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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for the function y=-1+6 cos(2 pi/7(x-5)) what is the maximum value
the maximum value of the function is y = -1 + 6cos(2π/7(26.75-5)) = 5.
The function y = -1 + 6cos(2π/7(x-5)) is a periodic function with a period of 7. The maximum value of the function occurs when the cosine function reaches its maximum value of 1.
So, we need to find the value of x that makes the argument of the cosine function equal to an odd multiple of π/2, which is when the cosine function is equal to 1.
2π/7(x-5) = (2n + 1)π/2, where n is an integer
Simplifying this equation, we get:
x - 5 = (7/4)(2n + 1)
x = 5 + (7/4)(2n + 1)
Since the function has a period of 7, we can restrict our attention to the interval [5, 12].
For n = 0, we get x = 5 + 7/4 = 23/4
For n = 1, we get x = 5 + (7/4)(3) = 26.75
For n = 2, we get x = 5 + (7/4)(5) = 33.25
For n = -1, we get x = 5 + (7/4)(-1) = 1.75
For n = -2, we get x = 5 + (7/4)(-3) = -4.75
Out of these values of x, the only one that lies in the interval [5, 12] is x = 26.75.
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janelys has 62 m of fencing to build a four-sided fence around a rectangular plot of land. the area of the land is 220 square meters. solve for the dimensions (length and width) of the field.
Therefore, the dimensions of the rectangular plot are either 20 meters by 11 meters or 11 meters by 20 meters.
Let's assume that the length of the rectangular plot is x meters. Then the width would be (220/x) meters because we know that the area is 220 square meters.
The perimeter of the rectangular plot would be:
2x + 2(220/x) = 62
Simplifying this equation, we get:
2x^2 + 440 = 62
2x^2 - 62x + 440 = 0
x^2 - 31x + 220 = 0
Factoring this equation, we get:
(x - 20)(x - 11) = 0
Therefore, x = 20 or x = 11.
If x = 20, then the width would be 11 and if x = 11, then the width would be 20.
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A giant golf ball is being constructed for the final hole of a new mini-golf course. They used 38. 7 cubic feet of material to create the figure. What is the radius of the gaint gold ball?
2. 1
38
114
9. 1
The radius of the golf ball is given as follows:
2.1 feet.
What is the volume of an sphere?The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
The volume of the ball in this problem is given as follows:
V = 38.7 cubic feet.
Hence the radius of the ball is obtained as follows:
r³ = 3 x 38.7/4π
r³ = 9.2389
[tex]r = \sqrt[3]{9.2389}[/tex]
r = 2.1 feet
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Suppose you play a game where you toss three fair coins. If you get three tails, you win $10. Otherwise, you lose $2. If you were to play this game 15 times, how much would you expect to gain or lose?
Do not round until the final answer.
Enter an expected loss as a negative number.
The expected gain or loss from playing the game 15 times is -$75.00, indicating an expected loss of $75.00.
To determine the expected gain or loss from playing the game 15 times, we need to calculate the expected value.
The probability of getting three tails (winning) in a single coin toss is (1/2) * (1/2) * (1/2) = 1/8, since each coin toss is independent and has a 1/2 probability of landing tails.
The probability of losing in a single coin toss is 1 - 1/8 = 7/8.
If we play the game 15 times, the expected number of wins is (1/8) * 15 = 15/8, and the expected number of losses is (7/8) * 15 = 105/8.
The amount gained from winning is $10, and the amount lost from losing is $2.
Therefore, the expected gain or loss can be calculated as follows:
Expected gain or loss = (Expected number of wins * Amount gained) - (Expected number of losses * Amount lost)
= (15/8 * $10) - (105/8 * $2)
Simplifying this expression, we find:
Expected gain or loss = $187.50 - $262.50
= -$75.00
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It’s proportions
Need help with first four
The answers are explained below.
Given are the questions to be solved with the help of proportionality,
Let the unknown values be x,
a) 32 / x = 8 / 6
x = 24
Hence the height of the tree is 24 ft.
b) 3.5 / 5 = x / 3
x = 2.1
Hence the cups of flour needed is 2.1 cups.
c) 2 / 90 = 5 / x
x = 225
Hence 5 cubic ft sand will weigh 225 lbs.
d) 18.50 / 35 = 12.50 / x
x = 23
Hence $12.5 will costs for 23.
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In a secondary school class, 23 students study economics 48 students study either economics or government or both (I) what is the total number of students study economics (I) how many students study government only
The answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.
It is given that:
In a secondary school class, 23 pupils study Economics, 6 pupils study both Government and Economics. 48 pupils study either Government or Economics or both.
Based on the information we can draw a Venn diagram:
From the Venn diagram:
A + B = 17 + 6
A + B = 23
B = 6
A + B + C = 48
A = 23 - 6 = 17
C = 48 - 17 - 6
C = 25
The total number of pupils who only study Government = 25
The total number of pupils who study Government = 25 + 6 = 31
The total number of pupils who study Economics only = 17
Thus, the answer for (1) is 31, the answer for (2) is 25, and the answer for (3) is 17.
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help help help help help help !!!!
Answer:
Yes because if you were to continue enlarging the shape it would continue to follow the path/line of 10,1
Step-by-step explanation:
1. Find the point on the directed line segment from (-2, 0) to (5, 8) that divides it in the ratio of 1:3.
Step-by-step explanation:
1:3 means you need to find 1 /(1+3) = 1/4 th of the way to 5,8 from -2,0
x: from -2 to +5 is 7 units 1/4th * 7 = 7 /4 added to -2
is - 1/4
y: from 0 to 8 is 8 units 1/4 th * 8 = 2 added to 0 is 2
(-1/4 , 2)
Solve for y.
-5(-5y+2)-8y=3(y-7)-7
Simplify your answer as much as possible.
Question 3 of 15
Answer:
y=-[tex]\frac{9}{7}[/tex]
Step-by-step explanation:
Your patient has an order to be injected with 2 grams of medication. One milliliter of liquid contains 0.1 grams of medication. How many milliliters should be injected into the patient?
Question 5
A player randomly selects a marble from a bag. The bag has 5 blue marbles, 6 red, 1 orange, and 1 yellow. How many outcomes are in the sample space?
The sample space has 13 outcomes.
We have to given that;
A player randomly selects a marble from a bag.
And, In the bag which has 5 blue marbles, 6 red, 1 orange, and 1 yellow.
Since, The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Now, We can formulate;
Total number of marbles = 5 + 6 + 1 + 1
Total number of marbles = 13
Hence, there are 13 possible outcomes for the player's selection.
Therefore, We get;
The sample space has 13 outcomes.
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What is the test statistic if
the sample proportion is 20/50 and the hypothesized proportion was 0.5?
Please help Urgent
The test statistic if the sample proportion is 20/50 and the hypothesized proportion was 0.5 is: -1.414.
What is the test statistics?Using z-test formula to determine the test statistic
z = (p - P) / [tex]\sqrt[/tex]((P(1-P))/n)
Where:
p = sample proportion = 20/50 = 0.4
P = hypothesized proportion = 0.5
n= sample size = 50
Let plug in the formula
Test statistic = (0.4 - 0.5) / [tex]\sqrt[/tex]((0.5(1-0.5))/50)
Test statistic = (-0.1) / [tex]\sqrt[/tex]((0.25)/50)
Test statistic = (-0.1) / [tex]\sqrt[/tex](0.005)
Test statistic = (-0.1) / 0.0707
Test statistic = -1.414
Therefore the test statistic is -1.414.
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A 95% confidence set for two or more coefficients is a set that contains: A) the sample values of these coefficients in 95% of randomly drawn samples. B) integer values only. C) the same values as the 95% confidence intervals constructed for the coefficients. D) the population values of these coefficients in 95% of randomly drawn samples.
A 95% confidence set for two or more coefficients is a set that contains: D) the population values of these coefficients in 95% of randomly drawn samples.
A 95% confidence set for two or more coefficients is a set that contains the same values as the 95% confidence intervals constructed for the coefficients. This means that the set includes all possible values for the coefficients that are consistent with the observed data and the level of uncertainty indicated by the confidence level. It is important to note that the confidence set is not guaranteed to contain the true population values of the coefficients in 95% of randomly drawn samples, as the true values are unknown.
The confidence set provides a range of plausible values that can be used for inference and decision making. The concept of a 95% confidence set.
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Rewrite each of the following expressions without using absolute value 20 POINTS!
Equation: |z-6|-|z-5| If z<5
A) (6-z)+(5-z)
B) (z-6)-(5-z)
C) (6-z) +(z-5)
After rewriting the final answer will be 1.
Given,
|z−6|−|z−5| , if z<5
Now,
|z-6| will be less than 0 since z is less than 5 and |z-5| will be less than 0 since z is less than 5.
So we can rewrite it as 6-z and 5-z by removing the absolute value signs and converting them in positive .
(6-z) - (5-z)
Further,
6-z-5+z
= 1
Hence Rewriting can be done without absolute values.
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help me please
Which of the following represents the polar equation r = (cot^2 θ)(csc θ) as a rectangular equation?
x2 + y2 = 1
y = 1
y2 = x3
y3 = x2
The rectangular equation that represents the polar equation r = (cot²θ)(csc θ) is y³ = x², which is an option (d).
The polar equation r = (cot²θ)(csc θ) can be written in rectangular form using the relationships x = r cos θ and y = r sin θ.
Substituting these expressions into the polar equation, we get:
r = (cot²θ)(csc θ)
r = (cos θ/sin θ)²(1/sin θ)
r = cos² θ/sin³ θ
x = r cos θ = cos³ θ/sin³ θ
y = r sin θ = cos² θ/sin² θ
As per the variable of x and y,
y³ = x².
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tom has 5 books with red covers and 5 books with white covers to place on a shelf. in how many ways can he arrange the books if the are to alternate red, white, red, white?
By probability , Tom can arrange his 5 red and 5 white books in an alternating pattern in 48 ways
There are 5 red books and 5 white books to arrange in an alternating pattern on the shelf.
To do this, Tom can start with either a red or a white book. If he starts with a red book, he can arrange the rest of the books in 4! (4 factorial) ways. Similarly, if he starts with a white book, he can arrange the rest of the books in 4! ways. Therefore, the total number of ways Tom can arrange the books in an alternating pattern is 2 x 4! = 48.
Tom can arrange the 10 books in an alternating pattern by starting with either a red or a white book. If he starts with a red book, he can arrange the rest of the books in 4! ways, and if he starts with a white book, he can also arrange the rest of the books in 4! ways. Therefore, the total number of ways to arrange the books is 2 x 4! = 48.
Tom can arrange his 5 red and 5 white books in an alternating pattern in 48 ways.
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William asked 20 of his friends if they own a car and wrote a report on his
findings.
The headline of his report was "65% of people do not own a car".
a) How many of the people William asked did not own a car?
b) Write a sentence to describe a problem with William's headline and a
problem with his survey.
(a) The people that did not own a car are 13
(b) The sentence to describe the problem is "13 of every 20 people do not own a car"
(a) People that did not own a carGiven that
Number of friends = 20
Percentage that do not own a car = 65%
Using the above as a guide, we have the following:
People = 65% * 20
Evaluate
People = 13
(b) The sentence to describe the problemWriting a sentence to describe the problem, we have:
The statement is given as
65% of people do not own a car".
This can be rewritten as
"13 of every 20 people do not own a car"
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Light bulbs are labeled with the number of watts of electricity they use as shown by the table. What are the attributes, measurements used, and observations of the data?
The attributes, measurements used, and observations of the data are listed below:
The attributes, measurements used, and observations of the dataAttributes:
- Light bulb
- Wattage (number of watts of electricity used)
Measurements used:
- Watts (units of measurement for the amount of electricity used by a light bulb)
Observations:
- The data shows the wattage for different types of light bulbs.
- The wattage varies widely among different types of light bulbs.
- Incandescent bulbs have the highest wattage, followed by halogen bulbs, fluorescent bulbs, and LED bulbs.
- The wattage for each type of bulb can vary within a certain range, with some bulbs having higher or lower wattage than others within the same category.
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Answer:
Step-by-step explanation:
The sum of the measures of the angles of a triangle is 180 m
The sum of the measures of the angle of a triangle is 180 degrees.
Sum of angles in a triangleThe given triangle is a type of triangle and the type of triangle a scalene triangle.
For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.
Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.
We can therefore conclude that:
m<A + m<B + m<C = 180 degrees
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Is 84 cubed an irrational number?
Answer:Yes, because ∛84 = ∛(2 × 2 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 84 is an irrational number.
Step-by-step explanation:
Answer: i think so
Step-by-step explanation:
a tree was 59 inches tall. two years later it was 89 inches tall. what was the percent increase, to the nearest hundredth, of the height of the tree? enter the answer in the box.
Answer:
50.85% increase
Step-by-step explanation:
The formula for % change is (new-old)/old.
So (89-59)/59 = 30/59 = 0.5084745763 = 50.85% increase
Unit 7
1. For each equation, find the initial value and the percent increase or decrease.
a. f(x) = 37(1.04)*
i. IV:
ii. % Inc/Dec:_
b. f(x) = (-0.7) (0.6)*
i. IV:
ii. % Inc/Dec:___
Please help me
a.
i. The initial value (IV) is 37.
ii. The percent increase or decrease is 4%.
b.
i. The initial value (IV) of the function is -0.7.
ii. The percent decrease is 40%.
a.
i. The initial value (IV) of the function is 37.
ii. The percent increase or decrease is 4%, because the base of the exponential function is 1.04, which is 1 plus 4% (0.04).
b.
i. The initial value (IV) of the function is -0.7.
ii. The percent decrease is 40%, because the base of the exponential function is 0.6, which is 60% (0.6) of the initial value (-0.7).
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The complete question:
1. For each equation, find the initial value and the percent increase or decrease.
a. f(x) = 37(1.04)ˣ
i. IV:__
ii. % Inc/Dec:_
b. f(x) = (-0.7) (0.6)ˣ
i. IV:
ii. % Inc/Dec:___
mike pays $2.79 for coffee every weekday morning on his way to work. on saturdays, he goes to visit his mother and takes her out to her favorite coffee shop where he spends $7.83 for two coffees. how much does he spend per week for coffee? $21.78 $26.91 $13.95 $29.61
Answer:
$21.78
Step-by-step explanation:
2.79 X 5 = 13.95
13.95 + 7.83 = 21.78
Use the formula to find the surface area of the figure. Show your work.
Answer:
150 square inches
Step-by-step explanation:
The formula is A=2(wl+hl+hw)
Plug in the values.
2(9+33+33)
Evaluate.
=150
(Assuming both the length and width is 3)
a production process produces 6% defective parts. a sample of five parts from the production process is selected. what is the probability that the sample contains exactly two defective parts? 0.0020 0.0299 0.9701 0.9980
The probability that the sample contains exactly two defective parts from a production process with a 6% defect rate is 0.0299. Option B is answer
To find the probability, we can use the binomial probability formula. The formula is P(X=k) = (n C k) * (p^k) * ((1-p)^(n-k)), where n is the sample size, k is the number of successes (defective parts), p is the probability of success (defect rate), and (n C k) represents the combination formula.
In this case, n = 5 (sample size), k = 2 (number of defective parts), and p = 0.06 (probability of a part being defective). Plugging these values into the formula, we get P(X=2) = (5 C 2) * (0.06^2) * ((1-0.06)^(5-2)) = 10 * 0.0036 * 0.8464 = 0.0299.
Therefore, the probability that the sample contains exactly two defective parts is 0.0299 (Option B).
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Let f (x) = x^2.
A) which is greater: f(7) or f (-7)? Explain.
B) which is greater f(-10) or f(3)? Explain.
Evaluating the function we can see that:
a) f(7) is equal to f(-7)
b) f(-10) is greater than f(3).
How to see which value is greater?Here we have the quadratic function f(x) = x²
A) First we need to evaluate the function in x = 7 and x = -7 to see which one gives a larger value.
f(7) = 7² = 49
f(-7) = (-7)² = 49
Then neither of these two is greater, because are the same value.
B) now we need to evaluate in x = -10 and x = 3
f(-10) = (-10)² = 100
f(3) = 3² = 9
We can see that f(-10) is greater.
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A circle has a radius of 2. What is the area of the circle. Round to the nearest tenth
Answer:
The area is 12.57, rounded to the nearest then is 13.
Step-by-step explanation:
A=πr2=π·22≈12.56637
8. What is the circumference of the given circle in terms of "? *
7 mm
7Tt
14π
36▬
49m
The circumference of the given circle is 14π mm.
We have,
The circumference of a circle with radius r is given by the formula:
C = 2πr
In this case,
The radius of the circle is given as 7 mm.
Substituting the value of r in the above formula.
C = 2π(7) mm
Simplifying this expression, we get:
C = 14π mm
Therefore,
The circumference of the given circle is 14π mm.
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working out the volume of a prism
Answer:
180 cm³
Step-by-step explanation:
split the side (the side facing us) into three rectangles. one rectangle immediately beneath top step, next under middles step and so on.
area under top step = (2 + 2 + 2) X 3 = 18.
area under middle step = (2 + 2) X 3 = 12
area under bottom step = 2 X 3 = 6
total area of this side (cross-section) = 18 + 12 + 6 = 36.
volume = 36 X length
= 36 X 5
= 180 cm³
(-2,-2) multiplied by the scale factor of 2
ANSWER:
(-4,-4)
EXPLANATION:
Just simply multiply the two points by 2. Since -2*2 is equal to -4, then the answer would be (-4, -4).
