Answers
17 minutes ⇒ 1 revolution = 2π
1 minute ⇒ 2π/17
Angle of rotation is 2π/17 per minute
Question c)
The period of the rotation is 2π/17
The wheel starts rotating from the height of 5 meters from the ground and the maximum height is 125 meter from the ground.
The amplitude is 125 - 5 = 120 ÷ 2 = 60
The midline of the rotation is at 125 - 5= 120 ÷2 = 60 + 5 = 65 (this is the location of the centre of the wheel). This value is a shift of 65 from the zero midlines (which in this case would be the ground)
Question C
The movement of the wheel can be described as starting from 0° then reaching its peak at 180° and come back to its original position as it stops and it makes a complete circular turn 360°.
If we sketch this on a graph, we will obtain a curve of -cos(x)
We need to apply the period, the amplitude and the shift produced by this rotation into the equation [tex]y = -cos(x)[/tex]
The period is [tex] \frac{2 \pi }{7} [/tex] ⇒ [tex]f(t)=-cos( \frac{2 \pi }{7}t) [/tex]
The amplitude of 60 ⇒ [tex]f(t)=-60cos( \frac{2 \pi }{7}t) [/tex]
The shift of the midline by 65 units upwards ⇒ [tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]
The final equation is
[tex]f(t) = -60cos( \frac{2 \pi }{7}t)+65 [/tex]
and the graph is shown in the third picture below
Related Questions
What is the inverse of 2x-6y=1
Answers
Answer the word problem:
Taylor and Blair are driving away from each other in opposite directions. If Blairs speed is 70mph and Taylors speed is 80mph, how many hours will it be before the two are 225 miles apart?
Answers
It will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
To find out how many hours it will be before Taylor and Blair are 225 miles apart, we can set up an equation based on the distance they travel.
Since they are driving away from each other in opposite directions, their distances add up to the total distance they will be apart.
Let t be the number of hours it takes for them to be 225 miles apart.
Distance traveled by Blair = Blair's speed * time (d = r * t)
Distance traveled by Taylor = Taylor's speed * time (d = r * t)
The total distance they will be apart is 225 miles:
Blair's distance + Taylor's distance = 225 miles
(70 mph * t) + (80 mph * t) = 225 miles
Now, solve for t:
70t + 80t = 225
150t = 225
t = 225 / 150
t = 1.5
So, it will take 1.5 hours (or 1 hour and 30 minutes) before Taylor and Blair are 225 miles apart.
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A rectangular area is to be fenced in with 600 feet of chicken wire. find the maximum area that can be enclosed.
Answers
the area of the area is max when it's a square
the length of the square is 600/4 = 150
so the max area that can be enclosed is:
150×150 = 22500 ft square
The maximum area that can be enclosed is 22500 feet²
A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.
Let x represent the length and y represent the width. Hence:
perimeter = 2(length + width)
600 = 2(x + y)
300 = x + y
y = 300 - x
The area of a rectangle (A) = length * width
A = x * (300 - x)
A = 300x - x²
The maximum area is at dA/dx = 0, hence:
dA/dx = 300 - 2x
300 - 2x = 0
2x = 300
x = 150 feet
y = 300 - x = 300 - 150 = 150 feet
The maximum area = x * y = 150 * 150 = 22500 feet²
The maximum area that can be enclosed is 22500 feet²
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On the evening news, the meteorologist states that there is a 70% chance that it will rain the next morning. Select all the statements that are true.
YOU CAN PICK MORE THAN ONE
A. It is neither unlikely nor likely that it will rain the next day.
B. It is certain that it will rain the next day.
C. It is likely that it will not rain the next day.
D. It is unlikely that it will rain the next day.
E. It is unlikely that it will not rain the next day.
F. It is likely that it will rain the next day.
Answers
Answer:
E. It is unlikely that it will not rain the next day.
F. It is likely that it will rain the next day.
Which function has the range (-infinity,0)u(2,infinity)?
A. y = sex x
B. y = cot (2x) - 1
C. y = cos (x+1)
D. y = csc(x) + 1
Answers
Answer:y=csc(x) -1
Step-by-step explanation:
The correct answer is option D. y = csc(x)+1
To determine which function has the range (-infinity, 0) U (2, infinity), we need to analyze each option:
A. y = sec(x): The range of sec(x) is [tex](-\infty,-1] \cup[1,\infty)[/tex], not matching our target range.B. y = cot(2x) - 1: The range of cot(x) is [tex](-\infty,\infty)[/tex], so cot(2x) also has a range of [tex](-\infty,\infty[/tex]). Shifting it down by 1 unit, the range becomes [tex](-\infty, \infty) - 1 = (-\infty, \infty)[/tex], also not matching.C. y = cos(x + 1): The range of cos(x) is [-1, 1], so cos(x + 1) still has a range of [-1, 1] after translating horizontally, which does not match.D. y = csc(x) + 1: The range of csc(x) is [tex](-\infty,-1]\cup[1,\infty)[/tex]. When we add 1 to it, we get [tex](-\infty,0]\cup[2,\infty)[/tex] - which simplifies to our target range of [tex](-\infty,0]\cup[2,\infty)[/tex].Therefore, the function is y = csc(x) + 1.
Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation: box plot labeled Orlando with min at 64.5, Q1 at 65.5, median at 67.5, Q3 at 71.5, max at 72.5. Box plot labeled Tampa Bay with min at 60, Q1 at 63.5, median at 66.25, Q3 at 72.5, max at 74 Which city should Dominick visit, and why? He should visit Orlando. It has a greater IQR. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. He should visit Tampa Bay. The highest temperature occurred there. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.
Answers
He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. This is the correct answer, as we are only interested in the average temperature in both cities in deciding which to go to. The larger the range (max - min values) or interquartile range (range of central box), the more spread out the temperatures are around the median. As Orlando's range and interquartile range is lower than Tampa Bay's, and its median (middle value in the data set of temperatures) is higher, Dominick would, on average, have more chance of visiting Orlando on a day when it was warmer than Tampa Bay than the other way around.
The correct answer is option b. Dominick should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
Option b is correct because if Orlando has a higher median temperature, this suggests that the middle value of the temperatures in Orlando is higher than in Tampa Bay. Additionally, a smaller range indicates less variability, suggesting more consistent warm temperatures. Therefore, the higher median and smaller range are strong indicators that, on average, the temperatures in Orlando are warmer.
Why other options are incorrect:
Option a is incorrect because the Interquartile Range (IQR) represents the middle 50% of the data. While a greater IQR indicates a larger spread in the middle 50% of the temperatures, it doesn't necessarily mean the average temperature is higher.
Option c is incorrect while Tampa Bay having the highest temperature might indicate that it reached the highest peak temperature, this single data point does not provide enough information about the overall average or consistency of warm temperatures. The highest temperature alone doesn't guarantee that the city is warmer on average.
Option d is incorrect because a larger range indicates a wider spread of temperatures, which could mean more variability. This does not necessarily mean that any given day will be warm; it could also mean that there are very low temperatures included in that range.
The complete question is
Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot shows the temperatures from the previous year during the time that Dominick will take his vacation:
Which city should Dominick visit, and why?
a. He should visit Orlando. It has a greater IQR.
b. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
c. He should visit Tampa Bay. The highest temperature occurred there.
d. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.
HELP! 20 POINTS!!! Graph the system of inequalities on your paper. Please provide only one ordered pair (x, y) that will work for both system of inequalities.
To earn full credit you must prove your answer by substituting the (x, y) order pair into both inequalities. Show all work for each inequality.
y < 4x + 3
y > -3x - 3
Answers
I need help answering number 8 please
Answers
One interior angle is 56°
One exterior angle is 103° ⇒ we can work out one interior angle 180°-103° = 77°
The other interior angle is 180° - (56°+77°) = 44°
Factor: 100x^2−121
x^2 is x to the second power
Answers
100x² - 121
= (10x +11)(10x-11)
I hope that helps!
express 7x^3/4 in radical form
Answers
If that is the case, [tex]7x^{ \frac{3}{4} }= \sqrt[4]{7x^{3}} [/tex] is the answer.
Answer:
7/34
Step-by-step explanation:
What is the measure of JL
A: 84 degrees
B: 42 degrees
C: 96 degrees
D: 168 degrees
Answers
The measure of arc JL is 168.
Option D is the correct answer.
What is the arc length of a circle?
The arc length of a circle is the distance between two points on the curve of the circle.
We have,
The angle subtended by the minor arc on the circle is half of the arc length.
So,
∠JKL = 84°
The length of arc JL.
= 2 x 84
= 168
Thus,
The length of arc JL is 168.
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y=4x-9
y=x-3
asking another question
appreciate any answers
edit: find x and y
(x,y)
Answers
4x=x+6
3x=6
x=2
y=(2)-3
y= -1
Final answer: (2,-1)
y=4x-9=y=x-3
4x-9=x-3
minus x both sides
3x-9=-3
add 9 to both sides
3x=6
divide by 3 both sides
x=2
sub ack
y=x-3
y=2-3
y=-1
x=2
y=-1
(x,y)
(2,-1)
Give an example of a compound inequality that has no solution
Answers
There is no value of c that is greater than -3 AND less that -8
An example of a compound inequality that has no solution:
x >5 and x < -4.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
|____|____|____|____|____|____|____|____|____|____|
-5 -4 -3 -2 -1 0 1 2 3 4 5
Here is an example of a compound inequality that has no solution:
x >5 and x < -4.
x may be both higher than 5 and less than -4.
Here it is not possible that x can be both lower than -4 and larger than 5.
Hence, these inequalities have no solution.
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A car moved at a constant velocity during the first hour. It stopped for 2 hours at a mall and then moved ahead again at a constant velocity for the next 3 hours. The car finally returned to its starting point with a constant velocity in the next 2.5 hours. Which of the following graphs best represents the car's motion?
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 3, 60, third straight line joins 3, 60 and 6, 30 and fourth straight line joins 6, 30 and 8.5, 0
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 3, 60, third straight line joins 3, 60 and 6, 100 and fourth straight line joins 6, 100 and 8.5, 0
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 3, 60, third straight line joins 3, 60 and 6, 100 and fourth straight line joins 6, 100 and 9.5, 0
First straight line joins ordered pairs 0, 0 and 1, 60, second straight line joins 1, 60 and 6, 100, and third straight line joins 6, 100 and 8.5, 0
Answers
Answer:
First straight line joins ordered pairs 0, 0 and 1, 60; second straight line joins 1, 60 and 3, 60; third straight line joins 3, 60 and 6, 100; and fourth straight line joins 6, 100 and 8.5, 0.
Step-by-step explanation:
Starting at home is starting at (0, 0).
Traveling at the same velocity for an hour will connect (0, 0) to (1, 60).
Stopping at the mall for 2 hours will connect (1, 60) to (3, 60).
Going ahead again at a constant velocity for 3 hours will connect (3, 60) to (6, 100).
Returning to the starting point for 2.5 hours will connect (6, 100) to (8.5, 0).
I need it asap!!!! Plz help 20 POINTS USED PLZ PLZ ASAP
What integer is closest to 13/3 divided by 2/11
Please give ur answer as a simplest fraction not a mixed number
Thanks
Answers
To divide 2 fraction, you multiply the first one by the 'invert of the second.
The 1st one is 13/3
The invert of the 2nd (2/11) is 11/2
Now you multiply: (13/3)x(11/2) = 143/6 ≈ 23.83, so this operation
is closest to 24
Solve 10p + 9 - 11 - p = -2(2p + 4) - 3(2p - 2)
Answers
9p - 2 = -4p - 8 - 6p + 6
9p - 2 = -10p - 2
9p + 10p = -2 + 2
19p = 0
p = 0 <===
The value of p is 0.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
Example:
33 + 3x + 4y = 7 is an expression.
24 - 87 is an expression.
We have,
10p + 9 - 11 - p = -2(2p + 4) - 3(2p - 2)
Simplifying we get,
10p - 2 - p = -4p - 8 - 6p + 6
Combining like terms.
9p - 2 = -10p - 2
Add 2 on both sides.
9p + 10p = -2 + 2
Divide 19 on both sides.
19p = 0
p = 0
Thus,
The value of p is 0.
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the base of a side of a ramp is 3 meters, and the height is 0.6 meters. what is the area of the triangular side of the ramp in square meters
Answers
area = base x height divided by 2
3*0.6 = 1.8/2=0.9 square meters
The coordinate plane below represents a town. Points A through F are farms in the town.
graph of coordinate plane. Point A is at 1, 3. Point B is at 3, 1. Point C is at 3, negative 3. Point D is at negative 4, 2. Point E is at negative 1, 5. Point F is at negative 3, negative 3.
Part A: Using the graph above, create a system of inequalities that only contains points D and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points D and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: Chickens can only be raised in the area defined by y > 3x − 4. Explain how you can identify farms in which chickens can be raised. (2 points)
Answers
Point D (-4, 2) and Point E (-1, 5)
y - y1 = [(y2 - y1)/(x2 - x1)](x - x1)
y - 2 = [(5 - 2/-1 -(-4))](x + 4)
y - 2 = x + 4
y = x + 6
To answer this, input the values of points D or E into the equation and make sure that they answer the equation in part A.
y = x + 6
2 = -4 + 6 = -2 so it satisfies the solution
what is the area of this rhombus?
Answers
(6 1/2 * 12 3/4)/ 2= 41 11/25
area= 41 11/25
****to make things make things easier when solving convert the fractions into decimals****
2p2+3p-4 less -2p2-3p+4
Answers
2p^2 + 3p - 4 + 2p^2 + 3p - 4 =
4p^2 + 6p - 8 <==
Answer:
[tex]4p^{2}+6p-8[/tex]
Step-by-step explanation:
Being a subtraction of polynomials, the second polynomial will change the signs of its terms and then the algebraic sum is done.
[tex]2p^{2} -3p-4 - (-2p^{2} -3p+4)[/tex]
changing the signs
[tex]2p^{2} -3p-4 +2p^{2}+3p-4[/tex]
performing indicated operations
[tex]4p^{2}+6p-8[/tex]
Choose the correct description of the graph of the compound inequality: 3x + 2 > 5 and 3x less than or equal to 9 A:number line with an open circle on 1, shading to the left, and a closed circle on 3, shading to the right B:number line with a closed circle on 1, shading to the left, and an open circle on 3, shading to the right C:number line with a closed circle on 1, an open circle on 3, and shading in between D:number line with an open circle on 1, a closed circle on 3, and shading in between
Answers
3x > 3
x > 1
3x<= 9
x <= 3
there will be an open circle on 1 because it does not include 1 But a closed circle on 3.
1 < x <= 3
So it is D.
Answer:
Step-by-step explanation:
D
write an equation thats parellel to the given line & that passes through the given point y=5/2x-10;(6,-29)
Answers
Explanation: Any lines that are parallel to each other share the same slope but have different y-intercepts. To solve for this problem, keep you would first need to find out the b-value or the y-intercept. To do this, set up the y=mx+b equation and plug the slope into m (5/2). Then, since you know the line has to pass through points (6, -29) you would plug those points into the equation: -29=5/2(6) + b . You will then solve for b and your b-value will be -44. Now, since you know your slope and your y-intercept, you now know your answer is y= 5/2x-44.
A company has an opportunity to bid on three contracts. Determine which would be the best investment given the information in the table below.
CONTRACT
PROFIT, (P)* OF PROFIT...(P)*. TO BREAK EVEN...LOSS, (P)* OF LOSS
Southeast
$45,000, 50%...30%...$6,000, 20%
Southwest
$60,000, 35%...40%...$10,000, 25%
California
$112,000, 20%...40%...$40,000, 40%
*(P)=PROBABILITY
a) Southeast
b) Southwest
c) California
d) All contracts include a probability for loss
Answers
CONTRACT PROFIT, (P)* OF PROFIT...(P)*. TO BREAK EVEN...LOSS, (P)* OF LOSS
Southeast $45,000, 50% 30% $6,000, 20%
Southwest $60,000, 35% 40% $10,000, 25%
California $112,000, 20% 40% $40,000, 40%
I think that the best contract would be with SOUTHEAST. It probability of having a profit is higher than the other two at 50% while its probability of incurring a loss is lesser than the other two at 20%.
Despite the bigger value of its contract profit of the other two, these value will still be greatly affected by its corresponding probabilities.
Answer:
It's A. Southeast
Step-by-step explanation:
What is the value of SM
Answers
9/15 = 12/x =
x = 180/9 = 20
answer is 20
In the diagram below, is an altitude of DEF. What is the length of ? If necessary, round your answer to two decimal places.
Answers
Right triangles EGD and FGE are similar:
(∠G =90, ∠F=∠EDG - having their sides respectively perpendicular)
Then we can write:
EG/FG = GD/GE
7/4 = GD/7 , by cross multiplication→ 7² = 4.GD→ 49 = 4.GD and GD=12.5
2nd Method:
The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse:
Then EG² = DG x GF
7² = 4 x GD and GD = 49/4 = 12.5
A conjecture becomes a theorem after it has been proven true by logic.
True or False
Answers
True, A conjecture becomes a theorem after it has been proven true by logic.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The sentence is,
''A conjecture becomes a theorem after it has been proven true by logic.''
Now, We know that;
Conjectures are unproven claims.
Hence, Once someone proves a conjecture, it is called a theorem.
Thus, A conjecture becomes a theorem after it has been proven true by logic.
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At an airport, its costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x represent the number of hours parked. Write a function that models the cost, C(x), of parking x hours, where x is an integer greater than 1.
A: C(x)=5x+12
B: C(x)=5(x+1)+7
C: C(x)=5(x-1)+7
D: C(x)=5x+7
Answers
the answer would be C
because it is taking the total hours ( x) and subtracting 1 ( the first hour that cost $7
and then multiplying x by the $5 per minute and then adding the $7 for the first hour
WILL GIVE A BRAINLIEST IF UR 100% CORRECT PLEASE HELP!!
On which of the following lines does the point (8, 41) lie?
a.
y=5x+1
b.
y=3x-2
c.
y=-x-7
d.
y=4x-5
Answers
41 = 5(8) + 1
41 = 40 + 1
41 = 41
So, A y = 5x + 1 is the answer.
where does the line y = 3x + 5 cross the y-axis
Answers
So, in the equation y = 3x + 5, 5 is the y-intercept.
When j = 32, m = 2, and p = 1/4. If j varies directly with m and inversely with p, what is the constant of variation?
Answers
32 = 2*k / (1/4)
Multiply both sides by 1/4.
8 = 2k
Divide both sides by 2.
4 = k
When j = 32, m = 2, and p = 1/4. If j varies directly with m and inversely with p, The k is the constant of variation that is 4.
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
When j = 32, m = 2, and p = 1/4. If j varies directly with m and inversely with p
j = mk/p
where k is the constant of variation.
32 = 2 x k / (1/4)
Multiply both sides by 1/4.
8 = 2k
Divide both sides by 2.
4 = k
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