to find the area under the velocity-time from t = 0 to t = t. The formula for displacement is the integral of the velocity function with respect to time:
s(t) = ∫v(t) dt = ∫(11 - 2t) dt = 11t - t²
Therefore, the displacement of the particle at time t is given by s(t) = 11t - t².
To find the total distance traveled by the particle in 2 seconds, we need to consider both the forward and backward motion. Since the velocity is decreasing at a constant rate of 2 m/s², the particle will come to rest at t = 11/2 seconds.
The total distance traveled by the particle in 2 seconds is given by:
d(2) = ∫|v(t)| dt = [tex]\int\limits^{11/2}_0[/tex] v(t) dt + [tex]\int\limits^2_{11/2}[/tex]|v(t)| dt from 11/2 to 2
= [[tex]\int\limits^{11/2}_0[/tex](11t - t²) ] + [[tex]\int\limits^2_{11/2}[/tex](-11t + t²) ]
= (121/2 - 121/4) + (4 - 121/2) = 9 meters
To learn more about velocity click on,
https://brainly.com/question/14488317
#SPJ1