The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter
As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.
The general form of the cosine function representing the displacement of the rider is:
f(t) = a cos(bt+c) + d, where:
amplitude = |a| which is the distance that travels above and below the midpoint
period = 2 π/|b| which is the time period i.e. time required to complete one cycle
-c/b is the phase shift.
d = vertical displacement of the function
Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.
So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.
The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.
The rider starts from the bottom position, so there will be no phase shift, so c=0
Given that the center of the wheel is 19 m above the ground, so d=19m
Therefore the equation will be
height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter
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Find the length of the unknown side. Round your answer to the nearest whole number.
Image of a right triangle with legs labeled 7 meters each. The hypotenuse is unknown.
7 meters
9 meters
10 meters
12 meters
Answer: 10
Step-by-step explanation:
√( 7^2 + 7^2 ) = 10
Using a left endpoint riemann sum approximation with four equal subintervals, the approximate value of integral from 0 to 8 g(x) dx is:
Subdividing [0, 8] into 4 equally-spaced subintervals, each one will have length ∆x = (8 - 0)/4 = 2, and the partition is
[0, 2] U [2, 4] U [4, 6] U [6, 8]
We approximate the integral with a left endpoint sum. The left endpoint of the i-th subinterval is
[tex]\ell_i = 2(i-1)[/tex]
where 1 ≤ i ≤ 4.
Then the integral is approximated by
[tex]\displaystyle \int_0^8 g(x) \, dx \approx \sum_{i=1}^4 g(\ell_i) \Delta x \\\\ = 2 (g(0) + g(2) + g(4) + g(6)) \\\\ = 2 (-1 - 3 - 1.25 - 1.5) = \boxed{-13.5}[/tex]
This is from the last question
Answer:
huh
Step-by-step explanation:
what are you trying to figure out-
Can someone help me please
===========================================================
Explanation:
Focus on the endpoints (0,15) and (10,0). They are the y and x intercepts in that order. This is the starting point and ending point of the ball.
The average rate of change is the slope of the line connecting these endpoints. This is when we consider the entire time the ball is in the air.
Let's use the slope formula to get the following:
[tex](x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (10,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - 15}{10 - 0}\\\\m = \frac{-15}{10}\\\\m = -\frac{3}{2}\\\\[/tex]
The slope is -3/2, which is the average rate of change.
It tells us that the height is decreasing by 3/2 = 1.5 meters per second, which is an average speed.
In other words, the ball is going downward at an average speed of 1.5 meters per second.
Keep in mind the instantaneous speed of the ball is changing all the time. The result of -3/2 = -1.5 only applies to the average speed.
------------
Note how the slope formula involves computing the change in y (which was us computing [tex]y_{2} - y_{1} = 0 - 15 = -15[/tex]. It indicates the ball had gone down 15 meters when going from the start point to the ending point. This is the change in distance. The change in time is the [tex]x_{2} - x_{1} = 10-0 = 10[/tex] portion, meaning the duration is 10 seconds.
In short,
slope = rise/run
slope = (change in distance)/(change in time)
slope = (-15)/(10)
slope = -3/2
So this may be a better way to see what's going on rather than rely on a formula in the previous section.
Construct a truth table for the following symbolic statement.
Use the type of truth table where each variable or operator in the given expression has its own column. Fill in the rows of the truth table one at a time.
The truth table is completed for each column as T T F F T T T
What is a truth table?A truth table is a mathematical table which shows all the truth values of a given combination of logic statements.
Analysis:
The truth table is shown in the attached file
in the attached file, the first two columns were given,
The third column is the negation of p, and P is true(T) which means its negation is false(F).
The fourth column is the negation of Q, which means Q is true(T) so its negation is false(F).
In the fifth column, negation P is implies negation Q. The truth table for implication, is only false if Q is false, else it is True.
Same as in the sixth column.
The last column is bi-implication, the truth table for this only true, if both statements are false or both are true else, it is false.
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Maggie and Tanya went to a fruit store. Maggie bought 10 oranges and 5 apples for $4. Tanya bought 9 oranges and 3 apples for $3. What is the cost of an orange and an apple?
Answer:
orange: 0.2$, apple: 0.4$
Step-by-step explanation:
we mark the price of an orange x and the price of an apple y. then we write down Maggie's and Tanya's purchases as a set of equations:
10 oranges and 5 apples for 4$ means:
[tex]10x + 5y = 4[/tex]
9 oranges and 3 apples for 3$ means:
[tex]9x + 3y = 3[/tex]
we use the second equation to isolate y:
[tex]3y = 3 - 9x \\ y = 1 - 3x[/tex]
and plug it in the first equation:
[tex]10x + 5(1 - 3x) = 4 \\ 10x + 5 - 15x = 4 \\ 1 = 5x \\ x = 0.2[/tex]
and then we find y:
[tex]y = 1 - 3 \times 0.2 \\ y = 0.4[/tex]
Can someone help me on this please
Answer:
17.7 (2 dp)
Step-by-step explanation:
[tex] \sqrt{ {16}^{2} + {7.5}^{2} }[/tex]
two identified lines are graphed below how many solutions are there to the system of equations?
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.
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:
= [tex]\frac{60° }{360°}[/tex] x 2π x 3
= 1/6 x 6π
= π
2. Note that radian measure:
= [tex]\frac{60° }{360°}[/tex] 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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A cube has edges measuring 8 centimeters.
Find its surface area.
(please)
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
•4/1001
• 15/1001
•10/143
•133/143
Answer:
The answer is 10/143
Step-by-step explanation:
In 2000, the number of people with a home phone in Indiana was 3,286,000. If the number of home phones have decreasing by 4% each year,
how many Hoosiers will have a home phone in 2011? Round to two-decimal places.
Hoosiers
Pause test
3286000x4/100=131440
131440x11=1445840
3286000-1445840=1840160
Answer: 1840160
this is the answer I got but for some reason the answer didn't turn out to be in decimal :( but I sware this is the answer I got
A building in a city has a rectangular base. the length of the base measures 65 ft less than twice the width. the perimeter of this base is 890 ft. what are the dimensions of the base? the width of the base is ft.
By solving a system of equations, we will see that the width is 170ft and the length 275 ft.
How to get the dimensions of the base?
For a rectangle of length x and width y, the perimeter is:
P = 2*(x + y).
Here we know that:
x = 2y - 65ft
p = 890ft = 2(x + y)
So we have a system of equations.
To solve this, we need to replace the first equation into the second one:
890ft = 2(x + y)
890ft = 2(( 2y - 65ft) + y)
Now we can solve this for y.
890ft = 4y - 130ft + 2y
890ft + 130ft = 6y
1020ft/6 = y = 170ft
So the width is 170ft, and we know that:
x = 2y - 65ft = 2*(170ft) - 65ft = 275ft
So the length is 275 ft.
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HELP IM TIMED!!!!
X
-2
-1
0
1
2
3
f(x)
20
0
-6
-4
0
0
Which is an x-intercept of the continuous function in the
table?
O (-1,0)
O (0, -6)
O (-6,0)
O
(0, -1)
Evaluate -3x² + 4x-2 for x = 2.
A. -2
B. -1
C. -6
D. 18
Answer:
C. -6
Step-by-step explanation:
-3(2)²+4(2)-2
-3(4) + 8 - 2
-12+8-2
-14+8
-6
Can someone help me out with this problem
From the given options the options B and C are correct for the given equation.
we have given the equation,
70=10+12r
We have to determine the correct option
What is the equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Therefore from the given options the options B and C are correct for the given equation.
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If you receive a 20% DISCOUNT off an item costing $20.00, how much money do you save?
Select all that apply. Which of the following corresponds to absolute zero?
In thermodynamic system, Absolute Zero is that temperature implies Lowest energy level i.e. option a) 0 K or -273° C.
What is Absolute Zero?
Absolute Zero can describe as, in a thermodynamic system, there are certain energy levels depending upon the potentials of temperature. At Absolute zero the potentials of temperature are 0 K in Kelvin scale and -273° C in Celsius scale.
The question seem's to be incomplete. The option could be.
a) 0 K and -273° C
b) 273 K and 0° C
c) -273 K and 0° C
d) 0 K and 273° C
Hence, As per theory Value of The absolute zero is 0 K and -273° C
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Work out the length of x.
Give your answer rounded to 3 significant figures.
8.6 cm+
x
The diagram is not drawn accurately.
Answer:
12.2cm
Step-by-step explanation:
Follow the steps in the image I send you to learn it if you don't get it tell me.
Enlarge shape by scale factor 3
Explanation:
When you change the size of a shape by a scale factor ("enlarge" means increasing the shape by a scale factor > 1), you increase all dimensions of that shape by a factor.
For example, if a rectangle's length is 2 units [two boxes in this case]. you make that size 6 units [2 · 3 = 6]; and if its width is 1 unit, you make that 3 units [1 · 3 = 3]
[scaling up our dimensions:]
So, we apply the same logic here. Any side length is now three times longer, so when the original length [along the bottom] was two boxes, that should now cover 6 boxes.
The height of 1 box [left side] will now be expanded to 3 boxes.
The other height of 2 boxes will now be 6 boxes [2 · 3 = 6]
The slanted portion should be easy to connect between your new side lengths and width
[but you could always use Pythagorean theorem to figure out the length; it would be 1² + 2² = c², or 5 = c², so the literal length of this side would be √5 ; you probably aren't expected to do this / you don't have to]
You didn't show the new graph to graph it on, but this is how you would graph it.
hope this helps!! have a lovely day :)
What are the values of x and y? A) x = 4sqrt(3) y 8√3 B ) x = 8; y = 4 ) x = 8sqrt(3); y = 4sqrt(3) D) x = 6sqrt(3); y = 3sqrt(3)
Answer:
C.
Step-by-step explanation:
IF YOU SEE A RIGHT ANGLED TRIANGLE APPLY THE TRIG RATIOS*
Simplify [tex]\sqrt{18}. \\[/tex]
[tex]A; 2\sqrt{3} \\B; 2\sqrt{9} \\C; 3\sqrt{2} \\D; 9\sqrt{2} \\[/tex]
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option C, 3}\sqrt{2}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\sqrt{18}[/tex]
Find: [tex]\textsf{Simplify the expression}[/tex]
Solution: In order to get a number outside of the square root there must be two of them inside of the square root. The first step that we need to take is to break down the number 18 into it's lowest factors and then take out the numbers can be taken out.
Break down the number 18
[tex]\sqrt{18}[/tex][tex]\sqrt{\textsf{2 * 3 * 3}}[/tex][tex]\sqrt{\textsf{2 * 3}^2}[/tex]Take 3 outside of the square root
[tex]\sqrt{\textsf{2 * 3}^2}[/tex][tex]\textsf{3}\sqrt{\textsf{2}[/tex]Therefore, the option that would best match the results that were solved for is option C, [tex]\textsf{3}\sqrt{\textsf{2}[/tex]
pls help asap!!!!
Which number best represents the slope of the graphed line?
Answer:
C: 1/2
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: C. \cfrac{1}{2}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Slope of line - } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 4)}{8 - 0} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 4}{8 } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 1}{2} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A researcher finds that the more hours students party per week, the lower their gpas (grade point averages). she questions whether there may be other issues affecting the students' gpas that weren't taken into account, such as the number of hours spent studying, class attendance, or the number of hours worked at campus jobs. what are these additional factors called
Answer:
I believe "uncontrolled variables."
Step-by-step explanation:
Since there was no measure, nor control, of these other variables, the data may be questionable.
There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
How many people didn't use any facilities?
Answer:
200wuwusjjdhsuauuaiajjduwiqisidiwiwia
Answer:
n(U) = n(G)+n(S)+n(T)-n(GnS)-n(GnT)-n(TnS)+n(GnTnS) + n(GnTnS)^c
135= 73+59+31-19-9-16+4+ n(GnTnS)^c
no. of people not using any facility =12
A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area
of 135 square units.
Part A
•
Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B
What is the perimeter of the expanded rectangle?
Answer:
The perimeter is 48
Step-by-step explanation:
If the width is W
AT first , Length is 10 +w
According to the question,
[tex](w+8) (10+w+4) = 135\\(w+8) (w+14) = 135\\\\w^{2} + 14w + 8w + 112- 135 = 0\\\\ w^{2} + 22w - 23 = 0\\(w+23) (w-1) = 0\\\\w+ 23 = 0 w-1=0\\\\w= -13 or w = 1[/tex]
Expended width will be w +8 = 1+8 = 9
Length is 10+w+4 = 15
So the perimeter is
= i2 x (9+15)
= 2x 24
= 48
The Solution to the problem of the rectangle is given below
For Part A:
equation model: (14 + w) * (w +8) = 132Length = 15For Part B
Perimeter = 46Meaning of Perimeter
The perimeter of any shape can be defined as the total sum of the sides of the shape.
AnalysisFor Part A
equation model= (14 + w) * (w +8) = 135
14w + 112 + 8w + [tex]w^{2}[/tex] = 135
[tex]w^{2}[/tex] + 22w - 23 = 0
solving the quadratic equation
w = -23 or 1
Because we are dealing with a physical quantity we will make use of the value 1
lenght of original rectangle = 10 + 1 = 11
Part B
Perimeter= 2(length) * 2 (breadth) = 2(11 + 4) * 2 (1 + 8)
Perimeter = 48
In conclusion, The Solution to the problem of the rectangle is given above.
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-m-2=2+
m
O 2
O 3
04
O 5
Which statement is true about the information in the double line graph?
A. The number of customers at 12:00 was less on Friday than Saturday.
B. There were more customers on Saturday than Friday.
C. The number of customers was less Saturday than Friday at 10:00 a.m. because many customers slept later.
D. The highest number of customers on both days was at 12:00 p.m.
Answer:
the answer is d as 38 31 which are highest
Step-by-step explanation:
a is false as 38>31 which is on Saturday
b is false as Saturday customers were less we can infer from the last three on Friday
c false as Saturday was 12 people and Friday 6 people
This is math proportion :
I change $60 into 45 euros
How many euros would i get for 50$?
Answer:
33.75 Euros
Step-by-step explanation:
Trust me bro, I did the working.
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, , of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate . Assuming that the standard deviation of the population of shopping times at the supermarkets is minutes, what is the minimum sample size she must collect in order for her to be confident that her estimate is within minutes of
The sample size is 289.
Zα/2 = [tex]Z_{0.025}[/tex]
= 1.96
Sample size = n
n = [Zα/2* σ / E] 2
n = [1.96 * 26 / 3 ]2
n = 288.54
n = 289.
In records, the pattern size is the measure of the number of man or woman samples used in an experiment. As an example, if we are testing 50 samples of folks that watch tv in a town, then the sample length is 50.
An awesome sample length is normally 10% as long because it no longer exceeds a thousand. A very good sample length is commonly around 10% of the populace, as long as this doesn't exceed one thousand. for example, in a populace of 5000, 10% could be 500. In a populace of 200,000, 10% would be 20,000.
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