let c be a curve drawn by: p(t)=⟨2cos(t),−2sin(t)⟩ find the length of the curve drawn by p as t runs from 0 to π:
Answers
The length of the curve drawn by
\(p(t) = ⟨2cos(t), -2sin(t)⟩\)
as t runs from 0 to π, we need to compute the arc length. First, find the derivative of p(t) with respect to t:
\(dp(t)/dt = ⟨-2sin(t), -2cos(t)⟩\)
Next, find the magnitude of the derivative:
\(||dp(t)/dt|| = √((-2sin(t))^2 + (-2cos(t))^2) = √(4sin^2(t) + 4cos^2(t))\)
Using the identity
\(sin^2(t) + cos^2(t) = 1,\)
\(||dp(t)/dt|| = √(4(sin^2(t) + cos^2(t))) = √(4) = 2\)
Now, integrate the magnitude of the derivative over the given interval [0, π]:
Length = \(∫(||dp(t)/dt||) dt from 0 to π = ∫(2) dt\) from 0 to π
Evaluate the integral:
Length =\( 2t |_0^π = 2π - 2(0) = 2π\)
So, the length of the curve drawn by p(t) as t runs from 0 to π is 2π.
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Related Questions
I really need help!!!
Solve each equation by using the Quadratic Formula. Round to the nearest tenth
if necessary.
72. x²-25=0
75. 2r²+r- 14 = 0
73. r²+25=0
76. 5v^2-7v = 1
Answers
Answer:
72. 5
73. -5
74.r =2.40753645…,−2.90753645
75. v =1.53066238…,−0.13066238
Step-by-step explanation:
Which of the following statements should the salesperson use if he wished to ignore the objection?
a. "I think I might be able to explain that better to you after showing you this diagram."
b. "I think you have a point there; do you have any idea how we can improve that situation?"
c. "That's true. It does have a shorter shelf life, but that hasn't really been a problem. It is so popular it never gets to stay on the shelf that long anyway."
d. "Where did you hear that? Your source must have erroneous information."
e. "As I was saying, . . . "
Answers
E, "As I was saying, . . .". The salesperson should use this statement if they wished to ignore the objection.
Option E is the best choice to ignore the objection because it allows the salesperson to redirect the conversation back to their main point without directly addressing the objection. The statement implies that the objection is not important enough to interrupt the flow of the conversation.
Ignoring objections is not always the best approach in sales, but if the salesperson chooses to do so, they should use a statement like option E to redirect the conversation back to their main point.
When a salesperson wants to ignore an objection, they should choose a response that does not address the concern raised and instead redirects the conversation back to the topic they were discussing. Option e does this effectively by not acknowledging the objection and continuing with the original discussion.
To ignore an objection, a salesperson should use a statement like option e, which allows them to refocus the conversation without addressing the concern raised.
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what is the unit rate of gallons used per minute
Answers
Directions: Determine whether each statement is always, sometimes, or never true.Name the theorem that will support your answer. Write your answers on the spaceprovidedStatementAnswerReason1. A line and a point are coplanar.2. Congruent angles form vertical angles.3. Linear pair that are congruent are rightangles.4. The sum of angles that formed linear pairis less than 180'.5. Vertical angles are complementary.
Answers
The given statement is 1. Always true
2. Always true
3. Always true
4. Sometimes true
5. Never true
Statement 1: A line and a point are always coplanar.
Answer: Always true.
Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.
Statement 2: Congruent angles form vertical angles.
Answer: Always true.
Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.
Statement 3: Linear pairs that are congruent are right angles.
Answer: Always true.
Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.
Statement 4: The sum of angles that form a linear pair is less than 180 degrees.
Answer: Sometimes true.
Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.
Statement 5: Vertical angles are complementary.
Answer: Never true.
Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.
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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.
To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.
Statement 1: A line and a point are coplanar.Answer: Always true.
The statement is always true because a line and a point lie in the same plane. This is supported by the Coplanar Points Theorem.Statement 2: congruent angles form vertical angles.
Answer: Sometimes true.
Congruent angles can form vertical angles, but it is not always the case. Vertical angles are formed by two intersecting lines, and they are always congruent. However, congruent angles can also be formed by other angle relationships, such as corresponding angles or alternate interior angles.Statement 3: linear pairs that are congruent are right angles.
Answer: Sometimes true.
Linear pairs are adjacent angles formed by two intersecting lines. While congruent linear pairs are always supplementary (their sum is 180 degrees), they are not always right angles. Right angles are a specific type of angle measuring 90 degrees.Statement 4: The sum of angles that form a linear pair is less than 180 degrees.
Answer: Never true.
The sum of angles that form a linear pair is always 180 degrees. This is supported by the Linear Pair Theorem, which states that if two angles form a linear pair, then their measures add up to 180 degrees.Statement 5: Vertical angles are complementary.
Answer: Never true.
Vertical angles are always congruent, but they are not always complementary. complementary angles are pairs of angles that add up to 90 degrees.Learn more:
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a circular garden is enlarged so that the new diameter is twice the old diameter. what is the ratio of the original area to the enlarged area? express your answer as a common fraction.
Answers
Answer:
The ratio of original area to enlarged area is 1/4.
Step-by-step explanation:
Area of original circular garden is
\(\pi {( \frac{d}{2} )}^{2} = \pi \frac{ {d}^{2} }{4} \)
Area of enlarged circular garden is
\(\pi ( { \frac{2d}{2}) }^{2} = \pi {d}^{2} \)
So the ratio of original area to enlarged area is 1/4.
Where is the circumcenter of this obtuse triangle located?
a. inside the triangle
b. on the side of the triangle
c. outside the triangle
d. at a vertex of the triangle
An obtuse triangle is made. The base of the obtuse triangle is slightly inclined with a horizontal in a downward direction and the other vertex is above the base.
Answers
The location of the circumcenter, of the obtuse triangle, which is the center of the circle that inscribes the triangle is at a point lower than the base of the triangle, and therefore, outside the triangle, because the angle of the arc formed by the base at the center is larger than 180°, which is the angle formed by the diameter/ The correct option is option c.
c. Outside the triangle
What is the circumcenter of a triangle?The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle.
The location of the circumcenter can be inside the triangle, outside the triangle, or on the triangle.
The circumcenter is located on the inside of an acute triangle, while it is located on the hypotenuse side of a right triangle.
The circumcenter of an obtuse triangle is located outside the triangleThe circumcenter is the location of the center of the circle that circumscribe the triangle, such that in an acute triangle, the angle at the center (twice the angle at the circumference), is always less than 180°, which is the angle made by the diameter, which keeps the diameter line and the circumcenter, passing inside the triangle.
However, in an obtuse triangle, the angle at the center, is larger than 180°, such that the line joining the base of the triangle, inscribed in the circle is located above the diameter, and therefore, located above the circumcenter.
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Jamar helped in a community garden for 21/10 hours this week that was 2 4/5 equal length shifts because Ja’Marr shop early one day when it started train what does 21 over 10÷2 and 4/5 representing the situation
Answers
Answer: The expression 21/10 ÷ 2 4/5 represents the number of hours Jamar worked per shift in the community garden, given that he worked for a total of 21/10 hours over 2 4/5 shifts.
To simplify this expression, we need to convert the mixed number 2 4/5 to an improper fraction:
2 4/5 = (2 x 5 + 4)/5 = 14/5
Now we can rewrite the expression as:
21/10 ÷ 14/5
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
21/10 x 5/14 = 3/4
Therefore, Jamar worked an average of 3/4 hours per shift in the community garden.
Step-by-step explanation:
if each day you work is 8 hrs & u work for 121 days how much hrs would that be
Answers
At a farm stand, every basket of strawberries weighs more than 3/4 lb. Draw a graph and write an inequality to represent the weight in pounds, w, of a basket of strawberries
Answers
The inequality of the statement At a farm stand, every basket of strawberries weighs more than 3/4 lb. is w > 3/4
How to determine the inequality of the statementFrom the question, we have:
Every basket weighs more than 3/4 lb
We can represent the weight of a basket of strawberries as the variable w.
Since the weight is always more than 3/4 lb, we can write the inequality:
w > 3/4
To graph this inequality, we can plot a dashed line at 3/4 on a number line
And shade the region to the right of the line to represent all values greater than 3/4.
The graph would look like the attached graph
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Should’ve paid attention, anyone got an answer! Thank you
Answers
Answer:
4x^4Step-by-step explanation:
Hope this helps!! Please consider marking brainliest! Have a good one!!
Answer:
4x^4
Step-by-step explanation:
Hope this helps and have a nice day :)
Find the median of 3,4,6,2,2,9,2,10
Answers
The answer is 4.75 you just need to add all of the numbers and then divide it to the total sum :)
Carry On Learning (◕ᴗ◕✿)
2,2,2,3,4,6,9,10
Then find the middle number. This set has two numbers since it is an even amount. 3,4
So you add those numbers
3 + 4 = 7
Then divide by 2
7/2 = 3.5
3.5 is the median for this set
I always think of the median of a highway. It is in the middle between both sides.
Ellora wants to accumulate $150000.00 in an RRSP by making annual contributions of $5000.00 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.
a. 18.202125
b. 18.676765
c. 17.455483
d. 17.585794
e. 18.076686
Answers
Option A is the correct answer. Ellora wants to accumulate 150,000 in an RRSP by making annual contributions of 5,000 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.
First, we have to find the interest rate per quarter, which will be
\(5.5% / 4\)= 1.375%.
The formula for the future value of an annuity is:
\(FV = (C * [(1 + r)^n - 1] / r)\),
For Ellora, \(FV = $150,000, C = $5,000, and r = 1.375%.\)
Substituting these values into the formula gives:
\(150,000 = 5,000 * [(1 + 0.01375)^n - 1] / 0.01375\)
Simplifying this equation gives:
\(30 = [(1.01375)^n - 1]\)
We can solve this using logarithms:
\(ln 30 = ln [(1.01375)^n - 1]\)
\(ln 30 = n * ln 1.01375 - ln 1.01375e^(ln 30) / e^(-ln 1.01375) = n18.202125 = n\)
Therefore, it will take Ellora 18.202125 years to accumulate 150,000 in her RRSP through \($5,000\)annual contributions made at the beginning of each year with interest of \(5.5%\) compounded quarterly.
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Please help!!! I will give brainliest and 50 points
The question is attached below
Answers
Answer:
1 + ln 2 - ln x
Step-by-step explanation:
ln ( 2e /x)
We know that ln ( a/b) = ln ( a) - ln (b)
ln (2e) - ln (x)
We also know that ln ( a*b) = ln a + ln b
ln ( 2) + ln e - ln x
We know that the ln e = 1
ln 2 + 1 - ln x
Changing the order
1 + ln 2 - ln x
1. Find the sum of the measures of the interior angles of a convex hexagon.
a. 900°
b. 1080°
c. 720°
d. 1440°
Answers
Answer:
could you include a pic please?
Round to the nearest tenth 37,636 ? pls help
Answers
Answer:
37,640
Step-by-step explanation:
MATHSSSS
Answer:
37,640
Step-by-step explanation:
its so simple good luck
A study found that working adults ages 22-25 spend an average of $14.27 a day on food with a standard deviation of $2.25. The amount Jeremy spends per day is 4 standard deviations above the average. How much does Jeremy spend per day, rounded to 2 decimal places
Answers
If working adults aged 22-25 spend an average of $14.27 a day on food with a standard deviation of $2.25, then Jeremy would spend approximately $23.27 per day if his expenditure is 4 standard deviations above the average.
To calculate how much Jeremy spends per day, we need to find a value that is 4 standard deviations above the average.
Mean (average) = $14.27
Standard deviation = $2.25
To find the amount Jeremy spends per day, we multiply the standard deviation by 4 and add it to the mean:
Jeremy's daily spending = Mean + (4 * Standard deviation)
Jeremy's daily spending = $14.27 + (4 * $2.25)
Jeremy's daily spending = $14.27 + $9.00
Jeremy's daily spending = $23.27
Therefore, Jeremy spends approximately $23.27 per day, rounded to 2 decimal places.
The concept used to solve the problem is based on the standard deviation and the number of standard deviations above the mean.
In statistics, the standard deviation measures the amount of variation or dispersion in a dataset. It tells us how spread out the data points are from the mean.
To find Jeremy's daily spending, we are given the average daily spending ($14.27) and the standard deviation ($2.25). Since Jeremy's spending is described as 4 standard deviations above the average, we need to multiply the standard deviation by 4 to get the amount.
By multiplying the standard deviation ($2.25) by 4, we obtain the additional amount Jeremy spends above the average. Adding this to the mean ($14.27) gives us Jeremy's daily spending of $23.27.
This approach allows us to calculate the value of Jeremy's spending based on the average, standard deviation, and the given number of standard deviations above the mean.
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Question 1 of 25
Which of the following is equal to the expression below?
(5-672
O A
A.
O B. -54
O c.
O D. -512
Answers
Answer:
D -512
Step-by-step explanation:
All you have to do is just multiply the exponents and you are done.
Hope this helps
Write the equation √3z= √x²+y² in spherical coordinates.
(Simplify as much as possible).
Answers
In spherical coordinates, the equation can be represented as ρcos(φ) = ρsin(φ)cos(θ) + ρsin(φ)sin(θ). The simplified form of the equation √3z = √x² + y² in spherical coordinates is cos(φ) = cos(π/2 + θ - φ)
To simplify this equation, we can divide both sides by ρ and rearrange the terms:
cos(φ) = sin(φ)cos(θ) + sin(φ)sin(θ)
Next, we can apply trigonometric identities to simplify the equation further. Using the identity sin(φ) = cos(π/2 - φ), we can rewrite the equation as:
cos(φ) = cos(π/2 - φ)cos(θ) + cos(π/2 - φ)sin(θ)
Using the identity cos(A - B) = cos(A)cos(B) + sin(A)sin(B), we can rewrite the equation again as:
cos(φ) = cos(π/2 - φ + θ)
Finally, we can simplify the equation to:
cos(φ) = cos(π/2 + θ - φ)
This is the simplified form of the equation √3z = √x² + y² in spherical coordinates.
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One of the angles of a triangle is equal to the sum of the other two. If the ratio of the
other two angles is 2:3, then the angles are ______________.
Answers
Answer:
the correct answer is 60° and 30°( for the two angles that have the ratio 2:3)
The other angle will be 90°
The rectangular floor of a classroom is 38 feet in length and 30 feet in width. A scale drawing of the floor has a length of 19 inches. What is the perimeter, in inches, of the floor in the scale drawing?
Answers
68
The scale drawing is dividing everything by 2. So, the length is 19, and the width is 15. Then, you add 19 and 15 twice. So, the answer is 68.
I walk to a town at 3 1 2 321 kmph, rest there for 45 minutes and ride back at 7 1 2 721 kmph. Find the distance to the town, if the total time spent by me is 6 hrs 37 min.
Answers
the distance to the town is approximately 14 km.
To find the distance to the town, we need to use the formula:
Distance = Speed * Time
Given information:
Walking speed = 3.5 km/h
Resting time = 45 minutes = 45/60 = 0.75 hours
Riding speed = 7.5 km/h
Total time spent = 6 hours 37 minutes = 6 37/60 = 397/60
Let's break down the time spent into different components:
Time spent walking to the town:
Time1 = Distance / Walking speed = Distance / 3.5 km/h
Time spent resting in the town:
Resting time = 0.75 hours
Time spent riding back from the town:
Time2 = Distance / Riding speed = Distance / 7.5 km/h
Total time equation:
Time1 + Resting time + Time2 = Total time
(Distance / 3.5) + 0.75 + (Distance / 7.5) = 397/60
After solving
Distance = 14
Therefore, the distance to the town is approximately 14 km.
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Why did semyen dezhnev and the evenki fight each other?
Answers
Semeyn Dezhnev was a Russian explorer who discovered the Bering Strait in the early 17th century. It is not entirely clear why he and the Evenki, a tribe of indigenous people who inhabited the area, fought each other.
Some historians believe that the conflict may have been caused by a misunderstanding or a cultural clash. Others speculate that it could have been related to competition for resources, such as food or land. It is also possible that the conflict was instigated by outside forces, such as rival tribes or European powers seeking to establish dominance in the region.
Despite the lack of concrete information, it is clear that there was tension and violence between Dezhnev's expedition and the Evenki, which may have influenced the course of early Russian exploration and colonization in the region.
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choose the table thst represents g(x) =-2•f(x) when f(x) = x +4
Answers
Answer:
c
Step-by-step explanation:
x=1 g(x)=-10
x=2 g(x)=-12
x=3 g(x)=-14
f(x)=x+4
=＞ g(x)=-2·(x+4)
I added the question and the example for reference. Please help! whoever is correct i will give brainliest!
Answers
Answer:
It would be 828 inches cubed
Step-by-step explanation:
Because the boxes on top and bottom are both 6x8x6 and the middle portion is 6x7x6
6x8x6=288
6x7x6=252
288+288+252=828
Find the measure of angle b
Answers
Answer:
130°
Step-by-step explanation:
a straight line is 180°
so you have
180°-50°= 130°
b and 50 are supplementary angles (they add up to 180), so create an equation by adding them up to equal 180:
b + 50 = 180
we want the x by itself, so subtract both sides by 50 to get:
b = 130°
John's son will start college in 10 years. John estimated a today's value of funds to finance college education of his son as $196,000. Assume that after-tax rate of return that John is able to earn from his investment is 8.65 percent compounded annually. He does not have this required amount now. Instead, he is going to invest equal amounts each year at the beginning of the year until his son starts college. Compute the annual beginning of-the-year payment that is necessary to fund the estimation of college costs. (Please use annual compounding, not simplifying average calculations).
Answers
John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.
To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.
The present value of an annuity formula is given by:
P = A * [(1 - (1 + r)^(-n)) / r],
where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.
In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:
196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].
Simplifying the expression inside the brackets:
196,000 = A * (1 - 0.469091).
196,000 = A * 0.530909.
Dividing both sides by 0.530909:
A = 196,000 / 0.530909.
A ≈ 369,238.68.
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Contribution margin is: Group of answer choices Excess of sales revenue over total variable costs. Excess of sales revenue over variable costs of goods sold. All of the answer choices are correct. Excess of sales revenue over costs of goods sold.
Answers
Contribution margin is the excess of sales revenue over total variable costs. This means that all of the answer choices are correct.
Contribution margin is an important financial metric used in managerial accounting to assess the profitability of a company's products or services. It represents the amount of revenue available to cover fixed costs and contribute to the company's operating income. The contribution margin is calculated by subtracting the total variable costs from the sales revenue. Variable costs are expenses that vary directly with the level of production or sales, such as direct materials, direct labor, and variable overhead. Fixed costs, on the other hand, remain constant regardless of the level of production or sales. By analyzing the contribution margin, managers can make informed decisions regarding pricing strategies, product mix, and cost control measures. A higher contribution margin indicates that a greater portion of each sales dollar is available to cover fixed costs and generate profits. It is important for companies to maintain a healthy contribution margin to ensure their long-term financial viability.
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Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. if we start with only one bacteria which can double every hour, how many bacteria will we have by the end of one day?
Answers
Answer:
Roughly 16 million bacteria.
Step-by-step explanation:
Multiply the rate of the bacteria going through mitosis times the amount of daughter cells per hour, for this case.
r x (m)ms x hr = bacteria in one day
Hope this helps!
note: ms and hr are millisecond and hour
A model car has a scale of 1:100, find the scale length in cm if the car is 4. 32m long
Answers
Answer:
4.32 cm
Step-by-step explanation:
let x = scale length of the car
1/100 = x/4.32
100x = 4.32
x = 4.32/100 = 0.0432 m
convert to m to cm: 0.0432 m x 100 cm/m = 4.32 cm
When hired at a new job selling jewelry, you are given two pay options:Option A: Base salary of $17,000 a year, with a commission of 8% of your sales for the year.Option B: Base salary of $21,000 a year, with a commission of 4% of your sales for the year.How many dollars of sales would need to be sold in order for the two options to produce the samesalary for you?$of jewelry each year.Round your answer to the nearest cent as needed.
Answers
let x be the cost of jwellery sold by you.
The equation for option A is given by:
\(y=17000+\frac{8}{100}x\)The equation for option B is given by:
\(y=21000+\frac{4}{100}x\)So the equality is given by:
\(\begin{gathered} 17000+\frac{8}{100}x=21000+\frac{4}{100}x \\ \frac{4}{100}x=4000 \\ x=100000 \end{gathered}\)Hence the sales should be 100000$ for you to make the same salary on both options.