find a parameterization for the circle starting at the point (,0) and moving clockwise once around the circle.
Answers
This parameterization will trace out the circle starting at (0,0) and moving clockwise once around the circle as t varies from 0 to 2π (or 0 to 360 degrees).
A parameterization for the circle starting at the point (0,0) and moving clockwise once around the circle, we can use the parametric equations for a circle.
A circle with radius r centered at the origin has the parametric equations x = r * cos(t) and y = r * sin(t),
where t is the angle in radians. Since we want to move clockwise once around the circle, we need to reverse the direction of t.
So, the parameterization for our circle starting at (0,0) and moving clockwise once around the circle is x = r * cos(-t) and y = r * sin(-t).
In this case, since we start at (0,0), the radius r will determine the size of the circle. If we want a unit circle (radius of 1), the parameterization would be x = cos(-t) and y = sin(-t).
This parameterization will trace out the circle starting at (0,0) and moving clockwise once around the circle as t varies from 0 to 2π (or 0 to 360 degrees).
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Related Questions
Find the measure of each numbered angle
<3
<4
<5
Answers
The measure of angle 3, 4 and 5 from the given figure are 36°, 72° and 72° respectively.
From the given figure,
50°+65°+x=180° (By angle sum of property of a triangle)
115°+x=180°
x=180°-115°
x=65°
∠2=65° (Vertically opposite angles)
140°+y=180° (Sum of adjacent angles is 180°)
y=40°
Now, 40°+68°+∠5=180°
108°+∠5=180°
∠5=180°-108°
∠5=72°
∠4=∠5=72° (Vertically opposite angles)
∠3+∠4+∠5=180°
∠3+72°+72°=180°
∠3+144°=180°
∠3=36°
Therefore, the measure of angle 3, 4 and 5 from the given figure are 36°, 72° and 72° respectively.
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c(n)=-6+5(n-1) Find the 8th term in the sequence
Answers
Answer:
-7
Step-by-step explanation:
c(8)=-6+5x7
c(8)=-1x7
c(8)=-7
(i)Express 2x² – 4x + 1 in the form a(x+ b)² + c and hence state the coordinates of the minimum point, A, on the curve y= 2x² 4x+ 1.
The line x– y + 4 = 0 intersects the curve y= 2x² – 4x + 1 at points P and Q. It is given that the coordinates of Pare (3,7).
(ii)Find the coordinates of
(iii) Find the equation of the line joining Q to the mid-point of AP.
I already get the (i) but hav no idea with no.(ii) and (iii)
Can anyone help me? Thank you
Answers
Answer:
(i). \(y = 2\, x^2 - 4\, x + 1 = 2\, (x - 1)^2 - 1\). Point \(A\) is at \((1, \, -1)\).
(ii). Point \(Q\) is at \(\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)\).
(iii). \(\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}\) (slope-intercept form) or equivalently \(x + 5\, y - 17 = 0\) (standard form.)
Step-by-step explanation:
Coordinates of the ExtremaNote, that when \(a(x + b)^2 + c\) is expanded, the expression would become \(a\, x^2 + 2\, a\, b\, x + a\, b^2 + c\).
Compare this expression to the original \(2\, x^2 - 4\, x + 1\). In particular, try to match the coefficients of the \(x^2\) terms and the \(x\) terms, as well as the constant terms.
For the \(x^2\) coefficients: \(a = 2\).For the \(x\) coefficients: \(2\, a\, b = - 4\). Since \(a = 2\), solving for \(b\) gives \(b = -1\).For the constant terms: \(a \, b^2 + c = 1\). Since \(a = 2\) and \(b = -1\), solving for \(c\) gives \(c =-1\).Hence, the original expression for the parabola is equivalent to \(y = 2\, (x - 1)^2 - 1\).
For a parabola in the vertex form \(y = a\, (x + b)^2 + c\), the vertex (which, depending on \(a\), can either be a minimum or a maximum,) would be \((-b,\, c)\). For this parabola, that point would be \((1,\, -1)\).
Coordinates of the Two IntersectionsAssume \((m,\, n)\) is an intersection of the graphs of the two functions \(y = 2\, x^2- 4\, x + 1\) and \(x -y + 4 = 0\). Setting \(x\) to \(m\), and \(y\) to \(n\) should make sure that both equations still hold. That is:
\(\displaystyle \left\lbrace \begin{aligned}& n = 2\, m^2 - 4\, m + 1 \\ & m - n + 4 = 0\end{aligned}\right.\).
Take the sum of these two equations to eliminate the variable \(n\):
\(n + (m - n + 4) = 2\, m^2 - 4\, m + 1\).
Simplify and solve for \(m\):
\(2\, m^2 - 5\, m -3 = 0\).
\((2\, m + 1)\, (m - 3) = 0\).
There are two possible solutions: \(m = -1/2\) and \(m = 3\). For each possible \(m\), substitute back to either of the two equations to find the value of \(n\).
\(\displaystyle m = -\frac{1}{2}\) corresponds to \(n = \displaystyle \frac{7}{2}\). \(m = 3\) corresponds to \(n = 7\).Hence, the two intersections are at \(\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)\) and \((3,\, 7)\), respectively.
Line Joining Point Q and the Midpoint of Segment APThe coordinates of point \(A\) and point \(P\) each have two components.
For point \(A\), the \(x\)-component is \(1\) while the \(y\)-component is \((-1)\).For point \(P\), the \(x\)-component is \(3\) while the \(y\)-component is \(7\).Let \(M\) denote the midpoint of segment \(AP\). The \(x\)-component of point \(M\) would be \((1 + 3) / 2 = 2\), the average of the \(x\)-components of point \(A\) and point \(P\).
Similarly, the \(y\)-component of point \(M\) would be \(((-1) + 7) / 2 = 3\), the average of the \(y\!\)-components of point \(A\) and point \(P\).
Hence, the midpoint of segment \(AP\) would be at \((2,\, 3)\).
The slope of the line joining \(\displaystyle \left(-\frac{1}{2},\, \frac{7}{2}\right)\) (the coordinates of point \(Q\)) and \((2,\, 3)\) (the midpoint of segment \(AP\)) would be:
\(\displaystyle \frac{\text{Change in $y$}}{\text{Change in $x$}} = \frac{3 - (7/2)}{2 - (-1/2)} = \frac{1}{5}\).
Point \((2,\, 3)\) (the midpoint of segment \(AP\)) is a point on that line. The point-slope form of this line would be:
\(\displaystyle \left( y - \frac{7}{2}\right) = \frac{1}{5}\, \left(x - \frac{1}{2} \right)\).
Rearrange to obtain the slope-intercept form, as well as the standard form of this line:
\(\displaystyle y= - \frac{1}{5}\, x + \frac{17}{5}\).
\(x + 5\, y - 17 = 0\).
Triangle MNP is dilated according to the rule DO,1.5 (x,y)Right arrow(1.5x, 1.5y) to create the image triangle M'N'P, which is not shown.
On a coordinate plane, triangle M N P has points (negative 4, 6), (2, 6), and (negative 1, 1).
What are the coordinates of the endpoints of segment M'N'?
M'(-6, 9) and N'(4, 9)
M'(-6, 9) and N'(3, 9)
M'(-2, 3) and N'(7, 9)
M'(-2, 3) and N'(1, 3)
Answers
Given:
The vertex of a triangle MNP are M(-4, 6), N(2, 6), and P(-1, 1).
The rule of dilation is:
\((x,y)\to (1.5x,1.5y)\)
The image of triangle MNP after dilation is M'N'P'.
To find:
The coordinates of the endpoints of segment M'N'.
Solution:
The end points of MN are M(-4, 6) and N(2, 6).
The rule of dilation is:
\((x,y)\to (1.5x,1.5y)\)
Using this rule, we get
\(M(-4,6)\to M'(1.5(-4),1.5(6))\)
\(M(-4,6)\to M'(-6,9)\)
And,
\(N(2,6)\to N'(1.5(2),1.5(6))\)
\(N(2,6)\to N'(3,9)\)
The endpoints of M'N' are M'(-6, 9) and N'(3, 9).
Therefore, the correct option is B.
Answer:
B on edge
Step-by-step explanation:
Carlos surveyed a random sample of 30 students in his school’s cafeteria about whether they like the schools pizza. 15 of the 30 students said that they had liked the pizza, and there is a total of 750 students that visit the cafe each day? Based on the results of the survey, how many of the 750 students who visit the cafe can be expected to like the pizza?
how many students they should expect
A: 720
B: 735
c: 375
D: 11250
Answers
Of all rectangles with a perimeter of 10 meters, which one has the maximum area? (Give both the dimensions and the area enclosed)
Answers
Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters.
Of all rectangles with an edge of 10 meters, the one that has the greatest zone(area) could be a square.
To see why, let's assume that a rectangle with a border of 10 meters has measurements of length L and width W.
At that point, we know that:
2L + 2W = 10
Rearranging this condition, we get:
L + W = 5
Presently, we need to discover the most extreme range encased by the rectangle, which is given by:
Area = L x W
Able to illuminate for one variable in terms of the other utilizing the condition L + W = 5:
L = 5 - W
Substituting this expression for L into the condition for the zone, we get:
Zone = (5 - W) x W
Extending and disentangling this expression, we get:
Area = 5W - W²
To discover the most extreme esteem of this quadratic expression, we will take its subsidiary with regard to W and set it to break even with zero:
dArea/dW = 5 - 2W =
Tackling for W, we get:
W = 2.5
Substituting this esteem back into the condition for the edge, we get:
L = 2.5
Hence, the measurements of the rectangle that has the greatest region are L = 2.5 meters and W = 2.5 meters, which implies it could be a square. The most extreme zone enclosed by the rectangle is:
Zone(area) = L x W = 2.5 x 2.5 = 6.25 square meters.
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It’s number 12 and i need help with it
Answers
Answer:
Train A weighs 241 tons while train B weighs 71 tons.Let x represent the weight of train A and y represent the weight of train B.Since they both weigh 312 tons, hence:x + y = 312 (1)The difference of their weight is 170, and train A is heavier, hence:x - y = 170 (2)Solving equation 1 and 2 simultaneously gives:x = 241, y = 71 Therefore train A weighs 241 tons while train B weighs 71 tons.
Step-by-step explanation:
Answer:
Train A weighs 241 tons
train B weighs 71 tons.
Step-by-step explanation:
312-170=142
142÷2=71
170+71=241
241+71=312
18 pizzas were orderd for a holiday party at reedy creek elementary there were cheese and pepperoni pizzas of 1/3 of the pizza was cheese how many pizzas were pepperoni
Answers
Answer:
12
Step-by-step explanation:
We know that 1/3 of a pizza is cheese meaning that 6 pizzas are made of cheese and there are only two leaving the rest pepperoni and 12 are left if we subtract the cheese pizzas minus the 18 pizzas we have 12 which are pepperoni.
What fraction is equivalent to 2.68
Answers
It converts to a mixed number
Answer:
67/25's
Step-by-step explanation:
2 and 68/100's
Reduce 68/100 to 17/25
50/25=2
So, add (50/25)+(17/25) to make (67/25)
describe how changing one score influences the mean and standard deviation. changing one score changes the mean, but the standard deviation remains unchanged. changing one score changes both the mean and the standard deviation. changing one score does not change the mean, but the standard deviation changes.
Answers
In conclusion, changing one score can have an impact on both the mean and the standard deviation of a set of data. The extent of the influence depends on the deviation of the changed score from the original mean.
Changing one score can have an impact on both the mean and the standard deviation of a set of data. The mean is the average of all the scores, so if one score changes, it can affect the overall mean. The standard deviation, on the other hand, measures the deviation of each score from the mean. If one score changes, it can also affect the standard deviation, as the deviation of that score from the mean will be different.
For example, let's say we have a set of scores: 2, 4, 6, 8, 10. The mean of these scores is 6, and the standard deviation is 2.86. If we change the score of 2 to a 12, the new set of scores will be 12, 4, 6, 8, 10. The new mean will be 8, and the new standard deviation will be 2.94. As you can see, changing one score influenced both the mean and the standard deviation.
In conclusion, changing one score can have an impact on both the mean and the standard deviation of a set of data. The extent of the influence depends on the deviation of the changed score from the original mean.
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n a survey of patients in a local hospital, 62.42% of the respondents indicated that the health care providers needed to spend more time with each patient. who makes up the population?
Answers
The survey is of the population of all the patients present in that particular hospital.
What is a survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population.
Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.
Surveys are used to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions.
Surveys might have narrow, focused objectives or they can have broad, more general objectives.
So, in the given situation the survey states that 62.42% of the respondents indicated that the health care providers needed to spend more time with each patient.
So, it is clear that the remaining respondents have the opposite view on this.
So, the respondents will be all the patients present in the local hospital.
Therefore, the survey is of the population of all the patients present in that particular hospital.
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how to calculate urine output from diaper weight
Answers
Answer:
Step-by-step explanation:
mass of the urine lol
What are the domain and range of the relation given in the table?
Answers
Answer:
C
Step-by-step explanation:
all x values is domain, all y values are range
Answer:
Its c
Step-by-step explanation:
Domain = x value
Range = y value
Complete the table of values for the function f(x) = 1 x. X f(x) −1 a −0. 1 b -0. 01 c −0. 001 d x f(x) 0. 001 e 0. 01 f 0. 1 g 1 h a = b = c = d = e = f = g = h =.
Answers
The value of the function a, b, c, d, e, f, g, and h are -1, -10, -100, -1000, 1000, 100, 10, and 1 respectively.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The given function is f(x).
\(\rm f(x) = \dfrac{1}{x}\)
The values of f(x) at a given point will be shown in the table.
x f(x)
-1 -1
-0.1 -10
-0.01 -100
-0.001 -1000
0.001 1000
0.01 100
0.1 10
1 1
Thus, the value of the function a, b, c, d, e, f, g, and h are -1, -10, -100, -1000, 1000, 100, 10, and 1 respectively.
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Answer:
a = -1
b = -10
c = -100
d = -1000
e = 1000
f = 100
g = 10
h = 1
☆
EDGE2022; Good Luck!!! :D
A person accepts a position with a company at a salary of \( \$ 34,000 \) for the frat year, The person is guaranteed a raise of \( \$ 1850 \) per year for the first 6 years. Determine the person's to
Answers
The person's total salary over the first 6 years is $231,750.
To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.
Given information:
- Initial salary: $34,000
- Annual raise: $1,850
- Number of years: 6
To calculate the total salary, we can use the arithmetic progression formula:
[ S = frac{n}{2} left(2a + (n - 1)dright) ]
Where:
- ( S ) is the sum of the salaries
- ( n ) is the number of terms (years)
- ( a ) is the first term (initial salary)
- ( d ) is the common difference (annual raise)
Substituting the given values, we have:
[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]
Simplifying the expression:
[ S = 3 left( 68000 + 5 times 1850 right) ]
[ S = 3 left( 68000 + 9250 right) ]
[ S = 3 times 77250 ]
[ S = 231750 ]
Therefore, the person's total salary over the first 6 years is $231,750.
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When given the diameter of a sphere how can the volume be calculated? Describe the steps needed to find the volume.
Answers
Answer:
First divide diameter in half to get radius, then use the Sphere Volume formula(V=) to get the volume of the sphere.
Step-by-step explanation:
The diameter of a sphere, in terms of the volume of the sphere, is .
The volume of the sphereThe volume of the sphere is defined as the total capacity applied on the sphere;
The diameter of a sphere, how can the volume be calculated.
The volume of the sphere is given by;
Where r is the radius of the sphere.
The relation between the radius of the sphere and the diameter of the sphere is given by;
On comparing both equations;
Hence, the diameter of a sphere, in terms of volume of the sphere is .
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Sample Response: When given the diameter, divide it in half to find the radius measure. Then, substitute the radius measure into the formula. Cube the radius and multiply by 4/3. Write the result followed by pi and the label for the units.Answer:
Step-by-step explanation:
Which set of ordered pairs represents y as a function of x?
Answers
Please please help I would give anything just please help and check if I’m right it’s algebra 2
Answers
Answer:
In no 4 you have written option B but it should be option C. All of the other except it is correct.
In ΔTUV, t = 900 inches, u = 830 inches and v=590 inches. Find the measure of ∠U to the nearest degree.
Answers
Answer:
The answer is 64
Step-by-step explanation:
Given a special license plate tag consists of 5 characters for a small country. The first
characters is a digit between 1-6. The second and third characters are letters that
can not repeat. The last two characters can be any digits. How many unique tags
are possible?
351,000 tags
405,600 tags
325,000 tags
390,000 tags
Answers
Answer:
D
Step-by-step explanation:
Remark
First characters: 6 choices
Second two characters: 25 * 26
Third set of 2: 10 * 10 = 100
6 * 25 * 26 * 100 = 390000
The ratio of pink rose to yellow roses in a flower arrangement is 5:3. If there are 15 yellow roses, then how many total flowers are in the arrangement?
Answers
Answer:
bat ang pogi ko hahahaha
Post-War voices emerge (1950s-1960s) Unit test.
Does anyone hv the answers already
Answers
The post-war period of the 1950s and 1960s saw the emergence of a number of important voices in literature, art, and politics. Here are some examples:
Allen GinsbergJames Baldwin How to explain the informationGinsberg was a prominent poet and a leading figure in the Beat Generation, a group of writers who rejected conventional norms and values. His most famous work, "Howl," was published in 1956 and became a landmark in American literature.
Baldwin was an African-American writer whose novels and essays explored issues of race and sexuality in America. His most famous works include "Go Tell It on the Mountain" (1953) and "The Fire Next Time" (1963).
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Explain the Post-War voices that emerge in (1950s-1960s)
Line Integrals over Plane Curves 19. Evaluate fex ds, where C is a. the straight-line segment x = 1, y = 1/2, from (0, 0) to (4,2). b. the parabolic curve x = 1, y = 1², from (0, 0) to (2, 4).
Answers
In the given problem, we are required to evaluate the line integral ∫(C) fex ds, where f(x, y) = ex and C represents a curve in the xy-plane. We need to evaluate the integral for two different cases: (a) for the straight-line segment from (0, 0) to (4, 2) and (b) for the parabolic curve from (0, 0) to (2, 4).
(a) For the straight-line segment, we have x = 1 and y = 1/2. The parameterization of the curve can be written as x(t) = t and y(t) = t/2, where t varies from 0 to 4. Using this parameterization, we can express ds in terms of dt as ds = √(dx/dt² + dy/dt²) dt = √(1² + (1/2)²) dt = √(5)/2 dt. Therefore, the line integral becomes ∫(C) fex ds = ∫(0 to 4) (\(e^t\))(√(5)/2) dt. This integral can be evaluated using standard techniques of integration.
(b) For the parabolic curve, we have x = 1 and y = t². The parameterization of the curve can be written as x(t) = 1 and y(t) = t², where t varies from 0 to 2. Using this parameterization, we can express ds in terms of dt as ds = √(dx/dt² + dy/dt²) dt = √(0² + (2t)²) dt = 2t dt. Therefore, the line integral becomes ∫(C) fex ds = ∫(0 to 2) (e)(2t) dt. Again, this integral can be evaluated using standard integration techniques.
In summary, to evaluate the line integral ∫(C) fex ds for the given curves, we need to parameterize the curves and express ds in terms of the parameter. Then we can substitute these expressions into the line integral formula and evaluate the resulting integral using integration techniques.
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Evaluate using the variables:
A=1 b=2 c=3 x=3 y=2 z=1
1. ab
Y square 2
2. 6
Abc
Respect my post be honest bukas na po ipapasa ty and have a nice day :)..
Answers
The variables are evaluated to give;
1. 2
2. 6
What is an algebraic expression?An algebraic expression can be defined as an expression that is made up of terms, variables, coefficients, factors and constants.
These expressions are also thought to consist of mathematical or arithmetic operations such as;
AdditionMultiplicationDivisionSubtractionBracketParentheses, etcFrom the information given, we have that;
A=1 b=2 c=3 x=3 y=2 z=1
1. ab
Let's substitute the values into the formula
1(2)
Multiply the values
2
2. Abc
Substitute the values
(1)(2)(3)
multiply the values
6
Hence, the values are 2 and 6
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Your financial history can affect what credit you have available in the future.
true or false
Answers
Answer:
True
Step-by-step explanation:
Credit scores play a huge role in your financial life. They help lenders decide whether you're a good risk. Your score can mean approval or denial of a loan. It can also factor into how much you're charged in interest, which can make the debt more or less expensive for you.
Answer:
True
Step-by-step explanation:
I had this conversation just recently and yes I can effect your credit
Think carefully about the angle relationship the following represents.
What is the value of ∠ZXY?
Answers
Answer:
55°
Step-by-step explanation:
Since ∠WXY has a square on ∠X, ∠WXY is a 90° angle. This means that the angles in between ∠WXY also sum up to 90°.
⇒ 35 + 4x + 7 = 90
⇒ 4x = 90 - 35 - 7
⇒ 4x = 48
⇒ x = 48/4 = 12
Substitute the value of x into the expression "4x + 7"
⇒ ∠ZXY = 4x + 7 = 4(12) + 7 = 48 + 7 = 55°
Answer:
We know that this is a 90° Angle.
We already have 35° so we subtract that from 90
90-35=55
So the value of ∠ZXY = 55°
Also, the value of X is equal to 12
Hope this helps!
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Jane wants to display her monthly expenses in a circle graph to help her budget her money. she determines that the sector representing her car payment will have a angle of 59 degrees. if janes total monthly expenses are 1,650 what is her monthly car payment?
Answers
Answer:
359 is her payment
Step-by-step explanation:.
Answer:
359 in total :)
Can a proportional relationship have more than 2 variables?
Answers
Answer: I dont think so
Lincoln and Natalie are workers in a factory making widgets. Lincoln can make 25 widgets per day in the factory. Natalie is able to produce 8% more widgets per day than Lincoln. How many widgets can Natalie make per day?
Answers
Answer:
27 widgets
Step-by-step explanation:
25÷100=0.25=1%
0.25×8=2=8%
25+2=17
Solve for x.
x + 1/2 = 3/4
x = - 1/4
x = - 1/2
x = 1/2
x = 1/4
Answers
Answer:
x = 1/4
Step-by-step explanation:
x + 1/2 = 3/4
- Subtract 1/2 from both sides of the equation.
x = 1/4
Answer:
the answe is x=1/4
Step-by-step explanation:
hope this helps