If regular hexagon, regular octagon are inscribed in circle, perimeter of hexagon is greater than perimeter of octagon, each perimeter is greater than circumference of circle. Therefore, statement B is true.
The perimeter of a polygon is the sum of the lengths of all its sides. In a regular polygon, all sides have equal length, so the perimeter is simply the number of sides multiplied by the length of one side. The circumference of a circle is the distance around its outer edge.
Since both polygons are inscribed in the same circle, they have the same circumcircle, which means that their perimeters are both less than the circumference of the circle.
To compare the perimeters of the two polygons, we need to know the number of sides of each polygon and the length of one side. A regular hexagon has six sides, and a regular octagon has eight sides. Since the circle is inscribed in both polygons, the sides of each polygon are tangents to the circle, forming right angles with the radii of the circle.
Thus, we can draw a right triangle with the radius of the circle as the hypotenuse, and the side of the hexagon (or octagon) as one leg. Using trigonometry, we can find the length of one side of the hexagon (or octagon) in terms of the radius of the circle.
After calculating the lengths of one side of each polygon, we can compare their perimeters. It turns out that the perimeter of the octagon is greater than the perimeter of the hexagon, since the octagon has more sides.
Therefore, statement B is true.
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Complete question is:
A regular hexagon and a regular octagon are both inscribed in the same circle. which of these statements is true?
A) the perimeter of the hexagon is less than the perimeter of the octagon, and each perimeter is less than the circumference of the circle.
B) the perimeter of the hexagon is greater than the perimeter of the octagon, and each perimeter is greater than the circumference of the circle.
13. d(-8, 1), e(-3, 6), f(7,4), g(2, -1) (distance formula)
The distances between the points are approximately 7.07, 10.20, and 7.07.
To find the distance between the points d(-8, 1) and e(-3, 6), we use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(-3 - (-8))^2 + (6 - 1)^2]
distance = √[5^2 + 5^2]
distance = √50
distance ≈ 7.07
To find the distance between the points e(-3, 6) and f(7, 4), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(7 - (-3))^2 + (4 - 6)^2]
distance = √[10^2 + (-2)^2]
distance = √104
distance ≈ 10.20
To find the distance between the points f(7, 4) and g(2, -1), we again use the distance formula:
distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the values, we get:
distance = √[(2 - 7)^2 + (-1 - 4)^2]
distance = √[(-5)^2 + (-5)^2]
distance = √50
distance ≈ 7.07
So, the distances between the points are approximately 7.07, 10.20, and 7.07.
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complete question:
Determine the distance between DE, EF and FG.
D(-8, 1), E(-3, 6), F(7, 4), G(2, -1)
Riley and her family move from the Midwest all the way to San Francisco. The equation
2x - 100 = 4,006
can be used to find x, the number of miles her family drove. How many miles did her
family drive?
Riley and her family move from the Midwest all the way to San Francisco. The equation 2x - 100 = 4,006 can be used to find x, the number of miles her family drove. Riley's family drove 2,053 miles from the Midwest to San Francisco.
Find the number of miles Riley's family drove from the Midwest to San Francisco, we need to solve the equation 2x - 100 = 4,006 for x.
First, we'll add 100 to both sides of the equation to isolate the variable term:
2x - 100 + 100 = 4,006 + 100
Simplifying:
2x = 4,106
isolate x, we'll divide both sides of the equation by 2:
2x/2 = 4,106/2
Simplifying:
x = 2,053
Therefore, Riley's family drove 2,053 miles from the Midwest to San Francisco.
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Ruth has a street lamp in front of her house, represented by AB . Her mom insists that at night she only plays within its light. If AB = 54,
Using trigonometry, the length that Ruth has to play in if she plays between her friend's house (point D) and the edge of the lighted area (point C) is 6.72 feet. Option C is the correct answer.
To solve this problem, we need to use trigonometry. We can see that triangle ABD is a right triangle, so we can use the tangent function to find the length of AD.
First, we need to find the length of BD. We can use the right triangle trigonometry again to find it.
tan(27) = BD/AB
BD = AB × tan(27)
BD = 54 × tan(27)
BD ≈ 24.12
Now, we can use the right triangle trigonometry on triangle BCD to find the length of CD.
tan(41) = CD/BD
CD = BD × tan(41)
CD ≈ 18.85
Finally, we can use the Pythagorean theorem on triangle ACD to find the length of AD.
AD² = AC² - CD²
AD² = 20² - 18.85²
AD ≈ 6.72
Therefore, the length that Ruth has to play is approximately 6.72 feet.
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The question is -
Ruth has a street lamp in front of her house, represented by Segment AB The street Lamp is 20 feet tall. Her mom insists that at night she only plays within its light. If AB = 54, the length that Ruth has to play in if she plays between her friend's house (point D) and the edge of the lighted area (point C)?
Options are:
a. 1.7 feet
b. 2.2 feet
c. 6.7 feet
d. 5.9 feet
Rewrite each equation without absolute value for the given conditions. y= |x+5| if x>-5
Answer:
When x is greater than -5, the expression inside the absolute value bars is positive, so we can simply remove the bars.
So the equation y = |x+5| can be rewritten as:
y = x+5 (when x > -5)
A number greater than 9 is called cute if when we add the product of the digits to
the sum of the digits, the result is the original number. For example 29 is cute since
2 + 9 + 2 × 9 = 29, but 513 isn’t cute since 5 + 1 + 3 + 5 × 1 × 3 6= 513. How many
cute numbers are there?
There are 6 cute numbers in total which are 14, 19, 49, 55, 79, 85.To find the cute numbers, we need to check all numbers greater than 9 and see if they satisfy the cute condition.
Let's start by analyzing the digits of a number. Suppose the number has two digits, x and y. The cute condition requires:
x + y + xy = 10x + y
Rearranging this equation, we get:
xy - 9x = y - x
xy - x - y = -9x
(x - 1)(y - 1) = 9x - 1
For a number to be cute, the right-hand side of the equation must be divisible by the left-hand side. Since 9x - 1 is odd, the left-hand side must also be odd, which means one of the factors (x - 1) or (y - 1) must be odd and the other even.
We can now check all possible pairs of (x,y) that satisfy this condition. We find that the cute numbers are:
14, 19, 49, 55, 79, 85. Therfore, there are total 6 cute numbers.
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What type of triangle would be represented by the vertices (1, 3), (4, -1), and (5, 6)?
I need help. Assume the base is 2
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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An appliance store manager noted that
sales varied directly with the amount of money
spent on advertising. If last week's sales were
$10,000 and $2000 was spent on advertising,
what should sales be during a week that $1200
was spent on advertising?
In the given problem, solving systematically, sales should be $6,000 during a week that $1,200 was spent on advertising.
How to Calculate the Sales?If sales vary directly with the amount of money spent on advertising, it means that the ratio of sales to advertising spending is constant. We can use this ratio to find out what sales should be during a week that $1200 was spent on advertising.
Let the ratio of sales to advertising spending be denoted by k. Then, we have:
k = sales / advertising spending
From the information given, we know that:
k = 10,000 / 2,000 = 5
This means that for every dollar spent on advertising, $5 in sales are generated.
To find out what sales should be during a week that $1200 was spent on advertising, we can use the ratio k:
sales = k * advertising spending
sales = 5 * 1200
sales = 6000
Therefore, sales should be $6,000 during a week that $1,200 was spent on advertising.
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100 POINTS!!!! PLEASE HELP!! ITS DUE IN 1 HOUR!!!!!!!!!!!!!!
A plane leaves Singapore airport at 07:45 to fly to Sydney. The plane flies at an average speed of 757.2 km/h. The distance from Singapore to Sydney is 6310 km. The time in Sydney is 2 hours ahead of Singapore time. Calculate the local time when the plane arrives in Sydney. Give your answer in the form hours:minutes using the 24-hour clock.
The local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
How to find arrival time for the plane?The time difference between Speed and Sydney is 2 hours, and the plane will take some time to fly from Singapore to Sydney at an Speed of 757.2 km/h over a distance of 6310 km.
The time it takes the plane to fly from Speed to Sydney can be calculated as:
time = distance / Speed= 6310 km / 757.2 km/h = 8.33Speed
So the plane will take 8.33 hours to fly from Singapore toSpeed
Now we need to add the 2-hour time difference between Singapore and Sydney to determine the local time in Sydney when the plane arrives.
07:45 (Singapore time) + 8.33 hours (flight time) + 2 hours (time difference) = 18:58
Therefore, the local time in Sydney when the plane arrives will be 18:58, or 6:58 PM on a 24-hour clock.
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Jules took the first piece of a pizza, and Margo noticed that, by doing so, Jules made an angle. Jules estimated he made a 20 degree angle and Margo estimated he made a 45 degree angle. Who is right? How did you determine your answer?
Margo is right; Jules made a 45 degree angle.
How can we determine who is right about the angle measurement?To determine who is right about the angle made by Jules while taking the first piece of pizza, we need to compare their estimates of 20 degrees and 45 degrees.
Since angles are measured using a protractor or other measuring tools, we rely on accurate measurement techniques to determine their values. If both Jules and Margo used appropriate measuring tools and techniques, we would expect their measurements to be close.
However, a 20-degree angle is significantly smaller than a 45-degree angle. Therefore, based on the provided information, Margo's estimate of a 45-degree angle seems more reasonable and likely to be correct.
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Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he
began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his
body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)' where Wis
his weight in pounds and t is the time in weeks that he has been on the diet.
What was his weight in pounds after 5 weeks?
How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Antonio's weight after 5 weeks was 202.34 pounds, and it took him 19 weeks to weigh in at 161.05 pounds.
To find Antonio's weight after 5 weeks, we can simply substitute t = 5 into the given exponential function:
W(5) = 235(0.985)⁵
W(5) ≈ 209.88 pounds
So his weight after 5 weeks was approximately 209.88 pounds. To find how long it took him to weigh in at 161.05 pounds, we can set the function equal to 161.05 and solve for t:
161.05 = 235(0.985)ᵗ
0.685106383 ≈ 0.985ᵗ
t ≈ 25.5 weeks
So it took him approximately 25.5 weeks to weigh in at 161.05 pounds
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Complete question - Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)ᵗ where W is his weight in pounds and t is the time in weeks that he has been on the diet. What was his weight in pounds after 5 weeks? How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Marcella drew a scale drawing of her plan to plant 6 rows of 8 trees in her orchard. The orchard is 70 meters long and 50 meters wide. Marcella used a 7-inch-wide rectangular grid for the drawing. What is the scale Marcella used for her drawing?
The scale Marcella used for her drawing is 7 inches : 50 meters
Calculating the scale used for her drawingThe statements in the question are given as
Dimension of the orchard is 70 meters long and 50 meters wide. Width of the scale drawing = 7 inches rectangular gridThe above statements imply that we have the following scale ratio
Scale = Scale measurement : Actual measurement
When the given values are substituted in the above equation, the equation becomes
Scale = 7 inches : 50 meters
The above cannot be simplified because 7 and 50 do not have common factors
So, it means that the scale Marcella used for her drawing is 7 inches : 50 meters
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1. Sanchez deposited $3,000 with a bank in a 4-year certificate of deposit yielding 6% interest
compounded daily. Find the interest earned on the investment. (4pts)
The compound interest generated on the investment is roughly $813.67, which is the solution to the question based on compound interest.
What is Principal?The initial sum of money invested or borrowed, upon which interest is based, is referred to as the principle. The principal is then periodically increased by the interest, often monthly or annually, to create a new principal sum that will accrue interest in the ensuing period.
Using the compound interest calculation, we can determine the interest earned on Sanchez's investment:
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}[/tex]
where A is the overall sum, P denotes the principal (the initial investment), r denotes the yearly interest rate in decimal form, n denotes the frequency of compounding interest annually, and t denotes the number of years.
In this case, P = $3,000, r = 0.06 (6%), n = 365 (compounded daily),
and t = 4.
Plugging in the values, we get:
[tex]A = 3000(1 + \frac{0.06}{365} )^{(365*4)}[/tex]
A= $3813.67
The difference between the final amount and the principal is the interest earned.
Interest = A - P
Interest = $3813.67 - $3000
Interest = $813.67
As a result, the investment's interest yield is roughly $813.67.
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1. Simplify (Write each expression without using the absolute value symbol. )
|120+x| if x<-120
2. Simplify (Write each expression without using the absolute value symbol. )
|x-120| if x<-120
3. Simplify (Write each expression without using the absolute value symbol. )
|x-(-12)| if x>-12
4. Simplify (Write each expression without using the absolute value symbol. )
|x-(-12)| if x<-12
By solving each expression without using the absolute value symbol are:-
1. -x-120 if x<-120
2. -(x-120) if x<-120
3. x+12 if x>-12
4. -(x+12) if x<-12
To simplify each expression without using absolute value symbols, we need to determine the cases when the expression inside the absolute value bars is positive and negative. Then we can remove the absolute value bars and simplify the expression accordingly.
For the first expression, |120+x|, if x is less than -120, then x+120 will be negative. Therefore, we can simplify the expression as -x-120.
For the second expression, |x-120|, if x is less than -120, then x-120 will also be negative. Therefore, we can simplify the expression as -(x-120).
For the third expression, |x-(-12)|, if x is greater than -12, then x-(-12) is positive. Therefore, we can simplify the expression as x+12.
For the fourth expression, |x-(-12)|, if x is less than -12, then x-(-12) is negative. Therefore, we can simplify the expression as -(x+12).
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For the function f (x) x = 2 to r 2 to X = 2.001. . x3, find the slope of secant over the interval A. slope = 10. 001001 B. slope = 1.006001 C. slope 2. 001001 D. slope - 12. 006001
To find the slope of the secant over the interval from x=2 to x=2.001, we need to use the formula for the slope of a secant line:
slope = (f(2.001) - f(2)) / (2.001 - 2)
First, we need to find the values of f(2.001) and f(2):
f(2) = 2^3 = 8
f(2.001) = 2.001^3 ≈ 8.012006001
Plugging these values into the formula, we get:
slope = (8.012006001 - 8) / (2.001 - 2)
slope ≈ 1.006001
Therefore, the slope of the secant over the interval from x=2 to x=2.001 is approximately 1.006001. So the answer is B. slope = 1.006001.
To find the slope of the secant line for the function f(x) over the interval [2, 2.001], we will use the slope formula:
slope = (f(2.001) - f(2)) / (2.001 - 2)
First, find the values of f(2) and f(2.001) by plugging the values of x into the given function f(x) = x^3:
f(2) = 2^3 = 8
f(2.001) = (2.001)^3 ≈ 8.006012
Now, plug these values into the slope formula:
slope = (8.006012 - 8) / (2.001 - 2) = 0.006012 / 0.001 = 6.012
The slope of the secant line over the interval is approximately 6.012. The given options do not match this result, so it's possible there is an error in the provided choices.
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A number 5 times as big as M
Answer:
Step-by-step explanation:
If we let M be a number, then 5 times as big as M would be 5M. Not that hard :/
Between which 2 days does the biggest change occour
Answer:
=Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year.
Step-by-step explanation:
Answer:Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year.
Step-by-step explanation:
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Which statements are true for both functions y = cos(8) and y = sin(0)? Select all that apply. 1 The function is periodic. The maximum value is 1. The maximum value occurs at 8 = 0. The period of the function is 27. The function has a value of about 0.71 when = The function has a value of about 0.71 when = 3
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Step-by-step explanation:
A plumber charges 14.95 to come to the house and 27.50 per hour the plumber sends a 138.70 bill
The plumber worked for 4.5 hours and charged $138.70 for their services
How we find the time plumber work?To find out how many hours the plumber worked, we first need to subtract the initial charge of $14.95 from the total bill of $138.70.
$138.70 - $14.95 = $123.75
This gives us the amount that the plumber charged for the hours worked. Now, we can divide this amount by the hourly rate to find the number of hours:
$123.75 ÷ $27.50 per hour = 4.5 hours
However, we need to convert the decimal part (0.5) into minutes. We can do this by multiplying it by 60:
0.5 x 60 = 30 minutes
But we need to add the initial charge of $14.95 to get the final answer.
4 hours and 30 minutes is equivalent to 4.5 hours.
4.5 hours x $27.50 per hour = $123.75
$123.75 + $14.95 = $138.70
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Find the exact values of sin 2. cos2u. and tan 2u using the double angle formulas Cos u =- 4/5 π/2 < u < π sin 2u = cos 2u= tan 2u =
The probability of drawing either a two or a ten from a standard deck of 52 cards is the sum of the probabilities of drawing a two and drawing a ten.
There are four twos and four tens in the deck, so the probability of drawing a two is 4/52 and the probability of drawing a ten is 4/52. Therefore, the probability of drawing either a two or a ten is:
4/52 + 4/52 = 8/52 = 2/13
The probability of drawing either a two or a club from a standard deck of 52 cards is the sum of the probabilities of drawing a two and drawing a club, minus the probability of drawing the two of clubs (since we have already counted it). There are four twos and 13 clubs in the deck, including the two of clubs. Therefore, the probability of drawing a two is 4/52, the probability of drawing a club is 13/52, and the probability of drawing the two of clubs is 1/52. Therefore, the probability of drawing either a two or a club is:
4/52 + 13/52 - 1/52 = 16/52 = 4/13
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2.
(03. 02 MC)
Kayla was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
−9, which represents the depth of water in the swimming pool
+10, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)
Part C: Kayla held a pole in the swimming pool. The bottom of the pole was at a depth of 3 feet. How should Kayla mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)
0 represents the surface level of the swimming pool.
The height of the slide in relation to 0 is +10 feet.
Part A: In this situation, 0 represents the surface level of the swimming pool on the number line, acting as a reference point between the depth of the water and the height of the slide.
Part B: The height of the slide in relation to 0 is +10 feet. This means the slide is 10 feet above the surface level of the swimming pool.
Part C: To mark the level of the bottom of the pole on the number line, Kayla should mark it at -3 since the bottom of the pole is at a depth of 3 feet below the surface level of the pool.
This is determined by using the negative value to represent the depth below the surface (0).
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1) A politician is about to give a campaign speech and is holding a 'stack of ten cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack? A) 0. 139% B) 3. 333% C) 0. 794% D) 0. 03%â
The probability that cards #1, #2, and #3 are still in order on the top of the stack is 0.03%. Therefore, the correct option is D.
To find the probability, we need to calculate the number of ways in which the first 3 cards can remain in order on the top of the stack, and divide it by the total number of ways the cards can be arranged.
The number of ways in which the first 3 cards can remain in order is 3! (3 factorial), because there are 3 cards and they can be arranged in 3! = 6 ways.
The total number of ways the cards can be arranged is 10!, because there are 10 cards and they can be arranged in 10! = 3,628,800 ways.
So, the probability is:
3! / 10! = 6 / 3,628,800 = 0.000166 = 0.0166%
We can convert it to a percentage by multiplying by 100:
0.0166 x 100 = 1.66%
However, this is the probability that the first 3 cards are in a specific order, not necessarily the original order. Since the question asks for the probability that the original order is maintained, we need to divide the probability by 3!, which gives:
0.0166 / 3! = 0.000277 = 0.0277%
This is closest to answer choice D) 0.03%.
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only answer if you know! NO SPAM PLEASE. Must show all calculations and answer both questions!! Please make sure you double check your answer! Will mark brainliest!
Answer:
5. 0
6. a: π/3; b: 45π/2 m ≈ 70.69 m; c: 30/π min ≈ 9.549 min; d: π/900 rad/s; e: 0.2°/s
Step-by-step explanation:
You want the exact value of cos(-39π/6), and some angles, distances, and speeds related to the London Eye Ferris wheel.
5. Exact valueThe argument of the cosine function can be reduced:
[tex]\cos{\left(-\dfrac{39\pi}{6}\right)}=\cos{\left(\dfrac{13\pi}{2}\right)}\qquad\text{using cos(-x)=cos(x)}[/tex]
We notice this is an odd multiple of π/2, so its value is 0.
cos(-39π/6) = 0
6. London Eyea) Angle in 5 minutesThe rate of movement is given as 2π radians (one revolution) in 30 minutes. Then the angle in 5 minutes is ...
(5 min)(2π rad)/(30 min) = (2π/6) rad = π/3 rad
The passenger will travel π/3 radians in 5 minutes.
b) Distance in 5 minutesThe arc length is given by ...
s = rθ . . . . . . where r is the radius and θ is the central angle in radians
For a radius of (135/2 m) and an angle of π/3 radians, the distance traveled is ...
s = (135/2 m)(π/3) = 45π/2 m ≈ 70.69 m
c) Time for 2 radiansWe know that 2π radians takes 30 minutes, so the time for 2 radians is ...
t = (2 rad)·(30 min)/(2π rad)
t = 30/π min ≈ 9.549 min . . . . about 9:32.96 min
d) Radians per secondThe angular velocity is ...
(2π rad)/(30 min) = (2π rad)/(30 min) × (1 min)/(60 s) = 2π/1800 rad/s
= π/900 rad/s
e) Degrees per second360 degrees in 1800 seconds is ...
360°/(1800 s) = (1/5)°/s
The wheel turns at the rate of 1/5 degree per second.
__
Additional comment
At one revolution per half hour, the wheel turns about twice as fast as the minute hand on a clock. This explains why the wheel never appears to be moving when observed from a distance, as when it appears briefly in a movie.
dy/dx = e√x/y, y(1) = 4
The solution to the differential equation is:
[tex]y = e^{(2\sqrt{y} - 0.6137)}[/tex]
To solve this differential equation, we can use the method of separation
of variables. This involves isolating the variables x and y on different
sides of the equation and then integrating both sides with respect to
their respective variables.
Starting with the given equation:
[tex]dy/dx = e^{(\sqrt{(x/y)} )}[/tex]
We can begin by multiplying both sides by dx:
[tex]dy = e^{(\sqrt{(x/y)} ) dx}[/tex]
Now we can separate the variables and integrate both sides:
[tex]\int(1/y)dy = ∫e^{(\sqrt{(x/y))dx} }[/tex]
ln|y| = 2√y + C1 ...where C1 is a constant of integration
To solve for y, we can exponentiate both sides:
[tex]|y| = e^{(2\sqrt{y} + C1)}[/tex]
Since y(1) = 4, we can use this initial condition to determine the sign of y and the value of C1:
[tex]4 = e^{(2\sqrt{4} + C1)} \\4 = e^{(4 + C1)}[/tex]
ln(4) = 4 + C1
C1 = ln(4) - 4 = -0.6137
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I NEED HELP this is grade 9 math
The measure of angles ADC is 30⁰.
The measure of angles DCA is 120⁰.
The measure of angles DCB is 180⁰.
The measure of angles AEB is 30⁰.
What is angle ADC?The measure of each of the angles is calculated as follows;
if length AB = length CD, then AC = AB
Also triangle ACB = equilateral triangle, and each angle = 60⁰.
Angle DAB = 90 (since line DB is the diameter)
Angle DAC = angle ADC
DAC = 90 - 60 = 30 = ADC
DCA = 180 - (30 + 30) (sum of angles in a triangle)
DCA = 120⁰.
The value of angle DCB is calculated as follows;
DCB = 180 (sum of angles on straight line)
angle AEB = angle ADC (vertical opposite angles )
angle AEB = 30⁰
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You invest ten thousand dollars in an account that pays eight percent APR compounded monthly. After how many years will the account have twenty thousand dollars.
As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.
what is percentage ?As a quarter of 100, a number can be expressed as a percentage. It is frequently used to describe distinctions or express changes in numbers. The symbol for percentages is %, and they are frequently utilized to describe ratios, rates, and certain other numerical connections. An 80 percent score on a test, for instance, indicates that the student correctly answered 80 of the 100 questions. Similar to this, if a retailer were offering a 20% discount on a $100 item, the sale price would be $80.
given
With P = 10000, r = 0.08 (8% stated as a decimal), n = 12 (compound monthly), and t to be found when A = 20000, the situation is as follows.
When these values are added to the formula, we obtain:
[tex]20000 = 10000(1 + 0.08/12)^(12t) (12t)[/tex]
By multiplying both sides by 1000, we obtain:
[tex]2 = (1 + 0.08/12)^(12t) (12t)[/tex]
When we take the natural logarithm of both sides, we obtain:
ln(2) = 12t ln(1 + 0.08/12)
When we multiply both sides by 12 ln(1 + 0.08/12), we obtain:
t = ln(2) / (12 ln(1 + 0.08/12))
Calculating the answer, we discover:
10.24 years is t.
As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.
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Help me please!
use either method to construct a line parallel to the given line through the given point. gl 3.1)
a lab 1 question 1
To construct a line parallel to a given line through a given point, there are two methods that can be used: the ruler and compass method or the parallel line equation method.
The ruler and compass method involves drawing a line through the given point that intersects the given line at a right angle. Then, using the compass, the distance between the given point and the intersection point is measured and transferred to a point on the given line. Finally, a line is drawn through the given point and the point on the given line to create a parallel line.
The parallel line equation method involves using the slope of the given line to find the slope of the parallel line. This is done by recognizing that parallel lines have the same slope. Then, using the point-slope equation of a line, the parallel line equation can be found by plugging in the given point and the calculated slope.
In summary, constructing a line parallel to a given line through a given point can be achieved using either the ruler and compass method or the parallel line equation method. Both methods are valid and can be used depending on personal preference and familiarity with the mathematical concepts involved.
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Last week, hayden rode his bike 5 times. each time, he biked a 3-mile path, a 2-mile path, and a 2 1 4 -mile path. which expression represents the total number of miles he biked? a. 5 × ( 3 2 2 1 4 ) b. 5 ( 3 × 2 × 2 1 4 ) c. 5 × ( 3 × 2 × 2 1 4 ) d. 5 ( 3 2 2 1 4 )
The correct expression to represent the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)
This is because each time Hayden rode his bike, he biked a 3-mile path, a 2-mile path, and a 2 1/4 -mile path. To find the total number of miles he biked, we need to add up the distance he biked each time and then multiply by the number of times he biked.
Using the distributive property of multiplication over addition, we can rewrite the expression as:
= 5 × (3 + 3 + 2 1/4)
Therefore, Hayden biked a total of 41 1/4 miles. The correct answer is A
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Can somebody please just give me an example problem for exponential decay? I will give brainliest, thanks!
Example problem:
A radioactive substance has a half-life of 10 years. If there are initially 100 grams of the substance, how much will be left after 30 years?Solution:
Using the formula for exponential decay:
[tex]\sf\qquad\dashrightarrow N(t) = N0 * e^{(-kt)}[/tex]
where:
N(t) is the amount of the substance at time tN0 is the initial amountk is the decay constante is the mathematical constant approximately equal to 2.718Since the half-life is 10 years, we know that:
[tex]\sf\qquad\dashrightarrow k = \dfrac{\ln(0.5)}{10} = -0.0693[/tex]
(where ln is the natural logarithm)Substituting the given values, we get:
[tex]\sf:\implies N(30) = 100 * e^{(-0.0693 * 30)}[/tex]
[tex]\sf:\implies N(30) = 100 * e^{(-2.079)}[/tex]
[tex]\sf:\implies N(30) = 100 * 0.126[/tex]
[tex]\sf:\implies \boxed{\bold{\:\:N(30) = 12.6\: grams\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, after 30 years, only 12.6 grams of the radioactive substance will be left.
In a ABCD Rhombus, B angle minus A equals 20 degrees. What degrees are all the angles of the Rhombus if B-A=20°?
All the angles of the Rhombus if B-A=20 is angle A = angle C = 80°, and angle B = angle D = 100°.
In a rhombus ABCD, if angle B minus angle A equals 20 degrees (B-A=20°), we can find the degree measures of all the angles.
Step 1: Recognize that in a rhombus, opposite angles are equal. Therefore, angle A = angle C and angle B = angle D.
Step 2: Remember that the sum of the angles in any quadrilateral is 360 degrees. In a rhombus, since the opposite angles are equal, we can represent this as: 2A + 2B = 360°
Step 3: Use the given information, B - A = 20°, to solve for one of the angles. For this, rearrange the equation to isolate B: B = A + 20°
Step 4: Substitute the expression for B from step 3 into the equation from step 2: 2A + 2(A + 20°) = 360°
Step 5: Solve the equation for angle A. 2A + 2A + 40° = 360° → 4A + 40° = 360° → 4A = 320° → A = 80°
Step 6: Now that we have angle A, use the expression from step 3 to find angle B: B = 80° + 20° = 100°
Step 7: Since A = C and B = D, we can now state all the angles of the rhombus ABCD: angle A = angle C = 80°, and angle B = angle D = 100°.
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