a) ∀x∃y(x < y): For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0)) : For any numbers x and y if x is greater tha or equal to 0 and y is greater than or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z) : For any numbers x and y there exist number z such that the product of x and y is equal to z.
We know that a mathematical statement is nothing but a sentence which is either true or false.
We need to translate these statements into English.
The meaning of some mathematical symbols:
∀ : for all
∃ : there exists exactly one
∧ : and
Here, x, y, z are real numbers.
Consider given mathematical statements.
a) ∀x∃y(x < y)
For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
For any numbers x and y if x is greater tha or equal to 0 and y is greater tha or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z)
For any numbers x and y there exist number z such that the product of x and y is equal to z.
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bridge is a card game in which the deck of 52 cards is randomly and equally divided among the 4 players. so each player gets 13 cards.
The formula for calculating the number of cards each player receives in Bridge is N/4, where N = number of cards in the deck.
For a standard deck of 52 cards, each player would receive 52/4 = 13 cards. This can be further simplified to 13.33, however, since cards cannot be divided, the result is rounded down to 13 cards. Therefore, each player in a Bridge game with a standard deck of 52 cards will receive 13 cards.
The total number of cards in the deck is 52, so each player will get 13 cards. This can be expressed mathematically using the formula P = 52/4, where P is the number of cards per player. Therefore, P = 13. We can also use the formula to calculate the number of players if we know the total number of cards. For example, if we have 156 cards, the number of players can be calculated using the formula P = 156/4, which gives us P = 39. Therefore, there will be 39 players in the game.
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in a survey it was found that studnets are talented at playing football. After assessment by coaches it was seen that 5% students possess football skills classed at professional level. A random sample of 10 studnets is obtained from the campus and measurements of their football skills were taken. Find the probability that 8 or more of these stundents were classed at professional level. the picture of quetsion is attached i have sloved the rest just cannot solve part d).
The probability that 8 or more of these students were classed at professional level is given as follows:
0%.
What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The values of the parameters for this problem are given as follows:
n = 10, p = 0.05.
Hence the probability of 8 or more of these students were classed at professional level is given as follows:
P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)
In which:
P(X = 8) = 45 x (0.05)^8 x 0.95² = 0.P(X = 9) = 10 x (0.05)^9 x 0.95^1 = 0.P(X = 10) = 0.05^10 = 0.Hence the probability is of 0%.
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I need to know the 10th term?
to find a given term, substitute the corresponding value of n into the ninth term formula. For example, if the ninth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the ninth term. 3 x 10 + 2 = 32 and so, the tenth term of the sequence is 32.
To find the nth term of an arithmetic sequence, use the following formula:
[tex]an = a + (n - 1)d[/tex]
an(nth term) = a(first term) + (n(term you are looking for) - 1) * d(common difference)
Para llegar desde un pueblo A hasta B existen 3 caminos, para llegar del pueblo B hasta el pueblo C hay 673 caminos distintos y para llegar desde el pueblo C hasta el pueblo D hay 2019 caminos, ¿Cuántos caminos distintos hay para llegar desde el pueblo A hasta el pueblo de pasando por los pueblos B y C?
⚘
what are you up for now and what time do you think you'll have time for
NO LINKS!!
43. For the following functions, state whether they are growth or decay, then determine each function's growth/decay rate. (NOT MULTIPLE CHOICE)
a. f(x) = 0.3(1.6)^x
b. g(x) = 0.8^0.5x - 7
c. h(x) = 3(-5)^x
d. f(x) = e^(-0.45x) + 4
Answer:
a) Exponential growth function: 60%
b) Exponential decay function: 20%
c) Neither
d) Exponential decay function: 45%
Step-by-step explanation:
[tex]\textsf{Exponential Growth}: \quad y=a(1+r)^x[/tex]
[tex]\textsf{Exponential Decay}: \quad y=a(1-r)^x[/tex]
where:
a = initial value (the amount before measuring growth or decay)r = growth/decay rate (in decimal form)Part aGiven function:
[tex]f(x) = 0.3(1.6)^x[/tex]
The function is an exponential growth function and the growth rate is:
[tex]1+r=1.6 \implies r= 0.6 = 60\%[/tex]
Part bGiven function:
[tex]g(x) = 0.8^{0.5x} - 7[/tex]
The function is an exponential decay function and the decay rate is:
[tex]1-r=0.8 \implies r=0.2=20\%[/tex]
Part cGiven function:
[tex]h(x) = 3(-5)^x[/tex]
This is neither an exponential growth or decay function as exponential functions cannot have negative bases.
Part dNatural base exponential function
[tex]y=ae^{rx}[/tex]
If a > 0 and r > 0, the function is an exponential growth function.
If a > 0 and r < 0, the function is an exponential decay function.
Given function:
[tex]f(x) = e^{-0.45x} + 4[/tex]
As a = 1 > 0 and r = -0.45 < 0, the function is exponential decay function and the decay rate is:
[tex]r=-0.45=45\%[/tex]
Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
D
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
The length of BC is 10.
What are similar triangles?When two triangles have some common corresponding properties, they are said to be similar. But they are no congruent.
In the given question, comparing triangles ABC and DEC. We have;
DE/ AB = EC/ BC
But,
BC = 2BE
= 2x
So that,
(x + 2)/ (4x - 6) = x/ 2x
(x + 2)/ (4x - 6) = 1/ 2
2(x + 2) = (4x - 6)
2x + 4 = 4x - 6
collect like terms
6 + 4 = 4x - 2
10 = 2x
x = 10/ 2
x = 5
Then,
BC = 2x
= 2*5
BC = 10
The length of BC is 10.
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P (n), given below, is the price in dollars for n grams of vitamins. P(n)=0.5n+6.4 Complete the following statements. Let P¹ be the inverse function of P. Take x to be an output of the function P. That is, x=P (n) and n=P-¹(x). (a) Which statement best describes P-¹(x)? The reciprocal of the price (in dollars) for x grams of vitamins. The amount of vitamins (in grams) for a price of x dollars. The price (in dollars) for x grams of vitamins. The ratio of the price (in dollars) to the number of grams, x. -1 (b) P(x) = - 1 (c) P (9.2) = log 010 X log No solution 0=0 Ś
The number of vitamins (in grams) for a price of x dollars. Then the correct option is B. The inverse function is P⁻¹(x) = (x - 6.4) / 0.50. And at x = 9.2, the value P⁻¹(x) will be 5.4 grams.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The function is given below.
P(n) = 0.50n + 6.4
The inverse of the function P(n) is given as,
x = 0.50P⁻¹(x) + 6.4
P⁻¹(x) = (x - 6.4) / 0.50
At x = 9.2, then we have
P⁻¹(9.2) = (9.2 - 6.4) / 0.50
P⁻¹(9.2) = 5.6 grams
The number of vitamins (in grams) for a price of x dollars.
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Which table shows a proportional relationship between X and Y?
K12
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
What is a ratio?If the ratios of two or more numbers or variables are equal to one another, they are said to be in proportion.
The answer to the query is
8; 10, 12; 14, given x
y : 5, 7, 9, 11
Ratios between various x and y values are not comparable.
( 8 /5)
≠ (10 / 7)
≠ (12 /9)
≠(14 /11)
We get to the conclusion that x and y have no proportional relationship.
Hence, Option(1) is the correct answer.
X and Y don't have a proportionate relationship.No, not all yx ratios are equal.
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The sum of the measures of angle P and angle Q is 100⁰.
• The measure of angle P is (3x - 15)°.
• The measure of angle Q is 25°.
What is the value of x? (7.11C, SS, RC3)
Answer:
x = 30
Step-by-step explanation:
You are given an angle and the sum of that angle with another that is (3x-15)°, and you want the value of x.
EquationThe sum of the two angles is given as 100°.
P +Q = 100°
(3x -15)° +25° = 100° . . . . . . use the given values for angles and sum
3x = 90 . . . . . . . . . . . . divide by ° and subtract 10
x = 30 . . . . . . . . . divide by 3
The value of x is 30.
determine whether the statement below is true or false. justify the answer. the solution set of the linear system whose augmented matrix is is the same as the solution set of the equation .
This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.
What are Linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.
An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.
Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.
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A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA= B+ Ph, since the vase has a bottom but no top. Use 3.14 for TT and round to the nearest tenth of a square inch.
Answer: To find the surface area of the cylindrical vase, we can use the formula:
SA = B + Ph
Where B is the area of the base (the circular top of the vase), P is the perimeter of the circular top of the vase, and h is the height of the vase.
We know that the diameter of the vase is 4.3 inches and the height of the vase is 11 inches. To find the radius of the base, we can divide the diameter by 2:
r = 4.3 inches / 2 = 2.15 inches
The area of the base is given by πr², so:
B = πr² = π * 2.15² = 14.65 square inches
To find the perimeter of the circular top we can use 2πr:
P = 2πr = 2 * 3.14 * 2.15 = 13.64 inches
Now we can substitute these values into the formula:
SA = B + Ph = 14.65 + 13.64 * 11 = 260.04 square inches
Rounded to the nearest tenth, the surface area of the vase is 260.0 square inches.
Step-by-step explanation:
I know each x_i (i = 1, 2, ..., n) is a random variable based on the sample size n obtained. Therefore, [tex]\frac{}{X}[/tex] is a random variable since it would be a different (random) value for each new sample size of n collected. How would I further elaborate on this explanation to answer the question in the screenshot?
The sample mean can be classified as a random variable because it is calculated from the sample which is built as random.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Hence the sample mean is obtained as the sum of all observations of the sample divided by the sample size.
As the observations of the sample are taken at random, the sum of these observations will be a random variable, and so will the sample mean.
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which of the following tables best shows the expected values in the f2 generation for a chi-square goodness-of-fit test for a model of independent assortment?
The chi-square goodness-of-fit test requires a comparison of the observed values with their expected values in the f2 generation.
Option A. Observed Values | Expected Values; this is the best choice for this comparison.The chi-square goodness-of-fit testThe chi-square goodness-of-fit test is used to determine how well observed values fit a model of independent assortment. The test requires a comparison of the observed values with their expected values in the f2 generation.
Option A is the best choice for this comparison, as it provides a direct comparison of the observed and expected values. This comparison allows for an assessment of the goodness-of-fit of the model, as any differences between the observed and expected values can be attributed to the model's performance.
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There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.
The theoretical probability is 25%, and the experimental probability is 27.5%.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.If two events A and B occur on a single performance of an experiment, this is called the intersection or joint probability of A and B, denoted as P(A ∩ B).Given is that There are 10 brown, 10 black, 10 green and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Thee given table is -
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
The probability of pulling out a gold ball will be -
P{gold} = 11/40 = 0.275 = 0.275 x 100 = 27.5%
P{gold} = 27.5%
Therefore, the theoretical probability is 25%, and the experimental probability is 27.5%.
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Which expression is equivalent to 250h² - 100h?
O 50h(5h - 2)
○ 50(5h - 2)
○ 50h (5h+2)
50(5h+2)
Answer:
50h(5h - 2)
Step-by-step explanation:
Open up all the parenthesis on each answer
only the first one is correct
Answer:
50h(5h-2)
Step-by-step explanation:
Solution given
250h² - 100h
50*5*h*h-50*2*h
taking common
50*h(5*h-2)
50h(5h-2)
here taking common and keeping remaining on bracket
50h(5h-2)
declare double variables x1, x2, x3, and x4, and read each variable from input in that order. find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
The answer is x4 = input.nextDouble() and double avgnumber = (x1 + x2 + x3 + x4) / 4.
Declare the double variables x1, x2, x3, and x4.
double x1, x2, x3, x4;
Read each variable from input in that order.
Scanner input = new Scanner(System.in);
System.out.println("Enter x1:");
x1 = input.nextDouble();
System.out.println("Enter x2:");
x2 = input.nextDouble();
System.out.println("Enter x3:");
x3 = input.nextDouble();
System.out.println("Enter x4:");
x4 = input.nextDouble();
To Find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
double avgnumber = (x1 + x2 + x3 + x4) / 4;
//This code takes four double variables from input and calculates the average by adding the four numbers together and dividing by four. The result is stored in the double variable avgnumber.
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a six sided dice is rolled 4 times, How many outcomes are there of rolling a 6 exactly 2 times?
The outcome that are there when a six sided dice is rolled four times is 2
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The p space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.
The sample space of getting a 6 from a die is 1. A die has six sides and are labelled 1-6
The outcome of 4 times is is 4
Therefore for two rolls, it will be 4/2 = 2
Therefore the outcome to get 6 exactly two times is 2.
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Given the figure below shows a regular hexagon, ABCDEF
What is the measure of each interior angle?
You go to the grocery store and purchase the items listed in the table. What is your total if
the sales tax is 7%?
Answer:
where is the table?
Step-by-step explanation:
repost it with a picture of the table so we can answer it or tell the details and I'll answer in the comments?
According to an article on The Guardian website, a British woman born in 2003 has probability 0.27 of living at least 100 years. Five high school friends all happen to be females born in 2003.Assuming that the survival of each one is independent of the others, what is the probability that at least one of them lives to be 100 years old?
The probability that at least one of the five female high school friends born in 2003 lives to be 100 years old is 0.054 or 5.4%.
What is the probability?Probability refers to the chance, odds, or likelihood that an expected outcome occurs when there are many possible outcomes.
Probability is a fractional value, lying between one and zero when the expected event is not 100% certain or uncertain.
Probability is computed as the quotient or ratio that results from dividing the expected value by the total weight.
The chance of British women born in 2003 living at least 100 years according to The Guardian website = 0.27
The probability that at least one of five female high school friends born in 2003 lives to be 100 years old = 0.27 x 1/5
= 0.054
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2/ ((s+1)(s+2) (0.5s+1)) inverse laplace
s3+5s2+8s+4
Step-by-step explanation:
Answer:
(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)
Where u(t) is the step function
Step-by-step explanation:
use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.
The average high temperature in degrees for a city are listed 58,61,71,77,91,100,105,102,95,82,66,57 if a value of 48 is added to the data how does the median change
If a value of 48 was added, the median of the data-set would remain decay from 79.5 to 77.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.
The ordered data-set for this problem is given as follows:
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105.
The data-set has an even cardinality of 12, hence the median is the mean of the 6th and the 7th elements, as follows:
(77 + 82)/2 = 79.5.
A value of 48 would be lowest value of the data-set, the cardinality would be odd, and thus the middle value would be of 77.
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which of the following are true of quantitative research and quantitative researchers? (select all that apply.)
The correct statement about quantitative research is:
It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
We know that the quantitative research is nothing but the process of collecting and analyzing numerical data.
It is used to find the patterns, make predictions, test the relationships, and generalize results to given populations.
Whereas the qualitative research involves collecting and analyzing non-numerical data.
Quantitative research is mostly used in the natural sciences and social sciences.
It collects data using sampling methods, or by sending out online surveys/ polls, and questionnaires.
It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
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The complete question is:
Which of the following is true of quantitative research?
1) It enables researchers and clients to get closer to their customers and potential customers than does qualitative research.
2) It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.
3) It is most often used with exploratory research designs.
4) It usually involves collecting detailed data from relatively small samples by asking questions or observing behavior.
5) It is superior for studying topics that involve complex psychological motivations not easily reduced to survey formats and quantitative analyses.
solve for . assume is a matrix. do not use decimal numbers in your answer. if there are fractions, leave them unevaluated.
The value of X in the given system of matrix is,
[tex]X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]
Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.
We have 2 by 2 matrix in the form,
[tex]\left[\begin{array}{ccc}9&9\\-9&-9\\\end{array}\right] X+\left[\begin{array}{ccc}6&3\\7&9\\\end{array}\right] =\left[\begin{array}{ccc}-1&8\\-4&6\\\end{array}\right] X\\\\Assume, X=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \\\\[/tex]
After multiplication,
[tex]9a+9c+6=-a+8c\\\\-9a-9c+7=-4a+6c\\\\9b+9d+3=-b+8d\\\\-9b-9d+9=-4b-6d\\\\[/tex]
After solving the given system of equations
[tex]a=\frac{-97}{145}\\\\b=-\frac{54}{145}\\\\c=\frac{20}{29}\\\\d={21}{29}\\\\Hence, \\X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]
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Complete the table of ordered pairs for the linear equation y=3x-11
What is the area of ΔABC such that b = 28 cm, c = 14 cm, and m∠A = 30°? Round the answer to three decimal places.
The area of the ΔABC is 98 cm²
How to find the area of ΔABC?In a triangle, we can use the sine formula to find the area of the triangle when we know one angle and the two side lengths opposite and adjacent to that angle.
Area of ΔABC = (1/2) bc sinA
Substitute b = 28 cm, c = 14 cm, and m∠A = 30° into the formula:
Area of ΔABC = (1/2) × 28cm × 14cm × sin 30°
Area of ΔABC = 98 cm²
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Find the equation of the line containing the point
P(1, 2)
and parallel to the graph of
5x + y = −2.
Answer:
y = -5x + 7
Step-by-step explanation:
Parallel lines on a graph have the same slopes/gradients.
m1=m2
First you want to rewrite the equation of the graph given. So put the 5x to the other side and you will have:
y = -5x -2
This means that the equation that we need must have the gradient -5 (bc it is m in y=mx+c)
The equation will be y = -5x + c
However we must still find c aka the y intercept.
Sub the point we are given (1,2) into the equation
We will have:
2 = -5(1) + c
2 = -5 + c
7 = c
Now that we know c, we know what the equation of the line is. Just sub it in (without 1 and 2)
y = -5x + 7
a ball suspended by a thread swings in a vertical plane so that its acceleration in the extreme position and lowest position are equal. The angle θ
of thread deflection in the extreme position will be:
(A) tan^−1(2)
(B) tan^−1(√2)
(C) tan^−1(1/2)
(D) 2tan^−1(1/2)
The angle θ of thread deflection in the extreme position is given by tan^−1(2).
The angle of thread deflection in the extreme position can be calculated by using the equation of motion of a simple pendulum.
The equation of motion for a simple pendulum is given by m g L sinθ = m a. Here, m is the mass of the ball, g is the gravitational acceleration, L is the length of the thread and θ is the angle of the thread.
From the given condition, the acceleration of the ball in the extreme and lowest positions are equal. This implies that the acceleration of the ball in the extreme position is equal to the acceleration due to gravity.
Therefore, the equation of motion reduces to g L sinθ = g. Solving for θ, we get sinθ = 1, which implies that θ = tan^−1(2).
Therefore, the angle θ of thread deflection in the extreme position is given by tan^−1(2).
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-5,-5)
(2,7)
(0, -3)
For it to be parallel, the point must follow the translation from (2,7) to that point similar to (0, -3) to (-5, -5) which is left 5 and down 2. So left 5 and down 2 for (2, 7) makes it (-3, 5)
4. Is 3 in the domain of the function ? Why or why not?
The domain of the function f(x) = √(x - 5) is x ≥ 5, thus, x = 3 is not in the domain.
Is 3 on the domain of the function?Remember that for a function y = f(x), we define the domain as the set of the possible inputs.
Here we have the square root function:
f(x) = √(x - 5)
Remember that the argument of a square root needs to be zero or larger, then the domain of the given function is:
x - 5 ≥ 0
Solving for x:
x ≥ 5
The domain is the set of values equal to or larger than 5, thus, the value 3 is not in the domain.
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