A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?
To find the speed at which the rider is rising, we use trigonometry and differentiation to calculate the rate of change of the height with respect to time. The speed is approximately -8.14 m/min.
Explanation:To find the speed at which the rider is rising, we need to find the rate of change of the height of the rider with respect to time. This can be done using the concept of trigonometry and differentiation.
Since the Ferris wheel completes one revolution every 2 minutes, the angular speed is given by 2π radians per 2 minutes, which simplifies to π radians per minute.
The height of the rider can be represented by a sinusoidal function, and by taking the derivative of this function, we can find the rate of change of the height with respect to time. In this case, the derivative would be -13sin(t), where t is the time in minutes.
Substituting t = 18 minutes into the derivative equation, we can calculate the rate at which the rider is rising. Plugging in the value, we get a speed of -13sin(18) m/min, which is approximately -8.14 m/min.
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What inequality represents the verbal expression? 1. all real numbers less than 69?
If s = {r, u, d} is a set of linearly dependent vectors. if x = 5r + u + d, determine whether t = {r, u, x} is a linearly dependent set
1. which expression is equivalent to 8 × 8 × 8 × 8?
A. 8 × 4
B. 8^5
C. 8^4
D. 4^8
2. which expression is equivalent to 4 × 4 × 4 × 4 × 4 × 4 × 4?
3. which expression is equivalent to 7 × 7 × 7 × 7 × 7 × 7?
4. which expression is equivalent to 4 × 4 × 4?
5. which expression is equivalent to 3 × 3?
What is the perimeter of a parallelogram if it has a base width of 3x+9 and it has a height length of 4x-5?
A machine is set to fill the small-size packages of m&m candies with 56 candies per bag. a sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. to test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?
In statistics, the amount of degrees of freedom is the quantity of values in the final computation of a statistic that are free to differ. In this case, you can get the answer by adding the number of bags and subtracting 1.
So in computation, this would look like: 3 + 2 + 1 + 2 - 1 = 7
Therefore, 7 is the degrees of freedom.
Final answer:
The number of degrees of freedom for the hypothesis test that the mean candies per bag is 56 is 7, calculated by subtracting one from the total number of sampled bags.
Explanation:
To calculate the number of degrees of freedom for the hypothesis test that the mean candies per bag is 56, we use the sample size minus one. The sample size is the number of observations, which is the total count of bags sampled. In this case, we have a total of 8 bags (three bags of 56, two bags of 57, one bag of 55, and two bags of 58). Therefore, the degrees of freedom for this test would be 8 - 1 = 7.
The ____ function can be used to ensure that a number has the appropriate number of decimal places.
What is the value of |−25|?
Two small fires are spotted by a ranger from a fire tower 60 feet above ground. The angles of depressions re 11.6° and 9.4°. How far apart are the fires? (The fires are in the same general direction from the tower.)
Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Small Medium Large Extra Large Total Framed 23 264 188 42 ? Unframed 152 544 496 81 1,273 Total 175 808 684 123 1,790 Which number is missing from the two-way table?'
The missing number in the two-way table is the total number of framed prints, which is 517. This is calculated by subtracting the total unframed prints from the total prints sold and then summing the known framed prints.
To find the missing number of prints in the table, we need to determine the total number of framed prints sold by Mr. Carandang. We know the following from the table:
Total prints sold: 1,790Unframed prints: 1,273To find the total number of framed prints:
Total framed prints = Total prints - Total unframed prints
Total framed prints = 1,790 - 1,273 = 517
Now we need to sum the known framed prints:
Framed small: 23Framed medium: 264Framed large: 188Framed extra large: 42The total of known framed prints is:
23 + 264 + 188 + 42 = 517
Thus, the total framed prints value was missing and it is 517.
Find all values of x that are simultaneously a solution to the congruences x ≡ 2 (mod 3), x ≡ 1 (mod 5), x ≡ 3 (mod 29).
explain how you could find 3/8% of 800
12 PTS!!!
John ordered two kinds of pizza for a party: sausage pizzas and veggie pizzas. He ordered three pizzas of each kind. The pizzas cost a total of $99. If the cost of each veggie pizza is $18, what is the cost of a sausage pizza?
1 veggie pizza cost 18 so 3 cost 18*3 = 54
99-54 = 45 for the 3 sausage pizzas
45/3 = 15 dollars each for sausage
Find the difference: 16.25 - 7.92
Which equation could you use to solve for x in the proportion 4/5=9/x ?
Answer:
4x = 45 Chi3 is completely wrong
Step-by-step explanation:
To solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction, you can use the cross multiplication method.
First, multiply the numerator of the left fraction (4) by the denominator of the right fraction (x). Then, multiply the denominator of the left fraction (5) by the numerator of the right fraction (9).
This gives you the equation: 4x = 5 * 9.
Simplifying the equation, you get: 4x = 45.
To isolate x, divide both sides of the equation by 4: x = 45/4.
So, the correct equation to solve for x in the given proportion is 4x = 45.
We wish to choose 7 cards from a usual deck of 52 playing cards. In how many ways can this be done if we are required to choose the cards in the following ways?
(a) with no restriction.
(b) all cards come from the same suit.
(c) exactly 3 Aces and exactly 3 Kings are chosen.
(d) all 7 cards have values between 2 and 7 inclusive.
(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).
what is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3
5x^7y^4+25xy^2+15xy^3/5xy^3
Use an algebraic rule to describe a translation right 4 units and down 2 units.
I keep getting 13. It's supposed to be 3. Can you show me how it's done? 3(a-5) = -6
The GCF of any two even numbers is always even. true or false?
Find the rate of change of the area of a square with respect to the length z , the diagonal of the square. what is the rate when z=2?
The rate of change of Area, A with respect to the diagonal length, z and the rate of change when z = 2 is :
[tex]\frac{dA}{dz} = z [/tex][tex]\frac{dA}{dz} = 2 \: when \: z = 2 [/tex]The area of a square is rated to its diagonal thus :
Area of square = ALength of diagonal = zThe relationship between Area and diagonal of a square is : [tex]A \: = 0.5 {z}^{2} [/tex]
The rate of change of area with respect to the length, z of the square's diagonal ;
This the first differential of Area with respect to z
[tex] \frac{dA}{dz} = 2(0.5)z \: = z[/tex]
Therefore, the rate of change of area, A with respect to the length, z of the diagonal is [tex]\frac{dA}{dz} = z [/tex]
The rate of change [tex]\frac{dA}{dz} [/tex] when z = 2 can be calculated thus :
Substitute z = 2 in the relation [tex]\frac{dA}{dz} = z [/tex]
Therefore, [tex]\frac{dA}{dz} = 2 [/tex]
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Express 9.21212121212... as a rational number, in the form pq
Given e(x + 4) = 10 and e[(x + 4) 2 ] = 116, determine (a) var(x + 4), (b)μ= e(x), and (c)σ 2 = var(x).
In the given statements, first 'x' is derived from the equation e(x + 4) = 10, then it is plugged into e(x) to find μ and the variance formula to obtain σ².
Explanation:The question presents a scenario with two equations: e(x + 4) = 10 and e[(x + 4) 2 ] = 116 .To solve these equations, you would need to employ various algebraic and statistical concepts. Given this information, let's procede as follows:
To find (a) var(x + 4), we first need to determine the value of 'x' which can be derived from the given e(x + 4) = 10. After calculating 'x', we can work out (b)μ= e(x) by inserting our calculated 'x' into the e(x) formula. Finally, σ 2 = var(x) can be computed by applying 'x' in the variance formula.
Please note, this solution requires a good understanding of the properties of exponential functions and the statistical representation of variance (var), mean (μ), and standard deviation (σ²). Due to the complexity of these equations, I recommend using a calculator to accurately work out each part.
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In Miss Marshalls classroom 6/7 of the students play sports of the students who play sports for fifth also play instruments if there are 35 students in her class how many play sports and instruments
If f(x) = 3x + 6, which of the following is the inverse of f(x)?
A. f –1(x) = 3x – 6
B. f –1(x) =
C. f –1(x) =
D. f –1(x) = 6 – 3x
To determine the inverse of the function f(x) = 3x + 6, you need to switch 'x' and 'f(x)', isolate f-1(x) on one side of the equation, then solve for f-1(x). The resulting inverse function is f-1(x) = (x - 6)/3.
Explanation:The function given is f(x) = 3x + 6. To find the inverse of this function, we first need to switch 'x' and 'f(x)', giving us: x = 3f-1(x) + 6. Next, we want to isolate f-1(x) on one side of the equation. To do this, we subtract 6 from both sides of the equation resulting in: x - 6 = 3f-1(x). Finally, we divide all terms by 3 to solve for f-1(x), which gives us f-1(x) = (x - 6)/3. So, the correct answer from the options given is not listed.
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Toby exercises 14 hours a week. John exercises 20% more than Toby and Jenny exercises two more hours than John. Which expression represents how much Jenny exercises? (w represents weeks)
the answer is 18.8w
Toby 14w
John 14(1.2)w
Jenny 14(1.2)w + 2w
thus, Jenny exercise
14(1.2)w + 2w
16.8w + 2w
18.8w
The driver of a car traveling at 54ft/sec suddenly applies the brakes. The position of the car is s=54t-3t^2, t seconds afyer the driver applies the brakes.
How many seconds after the driver applies the brakes does the car come to a stop
After time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.
What is time?" Time is defined as the measurable slot of period in which required action is done."
Formula used
[tex]y = x^{n} \\\\\implies \frac{dy}{dx} = nx^{n-1}[/tex]
According to the question,
Position of the car [tex]'s' = 54t - 3t^{2}[/tex]
[tex]'s'[/tex] represents the distance
[tex]'t'[/tex] is the time in seconds
When driver applies break [tex]v= 0[/tex],
[tex]v = \frac{ds}{dt}[/tex]
Calculate the first derivative with respect to time we get,
[tex]'s' = 54t - 3t^{2}\\\\\implies \frac{ds}{dt} = 54- 6t[/tex]
As [tex]\frac{ds}{dt} =0[/tex] we get the required time as per given condition,
[tex]54-6t =0\\\\\implies 6t =54\\\\\implies t = 9[/tex]
Hence, after time [tex]t = 9[/tex] seconds the driver applies the brakes does the car come to a stop.
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Suppose 8 out of every 20 students are absent from school less than 5 days a year.Predict how many students would be absent less than 5 days a year out of 40,000 students.
How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed
0 through 6 is 7 total numbers
1st digit can be 0-6 = 7 numbers
2nd digit can be 0-6 = 7 numbers
3rd digit can be 0-6 = 7 numbers
4th digit can be 0-6 = 7 numbers
7 * 7 *7 *7 = 2401 different combinations