DUE FRIDAY HELP!!!!!!!!!!!!!!!!
2. Where will point P be after the wheel has traveled π feet to the left? What about 10π feet? 100π feet?
3. After traveling some distance to the left, the point P is at the lowest location in its rotation. How far might the wheel have traveled?
Answers
2)
a) After the wheel has traveled for π feet, point P will be at the point labelled T.
b) After 10π feet, the point P will be at its starting position on the rightmost point of the circle, but with a different orientation.
c) after 100π feet, P will be back to where it started, and the orientation of the wheel has also completed 50 full rotations.
3)
The wheel must travel π/2 feet to reach its lowest point on the circle, assuming that it starts at the rightmost point on the circle and rolls to the left.
A circle is a two-dimensional geometric shape consisting of all the points that are at a constant distance from a given point, called the center.
2)
a) Let us assume that the wheel starts at a point on the circle, with P being the rightmost point on the circle. After the wheel travels π feet, it will complete half a revolution and reach the diametrically opposite point on the circle, which is the leftmost point labeled T.
To see why, note that the circumference of the circle is 2πr, where r is the radius of the circle. In this case, r = 1 foot, so the circumference is 2π feet. Therefore, after the wheel has traveled π feet, it has traveled half the circumference of the circle. Therefore, the point P will be at point T after the wheel has traveled π feet.
b)
After the wheel has traveled 10π feet, it has completed 5 revolutions around the circle. Each revolution brings the point P back to its starting position on the rightmost point of the circle, but with a different orientation.
To see why, imagine that we mark a point Q on the circumference of the wheel, which is a fixed distance from P. As the wheel rolls along the circle, the point Q traces out a circle that is centered at the center of the circle, with a radius equal to the distance from P to Q.
Since this circle has a circumference that is exactly 2π times the radius of the circle, it means that after one revolution of the wheel around the circle, the point Q returns to its starting position, and after n revolutions, it returns to its starting position n times.
Now, since the wheel has completed 5 revolutions, the point P has also completed 5 revolutions around the circle. This brings it back to its starting position on the rightmost point of the circle, but with a different orientation.
c)
After the wheel has traveled 100π feet, it has completed 50 revolutions around the circle. Each revolution brings the point P back to its starting position on the rightmost point of the circle, but with a different orientation, as we have seen in the previous answer.
Therefore, after the wheel has traveled 100π feet, the point P will be at its starting position on the rightmost point of the circle, but with a different orientation.
3)
If we assume that the point P starts at the rightmost point on the circle and rolls to the left, it will eventually reach its lowest point on the circle. This occurs when the wheel has rolled exactly one-quarter of the way around the circle from its starting position.
To see why, imagine that we mark a horizontal line passing through the center of the circle, which we can call the "ground" level. As the wheel rolls to the left, point P moves down along a vertical line until it reaches its lowest point, which is at ground level. At this point, the radius of the wheel is perpendicular to the ground level line, forming a right angle.
Since the wheel has traveled one-quarter of the way around the circle, this means that it has traveled a distance equal to one-quarter of the circumference of the circle. The circumference of the circle is 2π times the radius, which in this case is 2π feet. Therefore, the distance traveled by the wheel to reach its lowest point on the circle is:
distance = 1/4 * 2π
= π/2 feet
So the wheel must travel π/2 feet to reach its lowest point on the circle, assuming that it starts at the rightmost point on the circle and rolls to the left.
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Related Questions
Which numbers complete the blanks when solving the equation Cosine (x + 2 pi) = negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction over the interval [0, 2Pi]?
Cosine x times blank minus sine x times blank = negative StartFraction StartRoot 2 EndRoot Over 2 EndFraction
Answers
Answer:
Thus, the blanks should be completed with 1;0 respectively
Step-by-step explanation:
Cosine of the sum of angles
The formula for the cosine of angles \alpha and \beta is shown below:
\(cos(\alpha+\beta)=cos\alpha*cos\beta-sin\alpha*sin\beta\)
For the expression given in the question:
\(cos(x+2\pi)=cosx*cos2\pi-sinx*sin2\pi\)
Since
\(cos 2\pi=1, sin2\pi=0:\)
\(cos(x+2\pi)=cosx*1-sinx*0\)
Thus, the blanks should be completed with 1;0 respectively
Answer:
A. 1;0
Step-by-step explanation:
did on edge
Find the common ratio 24,18,37/2,81/8
Answers
Note: The third term of the sequence should be \(\dfrac{27}{2}\) instead of \(\dfrac{37}{2}\), otherwise the sequence has no common ratio.
Given:
The given sequence is
\(24,18,\dfrac{27}{2},\dfrac{81}{8}\)
To find:
The common ratio of the given sequence.
Solution:
The quotient of each pair of consecutive terms are:
\(\dfrac{18}{24}=\dfrac{3}{4}\)
Similarly,
\(\dfrac{\dfrac{27}{2}}{18}=\dfrac{27}{36}\)
\(\dfrac{\dfrac{27}{2}}{18}=\dfrac{3}{4}\)
And,
\(\dfrac{\dfrac{81}{8}}{\dfrac{27}{2}}=\dfrac{81}{8}\times \dfrac{2}{27}\)
\(\dfrac{\dfrac{81}{8}}{\dfrac{27}{2}}=\dfrac{3}{4}\)
Therefore, the common ratio of the given sequence is \(\dfrac{3}{4}\) or 0.75.
Sequences and Series
Algebra 2 Honors
Answers
Find the logarithm of 5.238 with solution
Answers
The logarithm of 5.238 with solution is 0.71916549409.
= log(5.238)
= log(5238/1000)
= log(5238) - log(1000)
= 3.71916549409 - log(\(10^{3}\))
= 3.71916549409 - 3log10
= 3.71916549409 - 3
= 0.71916549409.
Therefore the logarithm of 5.238 with solution is 0.71916549409.
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5. Find the Fourier coefficients of the periodic ( -5 to 5) function y(t) = -3 when -5
Answers
In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:
c₀ = -3 (DC component)
cₙ = 0 for n ≠ 0 (other coefficients)
To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:
cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt
where T is the period of the function and n is an integer.
In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).
To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:
c₀ = (1/T) ∫[-T/2, T/2] y(t) dt
Substituting the given values:
c₀ = (1/10) ∫[-5, 5] (-3) dt
= (-3/10) \([t]_{-5}^{5}\)
= (-3/10) [5 - (-5)]
= (-3/10) [10]
= -3
Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.
For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:
cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt
Since y(t) is constant, the integral becomes:
cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt
= (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt
The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.
all the coefficients cₙ for n ≠ 0 are zero.
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a rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, find the length. (all answers are given in inches.)
Answers
A rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, then the length is 13 inch.
What is a rectangle?A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
here, we have,
a rectangle's length is 5 inches greater than its width.
if the perimeter of the rectangle is 42 inches
let, width = x
then, length = x+5
so, perimeter= 2(x+5 +x)
= 4x+10
ATQ, 4x+10 = 42
solving we get,
x=8
the length = 13
Hence, A rectangle's length is 5 inches greater than its width. if the perimeter of the rectangle is 42 inches, then the length is 13 inch.
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PLEASE HELP IM GIVING 70 POINTS Figure A is a scale image of Figure B, as shown Х 3 Figure A Figure B The scale that maps Figure A onto Figure B is 1:7- 4
Answers
Answer:
stretching trifling preheated prejudicial irresistible
The product of 4 and the sum of a number x and 8
Answers
Answer:
8(x+3)
Explanation:
"The product of 8 and" means 8 is going to be multiplied times another quantity. "...the sum of a number x and 3" means that 8 is going to be multiplied times (x+3).
This is represented by 8×(x+3), which simplifies to 8(x+3).
to prove the following statement by contrapositive: for any positive real numbers x and y, if xy>400, then x>20 or y>20. what would be assumed to be true?
o xy>400
o x<20 and y<20
o xy<400
o x<20 or y<20
o x>20 or y>20
o x<20 and y<20
Answers
To prove the statement by contrapositive, we need to assume the negation of the conclusion and the negation of the hypothesis and then show that the contrapositive statement is true.
Negation of the conclusion: It is not the case that x>20 or y>20. In other words, x≤20 and y≤20. Negation of the hypothesis: xy≤400.
So, assuming x and y are positive real numbers, if x≤20 and y≤20, then xy≤400. Therefore, the negation of the hypothesis implies the negation of the conclusion. Thus, the contrapositive statement is: For any positive real numbers x and y, if x≤20 and y≤20, then xy≤400.
The assumed statement is: xy>400. Therefore, the contrapositive statement is false.
In conclusion, the assumed statement implies the original statement, but the contrapositive statement is untrue.
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The interior angle of the regular pentagon below measures 108, and the pentagon has rotational symmetry. Which of the following is the measure of an interior angle after a 90 rotation around the point of symmetry?
Answers
Answer:
108
Step-by-step explanation:
The measure of interior angle after a 9\(0^{o}\) rotation is 10\(8^{o}\)
What is pentagon?In the pentagon, the sum of the interior angles is equal to 540°. If all the sides are equal and all the angles are of equal measure, then it is a regular pentagon. Otherwise, it is irregular. In the regular pentagon, each interior angle measures 108°, and each exterior angle measures 72°.
according to the question
After rotation the size of the interior angle stays the same.
10\(8^{o}\) = 10\(8^{o}\)
Hence, the measure of interior angle after a 9\(0^{o}\) rotation is 10\(8^{o}\)
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what doe it mean to be happy to you?
Answers
To be happy wow it’s an amazing feeling and it’s a wonderful experience.To be happy you smile like crazy and your just feeling great.You feel like no one worries your in your own little world with smiles and sunshine.To be happy is great because I’m actually me and I can escape from reality.My oh my to be happy is wonderful I wish we all could be happy for then the world will be great
Needed urgently, with correct steps
Q4 (9 points) Use Gauss-Jordan elimination to solve the following system, 3x +9y+ 2z + 12w x + 3y2z+ 4w -2x - 6y - 10w = 1 = 2. = 0,
Answers
The solution to the given system of linear equations is x = 7/21 - (z/3) - (w/14), y = 5/63 + (z/7) + (w/21), z and w are free variables.
The given system of linear equations is
3x + 9y + 2z + 12w = 1 ... (1)
x + 3y + 2z + 4w = 0 ... (2)
-2x - 6y - 10w = 0 ... (3)
Using Gauss-Jordan elimination to solve the given system, we get:
[3 9 2 12| 1]
[1 3 2 4| 0]
[-2 -6 0 -10| 0]
Performing the following operations on each of the rows:
R1 ÷ 3 → R1 ... (4)
R2 - R1 → R2 ... (5)
R3 + 2R1 → R3 ... (6)
[1 3/9 2/3 4| 1/3]
[0 -6/9 4/3 -4/3| -1/3]
[0 0 14/3 -2/3| 2/3]
Performing the following operations on each of the rows:
R1 - 3R2/2 → R1 ... (7)
R2 × (-3/2) → R2 ... (8)
R3 × 3/14 → R3 ... (9)
[1 -1 0 -1/2| 2/3]
[0 1 -2/3 2/9| 1/9]
[0 0 1 -1/7| 1/7]
Performing the following operations on each of the rows:
R1 + R2/2 → R1 ... (10)
R2 + 2R3/3 → R2 ... (11)
[1 0 -1/3 -1/14| 7/21]
[0 1 0 1/21| 5/63]
[0 0 1 -1/7| 1/7]
Therefore, the solution to the given system of linear equations is
x = 7/21 - (z/3) - (w/14)y = 5/63 + (z/7) + (w/21)z and w are free variables.
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Which set of ordered pairs represents a function?
a
O {(7,4), (3,8), (-4, –4), (0,4)}
O {(-8,0), (-5,6), (-8, 1), (-6,5)}
{(-5, 1), (3, -7), (2, -4), (2,7)}
O {(4,2), (4, -9), (-9, -6), (7,1)}
Answers
(7,4), (3,8), etc
classify the quadrilateral by its most specific name. then find the missing angle measure(s)
Answers
The specific name of the quadrilateral is trapezoid
The measure of the missing angle is 55 degrees
How to determine the valueTo determine the measure of the angle, we need to know the following;
The properties of a trapezoid are listed as;
The bases are parallel to each other.Opposite sides of a trapezoid (isosceles) are of the same length.Angles next to each other sum up to 180 degreesThe median is parallel to both the bases.Median's length is the average of both the basesFrom the information given, we have that;
125 + x = 180
collect the like terms, we have;
x = 180 - 125
subtract the values, we get;
x = 55 degrees
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PLEASE HURRY, MARKING BRAINLIEST.
Solve for the value of x that makes lines a and b parallel.
Answers
You set the equations equal and then solvep
Answer:
x=16
Step-by-step explanation:
if the lines were parallel then that means that (7x+2) = (8x-14) because they are corresponding angles. just isolate the varible so subtract 7x from both sides and add 14 to both sides. and they you get x=16
I need help with this please help it’s due tonight
Answers
Answer:
OZQ=125°
OZP=62°
PZQ=OZQ+OZP
PZQ=125+62
PZQ=187°
Tom's Ice Cream Shop sold 7 sundaes with nuts and 5 sundaes without nuts. What is the ratio of the number of sundaes with nuts to the number of sundaes without nuts?
Answers
Answer:
20 : 28
5 : 7 = 20 : 28. And 7 is a fourth of 28.
Please help!! Needed asap, due soon!!:
Given line m and point O not on line m, the image of line m is constructed through a dilation centered at O with a scale factor of 3. Which of the following best describes the image of line m?
A. a line parallel to line m
B. a line intersecting with line m
C. a line passing through point O
D. a line perpendicular to line m
Answers
Answer:
The correct answer is A
Step-by-step explanation:
A line parallel to M
solve the inequality for 1x + 2 > 10
Answers
Answer:
x>8
Step-by-step explanation:
Hope that helps you!!
how many different ways could i choose three shirts to pack for a weekend trip, if i have 12 shirts to choose from? assume the shirts are selected without replacement.a. 12! / 3!b. 12! / 9!c. 12! / 8! 4!d. 12! / 9! 3!
Answers
Answer:
A
Step-by-step explanation:
According to the given question.
Total number of shirts, n = 12
Number of shirts to be selected, r = 3
As we know, the total number of ways of selection of r objects from n objects at a time without replacement is given by
C(n, r) = n!/r!(n - r)!
x^3 = -216/343
Round to the nearest tenth. Put the negative sign in the numerator.
Answers
Putting the negative sign to the numerator, we have the value of x = -6/7.
What is Algebraic expression?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
The given equation is:
x³ = -216/343
To solve for x, we can take the cube root of both sides of the equation:
∛(x³) = -∛(216/343)
x = -∛(216/343)
Solving for numerator:
216 = 6 × 6 × 6
∛216 = 6
Solving for denominator:
343 = 7 × 7 × 7
∛343 = 7
Therefore,
x = -∛(216/343)
x = -(6/7)
x = -6/7
Putting the negative sign to the numerator, we have the value of x = -6/7.
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a polygon has three of each interior angle to be 160 degrees each and others are 120° each calculate the number of sides in a polygon
Answers
The number of sides in the polygon are 18 and 6 sides respectively .
Interior angles of a polygonThe interior angles of a polygon can be calculated using the relation :
Number of sides (n) = 360° / (180° - Interior angle)
In this case, we have two different interior angles: 160° and 120°.
We can substitute the values for the interior angles using the value of the angles given .
For the angle of 160°Number of sides = 360° / (180° - 160°) = 360° / 20° = 18 sides
For the angle of 120°Number of sides = 360° / (180° - 120°) = 360° / 60° = 6 sides
Therefore, the number of sides in the polygon are 18 and 6 sides respectively .
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The chess club has 25% more males and females. If there were 20 males, how many females are there in the club.
How many less were the females?
Number of Females =
Thank You!!!!
Answers
Answer:
number of females =16
Step-by-step explanation:
100% + 25% =125%. 125%=number of males. 100\125 ×20=16. 20 - 16 =4
If 15x + 20=a(bx + c), where a, b and c are integers, and a > 1,what is
the value of a? 3, 4, 5, 10, or 15
Answers
Since a > 1, b cannot be greater than 15, hence the value of a can be 3, 4, 5, and 10
Given the expression 15x + 20=a(bx + c),
To get the value of a, we will need to factor out the given expression as shown:
15x + 20=a(bx + c)
15x + 20=abx + ac
Comparing both sides
15x = abx
15 = ab
a = 15/b
Since a > 1, b cannot be greater than 15
Hence the value of a can be 3, 4, 5, and 10
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Reaching out 2 standard errors on either side of the sample proportion makes us about _________ confident that the true proportion is capable within the interval
a. 90%
b. 99%
c. 95%
d. 68%
Answers
The correct answer is option c. 95%. Reaching out two standard errors on either side of the sample proportion gives us an interval of 95% confidence.
This is due to the fact that two standard errors on either side of the sample proportion will cover around 95% of the population's cases.
We can typically determine the true proportion in the population using this range of two standard errors on either side of the sample proportion.
This is because it helps us identify any potential outliers in the population and provides a range of population proportions for which we may be 95% certain.
We are 95% certain that the true percentage is capable inside the interval if we stretch out two standard errors on either side of the sample proportion.
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f(x) = sqrt(2x); g(x) = sqrt(8x) Find (fg)(x) Assume x >= 0
Answers
The functions f(x) and g(x) combine to form a composite functions
The value of the composite function f(g(x)) is \(\sqrt{4\sqrt{2x}\)
How to determine the function (fg)(x)The functions are given as:
\(f(x) = \sqrt{2x\)
\(g(x) = \sqrt{8x\)
To calculate (fg)(x), we have:
\(f(x) = \sqrt{2x\)
This gives
\(f(g(x)) = \sqrt{2g(x))\)
Substitute \(g(x) = \sqrt{8x\)
\(f(g(x)) = \sqrt{2*\sqrt{8x}\)
Simplify
\(f(g(x)) = \sqrt{4\sqrt{2x}\)
Hence, the value of the composite function f(g(x)) is \(\sqrt{4\sqrt{2x}\)
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Answer:
f.g x = 4x
Step-by-step explanation:
For which inequality is x = 7 a solution?
Answers
Answer:
letter C HOPE it helps.............
Answer:
B. 15 + x < 24
Step-by-step explanation:
12 + 7 = 19 which is > 16 not < so no
15 + 7 = 22 which is < 24 so yes
16 + 7 = 23 which is = 23 not < so no
17 + 7 = 24 which is < 26 not > so no
24 + 7 = 31 which is = 31 not > so no
.In order to increase the value of the F statistic, which of the following must occur?
a. MSwithin > MSbetween
b. MSwithin = MSbetween
c. MSwithin < MSbetween
d. Ratio = 1
Answers
If MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.
How the F statistic is calculated?The F statistic is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). Therefore, to increase the value of the F statistic, either the numerator (MSbetween) needs to increase, or the denominator (MSwithin) needs to decrease.
So, the answer is:
a. MSwithin > MSbetween
If the variance within groups (MSwithin) is reduced or the variance between groups (MSbetween) is increased, the F statistic will increase. Therefore, if MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.
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Which is an accurate conclution regarding the system of equations below ? Y=2/3x-1 and Y=3-2/3x
Answers
Answer:
Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 ...
Step-by-step explanation:
Answer:25
Step-by-step explanation: gnfxnhhfcngn bhh fxbx
a professor wanted to know what proportion of college students believe in ghosts. she polled 200 students and found that 58% said they believe in ghosts. create a 99% confidence interval for the true proportion of college students believing in ghosts.
Answers
Answer:
42%
Step-by-step explanation: