We get the following sine model for the vertical displacement y of a point on the blade at time t: y = 7.5 sin(2π(3t - 1)) + 40. This model gives the height above the ground of a point on the blade at time t, measured in minutes.
Assuming that the blades move in a circular motion, the vertical displacement of a point on a blade can be modeled using a sine function.
Let's start by finding the period of the function, which is the time it takes for the blade to complete one full rotation. Since the blade completes 3 rotations every minute, the period is:
T = 1/3 minutes
Next, we need to find the amplitude of the function, which is half the distance between the highest and lowest points of the blade's path. Since the blade is 15 feet long, the amplitude is:
A = 15/2 = 7.5 feet
Finally, we need to find the vertical displacement of the blade at time t, measured in minutes. Let's assume that t=0 corresponds to a blade pointing directly upwards. As the blade rotates, it moves in a circle with radius 15 feet, centered at a height of 40 feet above the ground. The vertical displacement of the blade is the y-coordinate of the point on the circle at angle θ, where θ is given by:
θ = 2π(3t - 1) (in radians)
This formula gives the angle in radians that the blade has rotated through at time t, taking into account the fact that the blade starts at a random angle at t=0. (The "-1" term ensures that the blade starts at the top at t=0.)
Putting it all together, we get the following sine model for the vertical displacement y of a point on the blade at time t:
y = 7.5 sin(2π(3t - 1)) + 40
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In AABC, mA = 58° and m2 B = 45°.
Select the triangle that is similar to AABC.
A. APQR, in which mZP = 58° and
mZR= 70°
B. AXYZ, in which mZX= 45° and
mZY= 103°
OC. AHIJ, in which mZH= 58° and
mZJ= 77°
OD. AMNP, in which m/M = 58° and
mZN = 103°
The triangle similar to ΔABC is ΔSTU, in which m∠S = 87° and m∠U = 70°. Option C
We have,
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
In ΔABC, we know that m∠A = 87° and m∠B = 23°.
The angle m∠C must therefore be 70°,
since the sum of the angles in a triangle is always 180°.
now, we have,
In ΔSTU, we are given that m∠S = 87°, which corresponds to ∠A in ΔABC.
We are also given that m∠U = 70°, which corresponds to ∠C in ΔABC.
so, we get,
as, This is because two triangles are similar if their corresponding angles are congruent.
Therefore, ΔSTU is similar to ΔABC.
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The above answer is in response to the full question below
In Δ ABC, m∠A = 87° and m∠B = 23°.
Select the triangle that is similar to ΔABC.
A. ΔXYZ, in which m∠X= 87° and m∠z = 50°
B. ΔLMN, in which m∠M=20° and m∠N=87°
C. ΔSTU, in which m∠s = 87° and m∠U=70°
D. ΔPQR, in which m∠P= 110° and m∠R = 23°
2. When making a full batch of tuna, you will mix one pouch of tuna with 26oz (737g) of mayonnaise. How much tuna and mayonnaise would you need when making a double batch?
These measurements are based on the Original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.
If one pouch of tuna is mixed with 26 oz (737g) of mayonnaise to make a full batch, then to make a double batch of tuna, we need to double the amounts of both the tuna and the mayonnaise.
we simply need to multiply the amount of tuna in a single batch by 2:
1 pouch of tuna x 2 = 2 pouches of tuna
So, we need 2 pouches of tuna for a double batch.
26 oz (737g) of mayonnaise x 2 = 52 oz (1474g) of mayonnaise
So, we need 52 oz (1474g) of mayonnaise for a double batch.
Therefore, to make a double batch of tuna, we would need 2 pouches of tuna and 52 oz (1474g) of mayonnaise. It's important to note that these measurements are based on the original ratio of 1 pouch of tuna to 26 oz (737g) of mayonnaise. If you prefer a different ratio of tuna to mayonnaise, the amounts needed for a double batch may be different.
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Find the area of the triangle. Simplify your answer.
The area of the triangle with base 2x and height (x - 7) in simplified form is x² - 7x
What is the area of the triangle?Area of a triangle = ½ × base × height
Base = 2x
Height = (x - 7)
Area of a triangle = ½ × base × height
= ½ × 2x × (x - 7)
= (2x² - 14x) / 2
= x² - 7x
Hence, the triangle given the dimensions has an area of x² - 7x
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questionthere are 76 ounces of fluid in container a. this is about 8 times the amount of fluid in container how many ounces of fluid are there in container b?select the numbers that correctly complete the are between choose... ounces of fluid in container b.
The amount of fluid in container B is 9.5 ounces.
to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.
To determine the amount of fluid in container B, we can divide the amount of fluid in container A by the given ratio of 8. Since container A contains 76 ounces, we divide 76 by 8 to find that each unit of the ratio represents 9.5 ounces. Therefore, container B would contain 9.5 ounces of fluid.
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Find the angles plssss hurry
Answer:
a = 157
b = 23
c = 157
Step-by-step explanation:
Angle b is a vertical angle to the angle measuring 23 so they are equal.
b = 23
Angle c and the angle measuring 23 forms a straight line so they add to 180.
c+23 =180
c = 180-23
c = 157
Angle c and a are vertical angles so they are equal.
c = a = 157
Answer:
a = 157°
c = 157°
b = 23°
Step-by-step explanation:
We know that vertically opposite angles are equal.
∴ b = 23°
We know that angles in a straight line are added up to 180°.
∴ b + c = 180
23 + c = 180
c = 180 - 23
c = 157°
a = 157° ( vertically opposite angles ⇒ c = a )
g) a car rental agency has ten mid-sized and fifteen compact cars on its lot, from which six will be selected. assuming that each is equally likely to be selected, and that they will be selected at random, what is the probability that exactly two mid-sized cars and four compact cars will be selected?
The probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.
The answer to this question involves using the formula for combinations and multiplying the probabilities of each selected car.
Calculate the number of ways to select two mid-sized cars and four compact cars.
- Choose 2 mid-sized cars from 10: C(10, 2) = 10! / (2! * (10 - 2)!) = 45 ways
- Choose 4 compact cars from 15: C(15, 4) = 15! / (4! * (15 - 4)!) = 1365 ways
There are a total of 25 cars to choose from and we need to select 2 mid-sized cars from the 10 available and 4 compact cars from the 15 available. Using the formula for combinations, we get:
C(10,2) * C(15,4) = 45 * 1365 = 61,425
This represents the number of ways we can select exactly 2 mid-sized cars and 4 compact cars. To find the probability, we divide this number by the total number of possible selections:
C(25,6) = 53,130
So the probability of selecting exactly 2 mid-sized cars and 4 compact cars is:
61,425 / 53,130 ≈ 0.1156 or 11.56%
In conclusion, the probability of selecting exactly two mid-sized cars and four compact cars out of a total of six cars is approximately 11.56%.
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if the standard error is smaller than the standard deviation when conducting a regression, what can you conclude?
If the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable.
When conducting a regression, the standard error is a measure of the precision of the estimated regression coefficient. On the other hand, the standard deviation is a measure of the variability of the data points from the mean. If the standard error is smaller than the standard deviation, it means that the estimated regression coefficient is more precise than the variation of the data points. This indicates that the model is more reliable and accurate in predicting the outcome variable.
In practical terms, a smaller standard error means that the predicted values of the outcome variable will be closer to the actual values, resulting in more accurate predictions. However, it is important to note that a smaller standard error does not necessarily mean that the regression model is better. Other factors such as the goodness of fit, significance of the coefficients, and the overall explanatory power of the model should also be considered when evaluating the performance of a regression model.
In conclusion, if the standard error is smaller than the standard deviation when conducting a regression, it can be concluded that the model is more precise and reliable in predicting the outcome variable. However, other factors should also be taken into account to evaluate the overall performance of the model.
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a manufacturer of shoes wanted to reduce the number of flaws per pair of shoes. data gathered from quality control measures indicated that brand a typically had 2.5 flaws per pair of shoes. a mechanical engineer for the company developed a modification of the current process that she thought might reduce the number of flaws. to determine if this was true, one of the machines in the plant was modified according to her specifications. a sample of 30 pairs of shoes was analyzed for flaws. the sample yielded a mean of 2.2 flaws per pair of shoes. assume the standard deviation of the measurements is 0.66. find the p-value of the test.
The p-value of the test is approximately 0.299.
To find the p-value of the test, we need to conduct a hypothesis test. Let's set up the hypotheses first:
Null Hypothesis (H0): The modification of the process did not reduce the number of flaws per pair of shoes.
Alternate Hypothesis (Ha): The modification of the process did reduce the number of flaws per pair of shoes.
We can use a one-sample t-test to analyze the data. The test statistic can be calculated using the formula:
t = ( - μ) / (s / √n),
where is the sample mean, μ is the population mean (2.5 flaws), s is the sample standard deviation (0.66), and n is the sample size (30).
Substituting the values into the formula, we get:
t = (2.2 - 2.5) / (0.66 / √30) ≈ -1.054
To find the p-value associated with this test statistic, we need to consult the t-distribution table or use statistical software. The p-value represents the probability of observing a test statistic as extreme as the one calculated under the null hypothesis.
Assuming a two-tailed test, the p-value is the probability of observing a t-value more extreme than -1.054 or more extreme than 1.054. Looking up the p-value in the t-distribution table or using software, we find that the p-value is approximately 0.299.
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A utility worker must reach the top of a telephone pole to fix an electric wire. if the pole casts a 39 foot 6 inch shadow at the same time the 6 foot 2inch man casts a 9 foot 4 inch shadow, how tall is the telephone pole? round to the nearest whole foot.
The height of the telephone pole is approximately 26 feet.
How to solve for the heightAccording to the given information, the height of the man is 6 feet 2 inches, which we can represent as 6.17 feet, and his shadow is 9 feet 4 inches, which is 9.33 feet.
Using the concept of similar triangles, we can set up the following proportion:
(man's height) / (man's shadow) = (pole's height) / (pole's shadow)
Simplifying the proportion:
6.17 / 9.33 = h / 39.5
To solve for 'h', we can cross-multiply:
6.17 * 39.5 = 9.33 * h
243.215 = 9.33 * h
Dividing both sides by 9.33:
h ≈ 26.06
Rounding to the nearest whole foot, the height of the telephone pole is approximately 26 feet.
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Jayna lives 2 ⅗ miles away from school. Ava lives 3 ⅖ miles away from school. How much further from the school is Ava than Jayna?
Answer:
Ava lives 8/5 or 1 3/5 miles further from the school compared to Jayna.
Step-by-step explanation:
PLEASE HELP I AM GROUNDED AND NEED THIS ANSWER
Answer: 39
Step-by-step explanation: 180-141= 39
Aiden is going to make concrete.
Answer:
8 bags of cement
9 bags of sand
3 bags of stone
Step-by-step explanation:
Hope this helps :)
What is the following product?
sq root 30 product sq root 10
2 sq root 10
3 sq root 10
4 sq root 10
10 sq root 3
The product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10}[/tex] is 10[tex]\sqrt{3}[/tex].
The correct answer would be 10[tex]\sqrt{3}[/tex].
To find the product of [tex]\sqrt{30}[/tex] and [tex]\sqrt{10\\}[/tex], we can simplify it by multiplying the square roots and simplifying the result.
[tex]\sqrt{30 * 10 = (30 * 10) = 300}[/tex]
Now, let's simplify [tex]\sqrt{300}[/tex]. To do this, we can find the prime factorization of 300:
[tex]300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2[/tex]
Taking the square root of 300:
[tex]\sqrt{300}[/tex] = ([tex]\sqrt{(2^2 * 3 * 5^2)}[/tex]
Using the properties of square roots, we can split the square root into separate square roots:
[tex]\sqrt{300}[/tex] = [tex]\sqrt{2^2}[/tex] * [tex]\sqrt{3}[/tex] * [tex]\sqrt{5^2 }[/tex]
Simplifying each square root separately:
[tex]\sqrt{2^2}[/tex] = 2
[tex]\sqrt{3[/tex] = [tex]\sqrt{3[/tex]
[tex]\sqrt{5^2 }[/tex]= 5
Combining the simplified square roots:
[tex]\sqrt{300}[/tex] = 2[tex]\sqrt{3}[/tex] * 5 = 10[tex]\sqrt{3}[/tex]
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Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram.
Which of these conclusions and justifications is the most reasonable?
The most reasonable conclusion is that the instruction to brake smoothly resulted in a decrease in gas consumption, as evidenced by the lower mean and negative difference in means between the two groups.
Based on the information provided, the most reasonable conclusion would be that the instruction given to the first group of drivers to brake smoothly when approaching a red light or stop sign resulted in a decrease in the mean gallons of gas used compared to the second group.
The justification for this conclusion is supported by the fact that the mean for the first group is 43.16 gallons of gas, which is lower than the mean for the second group, which is 54.63 gallons of gas. This indicates that the first group, who received the specific instruction to brake smoothly, consumed less gas on average.
The histogram displaying the differences in means after the data for both groups were combined and redistributed also supports the conclusion. It likely shows a distribution that is centered around a negative value, indicating that the majority of the redistributed groups had a lower mean gas consumption compared to the initial second group.
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Pump A and Pump B fill the pool in 35 minutes, Pump B and Pump C fill it in 40
minutes, and Pump A and Pump C fill it in 56 minutes. How many minutes will it take
all three pumps, working together, to fill the pool?
It will take all three pumps, Working together, 1.56 minutes to fill the pool.
The given information, we can write three equations as follows:
1) (1/A + 1/B)*35 = C ---(Equation 1)
2) (1/B + 1/C)*40 = C ---(Equation 2)
3) (1/A + 1/C)*56 = C ---(Equation 3)
We want how many minutes it will take all three pumps, working together, to fill the pool, so let's represent the time taken by all three pumps working together as "t".
When all three pumps work together, they can fill the pool in one minute, so their combined rate is 1/C.
Using the rate formula, we can write the following equation:
1/A + 1/B + 1/C = 1/t ---(Equation 4)
We have four unknowns (A, B, C, and t), so we need to solve for one of them to get the answer. Let's solve for "t".
First, we can simplify Equations 1, 2, and 3 as follows:
1) 1/A + 1/B = C/35
2) 1/B + 1/C = C/40
3) 1/A + 1/C = C/56
Next, we can substitute these equations into Equation 4 to get:
(C/35) + (C/40) + (C/56) = 1/t
Now, we can simplify and solve for "t":
LCD = 39200
1120C + 980C + 700C = 39200
2800C = 39200
C = 14
Substituting this value of "C" into any of the simplified equations, we can solve for "A" and "B". Let's use Equation 1:
1/A + 1/B = 14/35
5(A+B) = 98
A+B = 19.6
Now we can use A+B+C = 1/t to solve for "t":
t = 1 / (A+B+C) = 1 / (19.6 + 14) = 0.026 hours = 1.56 minutes
Therefore, it will take all three pumps, working together, 1.56 minutes to fill the pool.
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Biologists introduced a population of bacteria to a test environment. The function � ff models the population size (in thousands) as a function of time (in days) after introduction.
The number of bacteria that were present when the antibiotic was first introduced is 14
How many bacteria were present when the antibiotic was first introduced?From the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
The number of bacteria that were present when the antibiotic was first introduced is when the graph intersects with the y-axis
In this case, the graph intersects with the y-axis at
y = 14
Hence, the number of bacteria that were present when the antibiotic was first introduced is 14
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Complete question
Biologists introduced a population of bacteria to a test environment. The function f models the population size (in thousands) as a function of time (in days) after introduction.
The graph shows a bacteria population (see attacment)
How many bacteria were present when the antibiotic was first introduced?
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
0.714
Step-by-step explanation:
5/7
(5X100) / 7 = 500/7.
50/7 = 7 remainder 1. carry that one over and place it before last zero in 500.
10/7 = 1 remainder 3.
we have 71 remainder 3.
3/7: 300/7 = 42.83
we now have answer of 0.714282
= 0.714 to nearest thousandth
haylee Rolls two number cubes. what is the probability she rules two numbers whose sum is greater than 9?
Answer:
1/6 or 16.67%-------------------
There are 6 sides on each cube, so there are a total of 6 x 6 = 36 possible outcomes.
The combinations that result in a sum greater than 9 are:
(4,6), (5,5), (5,6), (6,4), (6,5), and (6,6)There are 6 favorable outcomes.
Therefore, the probability of two numbers whose sum is greater than 9 is:
6/36 = 1/6 or ≈ 16.67%.Someone please help...
If the chicken crosses the road at 7.35 miles every 30 minutes exactly how fast would it take to find out the answer of why he crossed in the first place. Please answer mathematically (And leave the reason why...! )
We can deduce here that the chicken is traveling at a speed of 0.245 miles per minute.
What is speed?Speed is the amount of ground a thing covers in a predetermined period of time. It has magnitude but no direction because it is a scalar quantity. Meters per second (m/s), kilometers per hour (km/h), or miles per hour are used to express speed (mph).
In order to find the speed of the chicken, here is the formula to make use of:
Speed = distance / time
Speed = 7.35 miles / 30 minutes = 0.245 miles per minute.
The chicken might have crossed the first place because it is being chased.
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Hi can someone who is great at math help me with this math questions and show the steps! I’m struggling with it. Find the area of the middle shape.
The calculated area of the middle shape is 18 square units
Finding the area of the middle shape.From the question, we have the following parameters that can be used in our computation:
The figures
From the figure, we have the middle shape to be a rectangle
The width of the rectangle is
Width = 6
The length of the rectangle is calculated as follows
15 = 3 * 5
27 = 3 * 3 * 3
The common factor is 3
So, we have
Length = 3
The area of the rectangle is calculated as
Area = Length * Width
So, we have
Area = 3 * 6
Evaluate
Area = 18
Hence, the area of the middle shape is 18 square units
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Blake recorded the high temperatures each day for a month in two different cities.
For City A, the mean high temperature was 59°F with a mean absolute deviation of 3.2.
For City B, the mean high temperature was 71°F with a mean absolute deviation of 2.9.
Compare the difference of the means in terms of the mean absolute deviations
Answer:
City B is significantly higher than in City A.
Step-by-step explanation:
To compare the difference of the means in terms of the mean absolute deviations, we can use the concept of standard deviation units. We divide the difference of the means by the average of the mean absolute deviations of the two cities:
D = (71 - 59) / ((3.2 + 2.9) / 2)
D = 12 / 3.05
D ≈ 3.934
The value of D tells us that the difference of the means between the two cities is almost 4 standard deviation units, which is a large difference. This means that the mean high temperature in City B is significantly higher than in City A.
what is the surface area
The total surface area of the pyramid is: 208.88 m²
What is the surface area of the pyramid?The surface area of the pyramid is simply the sum of the areas of all the given surfaces.
Formula for the area of a triangle is:
Area = ¹/₂bh
where:
b is base
h is height
Area of four side triangles = 4(¹/₂ * 8 * 12) = 192 m²
Using Pythagoras theorem, the height of the base triangle is:
x = 4.22
Area of base = ¹/₂ * 8 * 4.22 = 16.88 m²
Total surface area = 192 + 16.88
= 208.88 m²
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5x-4y=34
-x+8y=22
find the solution of the system of equations.
The solution of the system of equations 5x-4y=34 and -x+8y=22 is x = -6 and y = 4, or (x, y) = (-6, 4).
What is the solution to the system of equation?Given the system of equation in the question;
5x - 4y = 34 _____1
-x + 8y = 22 _____2
To solve the system of equation, first solve for x in equation 2 and plug it into equation 1.
-x + 8y = 22
x = 8y - 22 _____ 3
Plug equation 3 into equation 1
5x - 4y = 34
Plug in x = 8y - 22
5( 8y - 22 ) - 4y = 34
Solve for y
40y - 110 - 4y = 34
40y - 4y = 34 + 110
36y = 144
y = 144/36
y = 4
Plug y = 4 into equation 3
x = 8( 4 ) - 22
x = 32 - 22
x = 10
Therefore, the solution is x = 10 and y = 4.
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What is the growth factor?
Hint: the "growth factor" is the number that each term is multiplied by, to get the next term.
With exponential decay, the "growth factor" will be a fraction.
Growth Factor:
The calculated value of the exponential decay factor is 1/5
Calculating the growth factor or exponential decay?From the question, we have the following parameters that can be used in our computation:
The table of values
From the table of values, we can see that
x f(x)
1 625
2 125
3 25
This show that as x increases by 1, the function f(x) values decreases by a constant factor
This means that
The function is a decay function and the rate of decay is calculated as
Rate = 125/625
Evaluate
Rate = 1/5
Hence, the exponential decay factor is 1/5
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The formula PV - FV(1 + n) will determine the present value of $1. True/False
False. The formula PV - FV(1 + n) does not determine the present value of $1.
But rather it is a formula used to calculate the present value of a future cash flow or investment. PV stands for present value, FV stands for future value, and n represents the number of periods for which the investment will be held. The formula states that the present value of an investment or cash flow is equal to the future value of that investment or cash flow, discounted at a specified rate of return over a specific period of time.
In other words, the formula is used to determine the value today of a future cash flow or investment based on the time value of money. By discounting the future value of the cash flow or investment at a specified rate, the formula calculates the present value that would be equivalent to receiving that cash flow or investment at a future date.
Therefore, the correct statement would be: The formula PV - FV(1 + n) is used to determine the present value of a future cash flow or investment.
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find dy/dx and d2y/dx2. x = 2 sin t, y = 3 cos t, 0 < t < 2π
Therefore, the value of derivatives dy/dx = -3 tan t/2 and d2y/dx2 = -3(1 - cos t)/(2(1+cos t)^2).
To find dy/dx and d2y/dx2, we need to first express y in terms of x:
x = 2 sin t --> sin t = x/2 --> cos t = ±sqrt(1 - sin^2 t) = ±sqrt(1 - x^2/4)
y = 3 cos t = ±3sqrt(1 - x^2/4)
Since 0 < t < 2π, we can determine the sign of cos t by looking at the quadrant that x lies in. Since x = 2 sin t, we have x > 0 when 0 < t < π and x < 0 when π < t < 2π. Therefore, when 0 < t < π, we have:
cos t = sqrt(1 - sin^2 t) = sqrt(1 - x^2/4)
y = 3 sqrt(1 - x^2/4)
dy/dx = -3x/2 sqrt(1 - x^2/4)^(-1)
Taking the derivative of dy/dx with respect to x, we get:
d2y/dx2 = -3/2 [sqrt(1 - x^2/4)^(-1) - 3x^2/8 (1 - x^2/4)^(-3/2)]
Plugging in x = 2 sin t and simplifying, we get:
dy/dx = -3 sin t / sqrt(4 - 4 sin^2 t) = -3 sin t / 2 cos t = -3 tan t/2
d2y/dx2 = -3/4 (sec^2 t/2 - 3 tan^2 t/2) = -3/4 [(2/(1+cos t) - 3 tan^2 t/2)]
Using the identity cos^2(t/2) = (1+cos t)/2 and simplifying, we get:
d2y/dx2 = -3/4 [(4/(1+cos t) - 3) / (1+cos t)] = -3(1 - cos t)/(2(1+cos t)^2)
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How are the pairs of figures alike? How are they different?
Answer: they all have the same amount of squares but are placed differently in each example.
Step-by-step explanation:
there are 6 yellow squares and 10 blue squares for each of the 4 examples. The only difference is how they’re arranged.
use suitable property
(-128 x 46 )+ (128 x -36)
please answer the question I will mark them brainliest
The distributive property allows the formula (-128 x 46) + (128 x -36) to be simplified to -10496.
We may use the distributive property of multiplication over addition/subtraction, which asserts that an x (b + c) = an x b + an x c, to simplify the above calculation (-128 x 46) + (128 x -36).
Let's dissect the expression in detail:
(-128 x 46) + (128 x -36)Let's first assess the goods:
-128 x 46 = -5888
128 x -36 = -4608
Reintroduce these values into the phrase now:
(-5888) + (-4608)
We simply add the absolute values of the two negative numbers while maintaining the sign of the negative:
-5888 + (-4608) = -10496
Consequently, -10496 is the reduced expression.
Last but not least, the phrase (-128 x 46) + (128 x -36) becomes -10496. .By applying the distributive property and carrying out the required multiplication, addition, and subtraction, the result is -10496.
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a random sample of size 28 is collected from a normal population with unknown variance. the sample has the mean of 108.127 and the standard deviation of 30.4888. construct a 98% confidence interval for a population mean. group of answer choices (105.546, 110.707) (94.725, 121.529) (93.878, 122.376) (105.235, 111.018)
The correct confidence interval for a population mean at a 98% confidence level is approximately (94.685, 121.569). Therefore, the correct choice is (94.725, 121.529).
To construct a confidence interval for a population mean, we can use the formula:
Confidence Interval = sample mean ± (critical value * standard error)
First, we need to determine the critical value for a 98% confidence level. Since the sample size is large (n = 28), we can use the z-table to find the critical value. For a 98% confidence level, the critical value is approximately 2.33.
Next, we calculate the standard error using the formula:
Standard Error = sample standard deviation / √(sample size)
In this case, the sample standard deviation is 30.4888 and the sample size is 28. Therefore:
Standard Error = 30.4888 / √(28) ≈ 5.769
Now we can construct the confidence interval:
Confidence Interval = 108.127 ± (2.33 * 5.769) = (108.127 ± 13.442) = (94.685, 121.569)
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Use the compound interest formula A = P(1 + r) to find the annual interest rate, r, if in 2 years an investment of $5,000 grows to $6,050.
The annual interest rate, r, is 0.1 or 10%. A 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.
To find the annual interest rate, r, we can rearrange the compound interest formula A = P(1 + r) and solve for r.
Given that an investment of $5,000 grows to $6,050 in 2 years, we can substitute these values into the formula:
$6,050 = $5,000
[tex] {1 + r}^{2}[/tex]
Dividing both sides by $5,000, we have:
1.21 =
[tex](1 + r)^2[/tex]
Taking the square root of both sides, we get:
√1.21 = 1 + r
Simplifying, we have:
1.1 - 1 = r
0.1 = r
This means that the investment grew by 10% annually over the 2-year period. Compound interest is calculated by adding the interest earned to the initial amount, and as time passes, the interest is earned on both the initial amount and the accumulated interest from previous periods. In this case, a 10% annual interest rate resulted in the investment growing from $5,000 to $6,050 in 2 years.
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