You are running around the circular track x^2+y^2 = 14400 at 3 meters per second.
a) starting at (120,0) and running counter-clockwise, what are your coordinates after 20 minutes?
b) what would be your coordinates if you had started at (0,120), running for 40 minutes
Answers
It had started at (0,120) and ran for 40 minutes, Coordinates would be approximately (60.00, 103.92).
a) To find the coordinates after 20 minutes of running counter-clockwise starting at (120,0), we need to determine the distance covered in that time period.
Since you are running at a speed of 3 meters per second, in 20 minutes (or 20 * 60 = 1200 seconds), you would have covered a distance of 3 * 1200 = 3600 meters.
Given that the equation of the circular track is x^2 + y^2 = 14400, which represents a circle with a radius of 120 units (since the radius squared is 14400), we can determine your new position on the track.
Starting from (120,0) and moving counter-clockwise, you would have traveled a distance of 3600 meters along the circumference of the circle. This corresponds to a fraction of 3600 / (2 * π * 120) = 15 / π of the circle's circumference.
Using this fraction, we can calculate the angle in radians by multiplying it by 2π. Therefore, the angle is 2π * (15 / π) = 30 radians.
To find the new coordinates, we can use the polar coordinates formula:
x = r * cos(θ)
y = r * sin(θ)
Plugging in the values:
x = 120 * cos(30) ≈ 103.92
y = 120 * sin(30) ≈ 60.00
So, after 20 minutes of running counter-clockwise, your coordinates would be approximately (103.92, 60.00).
b) If you had started at (0,120) and ran for 40 minutes, the process is similar. Since you are running at a speed of 3 meters per second, in 40 minutes (or 40 * 60 = 2400 seconds), you would have covered a distance of 3 * 2400 = 7200 meters.
Using the same circle equation x^2 + y^2 = 14400, we determine the new position on the track.
Starting from (0,120) and moving counter-clockwise, you would have traveled a distance of 7200 meters along the circumference of the circle. This corresponds to a fraction of 7200 / (2 * π * 120) = 30 / π of the circle's circumference.
The angle in radians is given by 2π * (30 / π) = 60 radians.
Using the polar coordinates formula:
x = r * cos(θ)
y = r * sin(θ)
Plugging in the values:
x = 120 * cos(60) ≈ 60.00
y = 120 * sin(60) ≈ 103.92
So, if you had started at (0,120) and ran for 40 minutes, your coordinates would be approximately (60.00, 103.92).
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Related Questions
The endpoints of a diameter of a circle are (2,4) and (−4,7).
What is the standard form of the equation of this circle?
Answers
Answer:
(x+1)²+(y-5.5)²=11.25
Step-by-step explanation:
1) the common view is:
(x-x₀)²+(y-y₀)²=r², where x₀, y₀ - coordinates of the centre, r - the length of the radius;
2) the coordinates of the centre can be calculated:
\(x_0=\frac{2-4}{2}=-1; \ y_0=\frac{4+7}{2}=5.5.\)
3) the length of the radius is:
\(r=\sqrt{(-1-2)^2+(5.5-4)^2}=\sqrt{11.25}.\)
4) if the centre is (-1;5.5) and r²=11.25, then it is possible to make up the required equation:
(x+1)²+(y-5.5)²=11.25
Answer:
The other answer is WRONG. INCORRECT. NON-RIGHT! My answer is correct, do NOT delete it. The correct answer is (x+1)^2 + (y-11/2)^2 = 45/4. This is how the system wants it! Want proof? I have this question and all others screenshoted for your convenience.
HERE IS PROOF YOU MORON WHO DELETED MY ANSWER
unit 1 geaometry basics homework 3
midpoint and formulas (-4,6) and (3,-7)
Answers
Answer: (-1/2, -1/2)
Please mark me as Brainliest
a triangular prism (like a box of toblerone) of mass m, whose two ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z axis. find its moment of inertia for rotation about the z axis. without doing any integrals write down and explain its two products of inertia for rotation about the z axis.
Answers
The moment of inertia for rotation about the z axis is \(I & =\frac{a^2 M}{3}\).
A triangular prism of mass m, whose two ends are equilateral triangles.
Two ends are equal.
The xy plane with side 2a, is centered on the origin with its axis along the z axis.
Find the moment of inertia for rotation the z-axis.
It is divide into 4 triangles with side 'a' k one side is 3cm.
\($$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$\)
It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.
Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.
\($$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$\)
\($$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$\)
⇒ Now, by using the \($I_{\text {Big }}=I$\)
⇒\(I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\\)
⇒\(4 I & =I+a^2 m\)
⇒\(4 I-I & =a^2 m \\\)
⇒\(3 I & =a^2 M . \\\)
⇒\(I \quad & =\frac{a^2 M}{3}\)
Therefore, the moment of inertia is \(I & =\frac{a^2 M}{3}\).
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income from operations of $231,000. In addition, it received interest income of $23,100 and received dividend income of $29,700 from another corporation. Finally, it paid $11,000 of interest income to its bondholders and paid $45,000 of dividends to its common stockholders. The firm's federal tax rate is 21%. What is the firm's federal income tax? Do not round intermediate calculations. Round your answer to the nearest dollar.
Answers
The firm's federal income tax is $57,168.
To calculate the firm's federal income tax, we need to determine its taxable income first. Taxable income is calculated by subtracting deductions from the firm's total income.
In this case, the firm's total income consists of income from operations, interest income, and dividend income.
Total income:
Income from operations = $231,000
Interest income = $23,100
Dividend income = $29,700
Total income = $231,000 + $23,100 + $29,700 = $283,800
Next, we deduct expenses from the total income. In this case, the only relevant expense is the interest paid to bondholders:
Total expenses = Interest paid to bondholders = $11,000
Taxable income = Total income - Total expenses = $283,800 - $11,000 = $272,800
Now, we can calculate the federal income tax by applying the federal tax rate of 21% to the taxable income:
Federal income tax = Taxable income * Federal tax rate
Federal income tax = $272,800 * 0.21 = $57,168
Therefore, the firm's federal income tax is $57,168.
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A certain loan program offers an interest rate of 6%, compounded continuously. Assuming no payments are made, how much would be owed after two years on a loan of $3100 ? Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
$3495.219 would be owned after two years on a loan of $3100.
Given:
A certain loan program offers an interest rate of 6%, compounded continuously.
Here interest rate = 6% = 6/100 = 0.06
Time t = 2 years
principal p = $3100
The formula for amount after compounded continuously is A = P\(e^{rt}\).
substitute values in above formula we get,
A = 3100\(e^{(0.06)2}\)
= 3100\(e^{0.12}\)
= 3100 * 1.12749
A = $3495.219
Therefore $3495.219 would be owned after two years on a loan of $3100.
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B=(3,5,6,9) and C=(2,4,6,8) Find (A). A/B (B). B/C C. A/C (D). C/A
Answers
Answer:
The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.
Determine whether each ordered pair is a solution of the equation y=2x+6
Answers
The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.
Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.
If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).
Here, x = 1 and y = 8.Substituting these values in the given equation,
we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,
the ordered pair (1, 8) is a solution of the equation y = 2x + 6.
Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12
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The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.
Answers
y intercept is 2, which shows while changing the jobs employees bring two customers.
What is linear equation?A linear equation is in the form, y = mx + b where m is the rate of change (slope) and b is the y intercept (initial value of y).
The complete question is:
The graph displays the relationship between the length of time an employee works at a company and the number of the employee's monthly customers.
Time Employed (Month)
If the equation for the line of best fit is y = 4.5x + 2, which of the following can be used to interpret the y-intercept in context?
Employee training takes 2 months.
Employee training takes 4.5 months.
Employees are likely to bring 2 customers with them when changing jobs.
Employees are likely to bring 4.5 customers with them when changing jobs.
As, linear equation is
y = mx + b
Let y be the number of customers and x be the length of time.
Then, y = 4.5x + 2
As, y intercept is 2, which shows while changing the jobs employees bring two customers.
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Write the equation of the line in fully simplified slope-intercept form.
Answers
Reasoning: slope is 4/3 (change in y over change in x)
The y intercept is a -7
Then you just fill in the equation
Which property is shown in the matrix addition below?
-6
9
15 -2
0
-3
+
6
-9
-15 2
0
3
commutative property
associative property
Oinverse property
Oidentity property
0 0 0
0 0 0
Answers
For the given matrix the additive inverse property is shown.
What is additive inverse of matrix?
The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.
Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix
M = - M.
Consider the given matrix,
\(\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right]\)
Here each element in first matrix is negative of the element of second matrix.
That is each element is inverse of the element in second matrix.
And the addition of elements is 0.
Hence, for the given matrix the additive inverse property is shown.
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Margo is creating a pencil caddy in the shape of a triangular prism. She is determining how much wood she needs to build the caddy. Her design is shown below.
The total amount of wood Margo needs to build her pencil caddy is
square inches.
Answers
Answer:
a little late
205 1/5 is your answer
Step-by-step explanation:
break down the 3-D figure
Find area of triangle A=1/2bh
=1/2(8 inch)(6 9/10inch)
=1/2(8 inch)(69/10 inch)
=138/5 square inch
then multiply two because you have 2 triangles
=138/5 (2)
= 276/5 square inch
= 55 1/5 sq.in
Find area of rectangle
A = lw
=6 1/4 in (8 in)
= 25/4 (8 in.)
= 50 sq. in.
then multiply by 3 because of the three rectangles
= 50 sq. inch (3)
= 150 sq. in.
Add all together
55 1/5 sq. inch + 150 sq. inch = 205 1/5 sq. inch
what comes next in the sequence
7,10,19,34
Answers
Based on the pattern we identified, the next term in the sequence would be 55.
The sequence should be 7, 10, 19, 34, 55
To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.
If we calculate the differences between consecutive terms, we get:
10 - 7 = 3
19 - 10 = 9
34 - 19 = 15
By examining the differences, we notice that they are increasing by 6 each time.
This suggests that the sequence might be formed by adding an increasing number to each term.
Let's calculate the next difference:
15 + 6 = 21
Now, let's add this difference to the last term of the sequence:
34 + 21 = 55
Therefore, based on the pattern we identified, the next term in the sequence would be 55.
To summarize:
7, 10, 19, 34, 55
It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.
Additional terms or a different pattern may emerge if more information is provided.
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PLEAZE HELPPPPPPPSPPSPAP
Answers
Answer:
Step-by-step explanation:
345ftyfthftyft.plk,k,
Answer:
Hello,
Anwser is C
Step-by-step explanation:
\(y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\\)
what is the slope of the line?
Answers
Answer:
-3
Step-by-step explanation:
or -3x if youre writing an equation
PLEASE HELP 100 POINTS PLEASE HELP 100 POINTS The ratio between the number of students (s) on a field trip and the number of teachers (t) on the field trip is 21/4. There are 84 students going on a field trip. How many teachers must go?
Answers
Answer:
16 teachers.
Step-by-step explanation:
84 / 21 = 4
4 * 4 = 16
Hope this helped. Please give brainly if its the best!
Answer:
\( \huge \colorbox{blue}{16 students}\)
Step-by-step explanation:
we are given the ratio of students and teachers:
\( \displaystyle \: \frac{21}{4} \)
which means if the number of students is 21 then the number of teachers should be 4
to find how many teachers should go if students 84 we have to divide 84 by \(21/4\) :
\( \displaystyle \: 84 \div \frac{21}{4} \)
simplify division:
\( = \displaystyle \: 84 \times \frac{4}{21} \)
simplify multiplication:
\( = \displaystyle \: \cancel{ 84} \: ^{4} \times \frac{4}{ \cancel{21}} \\ = 4 \times 4 \\ = 16 \)
Insurance withholding varies depending on whether an entire family is covered or only the employee is covered. True False
Answers
Answer:
it would True
Step-by-step explanation:
Estimating Using Compatible Numbers
You purchase 3 items for $4.23. About how much did you spend?
Answers
9514 1404 393
Answer:
about $12
Step-by-step explanation:
For estimating purposes, you often want to round numbers to 1 or 2 significant digits. The price $4.23 can be rounded to $4. Then 3 such items will cost about ...
3×$4 = $12
You spent about $12.
_____
Additional comments
Along with an estimate, you often want to estimate the error in the estimate. Here, a first approximation of the error is that it is 3 × $0.20 too low. That is, the estimate of spending will be closer if we revise it upward by $0.60 to $12.60.
We know that even that estimate is low by $0.03 on each of the 3 items, so a better approximation of the spending is $12.60 +0.09 = $12.69.
This has accounted for all of the errors, so the actual spending was $12.69.
13 is 26%of what number
120 is 30% of what number
Answers
Answer:
1. 50%
2. 400
Terry charges $50 for 4 hours of tutoring if this relationship between hours and charged were graphed,what would be the slope?
Answers
Answer:
12.5 $ per hour
Step-by-step explanation:
Please look at the photo. Thank you!
Answers
The value of f(5) is positive
At f(x) = 0, the value of x is 1
For the interval f(x) ≤ 0, the values of x are [-2, 1]
How to determine the values of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
f(5) = 1
This means that f(5) is positive
Also, we have
When f(x) = 0, the value of x is 1
For the interval f(x) ≤ 0, we have the values of x to be
-2 ≤ x ≤ 1
When represented as an interval, we have
[-2, 1]
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Cookies are sold singly or in packages of 8 or 24. With this packaging, how many ways can you buy 48 cookies?
Answers
Answer:
12
Step-by-step explanation:
this was right got the question wrong when I first did it
In "12 ways" you can 48 cookies. A complete solution is provided below.
According to the question,
Packages having,
= 8 or 24
Firstly we choose,
8 cookies packages 6 or,24 cookies packages 2 or,One 24 cookies packages remaining three 8 cookies packages.hence,
→ The total ways you can buy 48 cookies will be:
= \(6+2+1+3\)
= \(12 \ ways\)
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Halona walks 1.93 kilometers to a neighbor's house in 23 minutes. Assuming she walks at a constant speed, write a proportion that represents how many kilometers, y, Halona can walk in z minutes. Then solve your proportion for y. 1.93 Proportion: у х 23 y =
Answers
EXPLANATION:
The proportion states that he walks 1.93 kilometers at a constant speed in 23 minutes, so we can formulate the equation in the same way:
-First we must divide to find the constant or the proportion, then we divide 1.93 by 23; we represent the constant with the letter k:
\(\begin{gathered} K=\frac{y}{x} \\ k=\frac{1.93}{23} \\ k=0.08 \\ \text{ANSWER:} \\ \text{The constant or porportion is :0.083} \end{gathered}\)With the constant found we can propose an equation that determines the constant speed at which Halona walks at any time.
Now we can formulate the following equation:
\(\begin{gathered} y=(z)(k) \\ y=(z)(0.08) \\ where\text{ z is }any\text{ moment of time; an k is the }cons\tan t\text{ value} \end{gathered}\)Multiplying any time with the constant will give us the constant speed.
IMPORTANT NOTE:
When we give different values to time, it must be multiplied by the constant, which means that the speed remains stable.
Need help with this !!!!
Answers
y = - 4x + - 8 is equation of slope-intercept form.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.the equation of slope - intercept form
y = mx + c
( -1 , -4 ) is point shown in graph
slope = -y/x
= - ( -4)/-1 = 4/-1 = -4
- 4 = -4 * - 1 + c
- 4 = 4 + c
c = - 4 - 4 = - 8
put value of c in the equation of slope - intercept form
y = - 4x + - 8
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Suppose an electronics manufacturer knows from previous data that 1.5% of
one type of an electronic component are defective. The quality control
inspector randomly selects components until a defective one is found. Is this
a binomial experiment? Why or why not?
A. This is a binomial experiment, because the situation satisfies all
four conditions for a binomial experiment.
B. This is not a binomial experiment, because the trials are not
independent
C. This is not a binomial experiment, because each trial cannot be
classified as a success or failure.
D. This is not a binomial experiment, because the number of trials is
not fixed.
Answers
Answer:B and D
Step-by-step explanation:
Answer: The answer is D: This is not a binomial experiment, because the number of trails is not fixed.
Step-by-step explanation: I took the test and chose the answer A and it was incorrect. The correct answer is D. I took the test on Ap3x.
Hope this helps
A bus can carry a maximum of 60 passengers. Each row accommodates the same number of passengers. If two rows are added then each row would accommodate one passenger less for the bus to carry maximum number of passengers. Determine number of rows in the bus and no. Of passengers per row
Answers
Answer:
10 rows with 6 passengers per row
Step-by-step explanation:
Let x be the number of rows and y the number of passengers per row.
Then we can interpret the story as the following two equations:
xy=60
(x+2)(y-1)=60
Solving these two equations:
y=60/x
(x+2)(60/x-1)=60 (substitute y)
60 - x + 120/x - 2 = 60 (multiply by -x)
x² + 2x - 120 = 0 (factor)
(x-10)(x+12) = 0
x = 10
y = 60/10 = 6
and indeed 10 * 6 = 60 and also 12 * 5 = 60
Write the opposite of each number. -25 _______ 0 _______
Answers
Answer:
25
0
Step-by-step explanation:
Help me please and thank you, and I will mark you brainliest!!
Answers
Answer:
270m^2
Step-by-step explanation:
30m*18m/2 = 270m^2
Answer:
270
Step-by-step explanation:
For what value of x is the rational expression below undefined?
3x+15/6-x
Answers
Let the function be (3x+15)/(6-x) then the value of x exists at -5.
What is the value of x?Given: Rational Expression (3x+15)/(6-x)
To find the value of x when given a rational expression equivalent to 0.
To estimate the value of x, convey the variable to the left side and convey all the remaining values to the right side. Simplify the values to estimate the result.
Consider, (3x+15)/(6-x) = 0
3x + 15 = 0(6-x)
3x + 15 = 0
Subtract 15 from both sides of the equation, e get
3x + 15 - 15 = 0 - 15
simplifying the above equation, we get
3x = 0 - 15
3x = -15
Divide both sides by 3, then we get
x/3 = -15/3
x = -5
Therefore, the value of x exists at -5.
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The commutative property does not work for which operations?check all that applys.
Answers
Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.
Step-by-step explanation:
Hope this is right!!!!
Help this is due today!!!!!!!!!
Answers
Answer:
n = 4Step-by-step explanation:
3n + 16 = 7n
3n - 7n = -16
-4n = -16
n = -16 : (-4)
n = 4
---------------- check
3 * 4 + 16 = 7 * 4
12 + 16 = 28
28 = 28
the answer is good