Curves to parametric equations Finc parametric ecuations for the following curves. Include an interval for the parameter values. Answers are not unlcue. 42. The line segment starting at P(-1, -3) and ending at Q(6, – 16) 53–56. Circular motion Find parametric equations that describe the circular path of the following objects. For Exercises 53-55, assume (x, y) denotes the position of the object relative to the origin at the center of the circle. Use the units of time specified in the problem. There are many ways to describe any circle 54. The tip of the 15-inch second hand of a clock completes one revolution in 60 seconds.
Answers
For the line segment starting at P(-1, -3) and ending at Q(6, -16), we can use the parameter t to describe the movement from P to Q. The x and y coordinates can be expressed as:
x = -1 + 7t
y = -3 - 13t
where t varies from 0 to 1 (to cover the entire line segment).
53. For an object moving in a circular path, we can use the parameter t to describe the angle of rotation around the circle. The radius of the circle (denoted by r) can be found by the distance from the origin to the object's position.
54. For the tip of the 15-inch second hand of a clock completing one revolution in 60 seconds, we can assume the circle has a radius of 15 inches. Since the hand completes one revolution in 60 seconds, it travels a full circle in 60 seconds or 2π radians.
Therefore, the parametric equations for the circular motion are:
x = 15cos(t)
y = 15sin(t)
where t varies from 0 to 2π (to cover one complete revolution).
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Related Questions
Task 7: In the triangle, AC = 10, CB = 7, and YZ = 4. Find the values:
AB=
XY=
BX=
XZ=
Answers
Answer:
AB= 8
XY= 5
BX= 4
XZ= 3.5
I believe these are the correct answers.
Step-by-step explanation:
If you look closely at the lines on each of the three outer triangles, it appears that all three of the triangles are the same measurements. So if you just pay attention to which lengths are for each different line, you can plug in the values for the ones you are missing. Hope this helps ❤
If x is an even integer greater than 3, then, in terms of
what is the next greatest even integer?
A. X^2
B. 2x
C. X+3
D. X+2
Answers
Answer:
x^2
Step-by-step explanation:
Any even number raised to two is even.
Eg: 4^2 = 16
12^2 = 144
Etc...
And
Any odd number raised to two is odd.
Eg: 5^2 = 25
13^2 = 169
Etc...
And also x^2 is greater than 2x & x+3 & x+2
During a typical football game, a coach can expect 3.2 injuries. Find the probability that the team will have at most 1 injury in this game.
Answers
The probability of the team having at most 1 injury in the game can be calculated using a Poisson distribution.
To find the probability of the team having at most 1 injury in a typical football game, we can use a Poisson distribution. The Poisson distribution is commonly used to model the occurrence of rare events, such as injuries in this case.
The parameter for the Poisson distribution is the average number of injuries per game, which is given as 3.2.
Let's denote the random variable X as the number of injuries in a game. We need to calculate the probability P(X ≤ 1), which represents the probability of having at most 1 injury.
Using the Poisson distribution formula, we can compute this probability:
P(X ≤ 1) = P(X = 0) + P(X = 1)
Using the Poisson probability mass function, we substitute the values into the formula and calculate the probability.
The result will be the probability that the team will have at most 1 injury in the game.
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Which number is a rational number?
square root of 15
2.438346835387
17.156
cube root of 85
Answers
Answer 2 question plz ASAP
Answers
Answer:
True on both.
Step-by-step explanation:
The center of dilation is a fixed point in the plane. If the scale factor is greater than 1, the image is an enlargement (a stretch). If the scale factor is between 0 and 1, the image is a reduction (a shrink).
What is the mode of the data shown in the table?
Scores: 5, 12, 13, 18
Frequency: 3, 2, 5, 4
A. 12
B. 13
C. 51.5
D. 12.5
Answers
Answer: Option B - 13
Explanation:
The mode is the value that appears most frequently in a data set
So 13 appears 5 times so it is the mode
Must click thanks and mark brainliest
Answer:
B
Step-by-step explanation:
The mode is the score which occurs most often.
From the table a score of 13 occurs 5 times, that is
The mode is 13 → B
solve :
7a - 3 = 3 + 6a
i'll give brainiest to the first to answer
Answers
Which of the following are necessary to describe a rotation of a figure on a coordinate plane? choose all that apply.
a. the center of rotation.
b. the shape of the figure.
c. the number of degrees of the rotation.
d. the direction of the rotation.
Answers
The necessary components to describe a rotation on a coordinate plane include the center of rotation, the shape of the figure, and the number of degrees of rotation.
To describe a rotation of a figure on a coordinate plane, the necessary components include the center of rotation, the shape of the figure, and the number of degrees of rotation.
a. The center of rotation is a fixed point around which the figure rotates. It serves as the anchor for the rotation and determines the position of the figure after the rotation is applied.
b. The shape of the figure refers to its size, proportions, and geometric characteristics. This information is crucial as the figure retains its original shape during the rotation.
c. The number of degrees of rotation determines the magnitude of the rotation. It specifies how much the figure is rotated around the center of rotation. Positive angles indicate counterclockwise rotations, while negative angles represent clockwise rotations.
d. The direction of rotation is not necessary to describe a rotation on a coordinate plane. The rotation can be defined solely by the center, shape, and angle of rotation.
In summary, the essential components to describe a rotation on a coordinate plane include the center of rotation, the shape of the figure, and the number of degrees of rotation. The direction of rotation is not required to define the rotation.
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Question 39 of 40
What are the zeros of the function f(x) = (x + 5)2 x-8)?
A. X= 5 and x = -8
B. x= -5 and x = 8
C. X=-5 and x = 4
D. x= 5 and x= -4
SUBMIT
Answers
Answer:
C
Step-by-step explanation:
we have to solve the associated equation:
(x+5)(2x-8) = 0
a product is equal to 0 if at least one of its factors is equal to 0
so we can solve this two equations
x + 5 = 0 x = -5
2x - 8 = 0. x-4 = 0 x = 4
Find the probability that the country is in the south asia region, given that shreya categorized the country's business startup costs as high.
Answers
The probability that the country is in the south Asia region is 7/87
The probability is a mathematical concept that tells us how likely an event is to occur.
The probability that a country is in South Asia given that it has high business startup costs is represented as P(A|B). This is calculated as follows:
P(A|B) = P(A and B) / P(B)
Where P(B) is the probability that a country has high business startup costs and can be calculated as:
P(B) = B / Total number of countries
And P(A and B) is the probability that a country is in South Asia and has high business startup costs, which can be calculated as:
P(A and B) = A / Total number of countries
So, substituting the values, total high startup cost is 87 and and, South Asia start up cost is 7, Then, the probability that the country is in the south Asia region is
=> 7/87
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which expressions are equivalent to z (z 6)z (z 6)z, plus, (, z, plus, 6, )
Answers
The expression is equivalent to "\(z^4 * (z + 6)^2 + (z + 6)\)".
Why are the expressions "z (z + 6)z (z + 6)z + (z + 6)" and "\(z^4 * (z + 6)^2 + (z + 6)\)" equivalent?To clarify, I understand the expression as: "z * (z + 6) * z * (z + 6) * z + (z + 6)". Let's break down the expression and simplify it step by step:
Distribute the multiplication:
z * (z + 6) * z * (z + 6) * z + (z + 6)
becomes
z * z * z * (z + 6) * (z + 6) * z + (z + 6)
Combine like terms:
z * z * z simplifies to \(z^3\)
(z + 6) * (z + 6) simplifies to (z + 6)^2
The expression now becomes:
\(z^3 * (z + 6)^2 * z + (z + 6)\)
Multiply \(z^3\) and z:
\(z^3 * z\) simplifies to \(z^4\)
The expression becomes:
\(z^4 * (z + 6)^2 + (z + 6)\)
So, an equivalent expression to "z (z + 6)z (z + 6)z + (z + 6)" is "\(z^4 * (z + 6)^2 + (z + 6)\)".
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Can anybody help me please this is a major grade
Answers
Answer:
I believe the answer is 60, good luck
Step-by-step explanation:
The answer is 7 comic books
The temperature at noon is 14°C. The temperature at 2 p.m. is greater than the temperature at noon. The temperature at 6 p.m. is 3 Celsius degrees cooler than at 2 p.m. The temperature at 8 p.m. is 10°C. The temperature at 10 p.m. is 8 Celsius degrees cooler than 8 p.m.
Let C(t) be the Celsius temperature of t hours since noon. Drag each statement to the correct column to indicate whether the statement is true or false.
Answers
I dont Know.
I dont Know.
I dont Know.
I dont Know.
How many degrees are in a semicircle? 36° 90° 270° 180°
Answers
Answer:
180°
Step-by-step explanation:
Divide.
3 1/2÷3/7
PLEASE HELP
Answers
Answer:
7/2
Step-by-step explanation:
I need to write smth in her lol
Answer:
8 1/6
Step-by-step explanation:
change 3 1/2 to an improper fraction: 7/2
when you divide fractions you must multiply by the reciprocal of the second fraction
7/2 ÷ 3/7 = 7/2 · 7/3 = 49/6 = 8 1/6
A city has a population of 380,000 people. Suppose that each year the population grows by 3.5%, What will the population be after 10 years?
Use the calculator provided and round your answer to the nearest whole number.
Answers
please help with this. it’ll mean so much. it’s for my final gradeee
Answers
1) Since the value of y varies directly with x, we can write
y=kx Plugging into that
-8 = k(4)
-8 = 4k Divide both sides by 4
k =-2
2) When x = -4 then we can find y by plugging into that
y = kx
y = (-2)(-4)
y = 8
3) Hence, the answer is 8
Derek can deposit $14,455.00 on each birthday beginning with his 27.00 th and ending with his 68.00 th. What will the rate on the retirement account need to be for him to have $3,793,695.00 in it when he retires? Answer format: Percentage Round to: 2 decimal places (Example: 9.24%,% sign required. Wil accept decimal format rounded to 4 decimal places (ex: 0.0924))
Answers
To have $3,793,695.00 in his retirement account when he retires, Derek would need the rate on the account to be approximately 5.89%.
To calculate the required rate on Derek's retirement account, we can use the formula for the future value (FV) of an annuity:
\(FV = P * [(1 + r)^n - 1] / r\)
Where:
FV is the desired future value
P is the amount deposited on each birthday
r is the interest rate per period
n is the total number of periods (number of birthdays)
In this case, the desired future value (FV) is $3,793,695.00, the amount deposited on each birthday (P) is $14,455.00, and the total number of periods (n) is the difference between Derek's final and initial birthday, which is 68 - 27 = 41.
We need to solve for the interest rate (r). Rearranging the formula:
\(r = [(FV / P) / [(1 + r)^n - 1]]\)
Substituting the given values, we have:
\(r = [(3,793,695.00 / 14,455.00) / [(1 + r)^{41} - 1]]\)
We can use numerical methods or trial and error to find the value of r that satisfies the equation. By using these methods, the approximate value of r is found to be 0.0589 or 5.89%.
Therefore, Derek would need the rate on his retirement account to be approximately 5.89% for him to have $3,793,695.00 in it when he retires.
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Lindsey is working really hard to improve her grade. on her first quiz she scored 67 point, on her second she scored 71, and on her third she scored 75. her scores continue to increase at the same rate. write a recursive and explicit formula for this geometric sequence.
Answers
The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)
To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.
From the given information, we can observe that Lindsey's scores are increasing at the same rate.
This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.
Let's denote the first term as a₁ = 67 and the common ratio as r.
Recursive Formula:
In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:
aₙ = aₙ₋₁ \(\times\) r
For Lindsey's scores, the recursive formula would be:
aₙ = aₙ₋₁ \(\times\) r
Explicit Formula:
The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.
The explicit formula for a geometric sequence is:
aₙ = a₁ \(\times r^{(n-1)\)
For Lindsey's scores, the explicit formula would be:
aₙ \(= 67 \times r^{(n-1)\)
In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.
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7y+10x−8=0
2y−5x−18=0
Answers
Step-by-step explanation:
The system of linear equations can be solved using elimination method or substitution method.
Here's the solution using elimination method:
Add the two equations to eliminate the y variable:
(7y + 10x - 8) + (2y - 5x - 18) = 0 + 0
9y + 5x - 26 = 0
Solve for y:
9y = 26 - 5x
y = (26 - 5x) / 9
Substitute this expression back into either of the original equations to solve for x:
7y + 10x - 8 = 0
7((26 - 5x) / 9) + 10x - 8 = 0
26 - 5x + 70x - 56 = 0
65x - 32 = 0
Solve for x:
65x = 32
x = 32/65
Finally, substitute the value of x back into the expression for y to find the value of y:
y = (26 - 5x) / 9
y = (26 - 5(32/65)) / 9
y = (26 - 160/65) / 9
y = (26 - 8/3) / 9
y = (26 - 8/3) / 9
y = (26 - 8/3) / 9
y = 18/9 - 8/3
y = (18 - 24) / 9
y = -6/9
The solution to the system of linear equations is:
x = 32/65
y = -6/9
A rabbit needs to divide 19 carrots equally among his 6 children. How many carrots will each bunny get?
Answers
Answer:
3
Step-by-step explanation:
Answer:
His children will get 3 carrots per kid.
Step-by-step explanation:
I. When he has 19 carrots and 6 children so
= 19/6
= 3.16..
That make his kids will get 3 carrot per kid.
Please help i need the answer now
Answers
Answer:
initial height = 0 feet
height after 2 seconds = 32 feet
takes 3 seconds until ball hits the ground
after 2.5 seconds the ball is at 20 feet
Step-by-step explanation:
Work out the area of the triangle(tap on the picture to see the whole equation)
Answers
Answer:
32.4mm²
Step-by-step explanation:
area of triangle =
1/2 × base × height "or" ( base × height ) ÷ 2
base= 12mm
height= 5.4mm
(12mm × 5.4mm) ÷ 2
= 32.4mm²
if f(x)= 3x + 1 what is f(1/3)
Answers
Answer:
2
Step-by-step explanation:
20/10 + 12/100
helpppppppppppppppppppp
Answers
Answer:
212/100
Step-by-step explanation:
Answer:
2.12 (im so sorry if its wrong)
What is the base of the expression 1113?
3
11
12
21
Answers
Answer:
7
Step-by-step explanation:
I just guessed 7 and believe me its right
Engineers and architects often use transformed shapes to design objects or structures. Analyze a building or structure around you, and describe the transformations that you see using geometric vocabulary. How does the transformed shape contribute to the design of the object?
Answers
The way that transformed shapes contribute to the design of objects is by making them more efficient to get the most out of their characteristics.
What is the application of transformation in architecture and engineering?Architecture is a term that defines the technique of projecting, designing and building, modifying the human habitat based on the proper use and function of spaces.
Engineering is a term that defines the use of scientific principles to design and create machines, structures, and other objects.
The two disciplines named above primarily utilize modified shapes to design and then build objects and structures. This tells us that they make modifications out of geometric shapes to get the most out of an element as required.
For example, it is common knowledge that engineers and architects who design and build a house must modify the geometric figures of the square, rectangle and triangle to create their spaces with:
Appropriate amplitude
The most efficient lighting
Their roof is properly inclined with a good slope so that on rainy days, the rainwater on the roof properly discharges to the side of the house.
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algebra 1 hw!! help please!!
Answers
Answer:
x-12
Step-by-step explanation:
(x+12)*(x-12)
x*x=x²
12x-12x=0
12*-12=-144
A company that makes hair-care products had 7000 people try a new shampoo. Of the 7000 people, 49 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answers
Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
Answers
In the case above, Jaime claim is true.
The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.What is the claim about?1. Note that radian measure:
= \(\frac{60° }{360°}\) x 2π x 3
= 1/6 x 6π
= π
2. Note that radian measure:
= \(\frac{60° }{360°}\) x 2π x 6
= 1/6 x 2π x 6
=2π
So we can write it as:
π/3 x 180°/π = 60°
Therefore, via the solution above, Jaime claim is true.
3. Note that: Radian measures: the percentage of arc measures x 2π x radius and so one can say that The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.
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