The tilde approximation of the growth function f(n) = n + 5n^4 + nlg(n) is ~5n^4.
The tilde notation is used to describe the asymptotic behavior of a function, which means how the function grows relative to other functions as the input gets very large.
To determine the tilde approximation of the function f(n) = n + 5n^4 + nlg(n), we need to identify the term that grows the fastest as n becomes very large.
Analyze the first term: n. As n gets larger, the term n becomes relatively smaller compared to the other terms in the function.
Analyze the second term: 5n^4. This term grows much faster than the first term as n becomes larger.
Analyze the third term: nlg(n). The logarithmic term grows slower than the polynomial term, meaning that it becomes relatively smaller as n becomes larger.
Based on the analysis above, we can conclude that the dominant term in the function is 5n^4.
Therefore, the tilde approximation of the function f(n) = n + 5n^4 + nlg(n) is ~5n^4, meaning that the function grows approximately as n^4 when n becomes very large.
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if the simple interest on $800 for 3 years is $54, what is the rate of interest per annum
Answer:
The rate of interest per annum is 3%.
Step-by-step explanation:
The rate of interest per annum is 3%.
This can be calculated using the formula:
Simple Interest = (Principal x Rate x Time) / 100
In this case, we know that the Simple Interest = $54 and the Principal = $800, Time = 3 years.
So, we can rearrange the formula to solve for the Rate:
Rate = (Simple Interest x 100) / (Principal x Time)
Plugging in the given values, we get:
Rate = (54 x 100) / (800 x 3)
Rate = 3%
Write an equation of the line that passes through (1, 1) and (3, 3).
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 2 }{ 2 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 1}(x-\stackrel{x_1}{1})\implies y-1=x-1\implies \boxed{y=x}[/tex]
Answer: y=x+2
Step-by-step explanation: to find the slope use the formula y2-y1/x2-x1 which will get 3-1/3-1= 2/2= 1 so the slope is one. then take formula (y-y1)=m(x-x1) m is slope so you will get (y-3)=1(x-1) distribute the one y-3=x-1 add three to both sides to get y=x+2
suppose that a1, a2, a3 form a partition of the universal set s. let b be an arbitrary set. assume that we know |b∩a1|=10, |b∩a2|=20, |b∩a3|=15.
from the given information in the question we have found that all the three sets form a partition from the universal sets
What is a set?
A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
As it is given that there are 3 sets where the first set A1 has 10 or more elements, A2 has 20 or more elements, and A3 has 15 or more elements.
1. If A1 ⊆ A2 and A2 ⊆ A3 then the union of these three will contain the same number of elements as that of A3.
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As a result of inflation, the purchasing power of a fixed quantity of money decreases by 5% every year. If a certain quantity of money can buy 175 frozen dinners this year, how many frozen dinners can it buy in 12 years?
If necessary, round your answer to the nearest whole number.
Same amount of money can buy 95 dinners after 12 years.
What is inflation?Inflation is a decrease in the purchasing power of money, reflected in a general increase in the prices of goods and services in an economy.
Given,
Purchasing power of a fixed quantity of money decreases by 5% every year
It can buy 175 frozen dinners today,
Principal value P = 175 frozen dinners
Rate of decrease R = 5% = 0.05
Time n = 12 years
Equation for the future value
A = P (1- R)ⁿ
Frozen dinners that can be bought in 12 years with same amount
A = 175 ( 1 - 0.05 )¹²
A = 175 (0.95)¹²
A = 175 × 0.540360088
A = 94.5630154 ≈ 95
Hence, 95 frozen dinners can be bought after 12 years with same amount of money.
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compute the complement 0.87
The complement of 0.87 is calculated by subtracting the given number from 1. Mathematically, this can be expressed as 1 - 0.87 = 0.13.
The complement of any number x is calculated by subtracting x from 1. This means that the complement of 0.87 is 0.13.
The complement of a number is used to find the remaining portion of a whole. For example, if the given number is 0.87, then the complement of 0.87 is 0.13. This means that 0.87 is 87% of the whole and 0.13 is the remaining 13%. Thus, the complement of 0.87 is 0.13.
Complements can also be used to find the probability of something happening. For example, if the probability of an event occurring is 0.87, then the probability of it not occurring is 0.13. This is because the sum of the probabilities must equal 1 (100%). Therefore, the complement of 0.87 is 0.13.
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The sum of the lengths of two adjacent sides of a rectangle is 16 cm and the length of a diagonal is 14 cm. Show that, when the breadth of the rectangle is taken as x cm, it satisfies the quadratic equation ² - 16x + 30 = 0, and find separately the length and the breadth of the rectangle to the first decimal place. (Use 5.83 for the value of √34.)
consider the following quiz game. there are 2 questions. question 1 can be answered with probability 0.8 with reward $100 and question 2 can be answered with probability 0.5 with reward $200. if your first attempt in answering the question of your choice fails, the game is terminated. which question you should choose first to maximize your expected reward?
Question 1 should be chosen first to maximize your expected reward.
To maximize the expected reward, we need to calculate the expected reward for each question, taking into account the probability of getting the answer right and the reward for a correct answer.
For Question 1, the expected reward is 0.8 * $100 = $80, since you have an 80% chance of getting the answer right and earning a reward of $100.
For Question 2, the expected reward is 0.5 * $200 = $100, since you have a 50% chance of getting the answer right and earning a reward of $200.
Since the expected reward for Question 1 is higher than the expected reward for Question 2, you should choose Question 1 first to maximize your expected reward.
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the state of Nevada is the shape of a right trapezoid. The bases measure 205 miles and 511 miles, respectively. The distance between the bases is 309 miles. Find the area of the state.
The area of the state of Nevada which had the shape of a right trapezoid would be = 110,622 miles²
How to calculate the area of a trapezoid?The area of a trapezoid can be calculated using the formula of the following;
A = ( a + b ) x h/2
where;
a = 205
b = 511
h = 309
Area (A) = (205+511) × 309/2
= 716 × 154.5
= 110,622 miles²
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The area of the state of Nevada with the shape of a right trapezoid is; 110622 miles²
How to calculate the area of a trapezoid?The area of a trapezoid can be calculated with the formula :
Area = ¹/₂(a + b) * h
where;
a and b are parallel sides
h is height
The parameters are;
a = 205
b = 511
h = 309
Thus;
Area = ¹/₂(205 + 511) * 309
Area = 716 * 154.5
Area = 110622 miles²
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what is the radius of the unit circle? 2) identify the sine, cosine and tan for either 30, 45, or 60 degrees in the 1st quadrant using exact values not decimal approximations. 3) what angle in each quadrant has the same reference angle as chosen in step 2? 4) how does the sine, cosine and tangent change in each quadrant for your chosen reference angle? 5) how do these changes relate to the coordinates on the unit circle in each quadrant?
The unit circle's radius is 1, that is 1 is the radius of the circle.
45 degrees' sine, cosine, and tan values are
[tex]sin \ 45^0=\frac{1}{\sqrt{2} }[/tex]
[tex]cos\ 45^0=\frac{1}{\sqrt{2 } }[/tex]
[tex]tan \ 45^0 =1[/tex]
Due to the fact that all angles are smaller than,
the reference angle coincides with the specified angle. In the first quadrant, 45 degrees is the reference angle, and sine, cosine, and tangent are all positive trigonometric functions.
In the second quadrant, sine is positive, cosine is negative, and tan is positive. In the fourth quadrant, sine and tan are negative, cosine is positive.
In the case of a unit circle, the cosine sine of the angle formed by the horizontal line is used to represent the unit circle's coordinates.
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The line a intersects the y-axis at the same point as the line 11x + 3y + 6 = 0 and is parallel to the line 3x - y + 1 = 0.
a) Define the equation of line a
The equation of line a is given as follows:
y = 3x - 2.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.The parallel line is defined as follows:
3x - y + 1 = 0.
In slope-intercept format, it is given as follows:
y = 3x + 1.
Hence the slope of line a is given as follows:
m = 3.
(as parallel lines have the same slope).
The intercept is the same as the line 11x + 3y + 6 = 0, hence:
3y + 6 = 0
3y = -6
y = -2
b = -2.
Hence the line a is defined as follows:
y = 3x - 2.
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Your Matchup
Write expressions, in terms of t, that could represent
two vehicles traveling at different rates with different.
starting positions that will eventually meet.
Once you create your match-up, go to the next screen.
Truck Position Expression:
Car Position Expression:
Answer:
The expression for the truck's position in terms of t would be xtruck = t × vtruck, where vtruck is the truck's velocity. The expression for the car's position in terms of t would be xcar = t × vcar + x0, where vcar is the car's velocity and x0 is the car's initial position. For the vehicles to eventually meet, these two equations must be equal, so vtruck = vcar + (x_0/t).
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36-30:[26-100:(10-12:b)=6
Answer:
36-30:[26-100:(10-12:b)]=6 - 10417845.
What is the discriminant of the quadratic equation 7x^2 - 13x - 5 = 0
A. 29
B. 309
C. -29
D. -309
Answer: B. 309.
Step-by-step explanation: The discriminant of the quadratic equation 7x^2 - 13x - 5 = 0 is D = b^2 - 4ac, where a = 7, b = -13, and c = -5.
Plugging in the values, we get:
D = (-13)^2 - 4 * 7 * -5 = 169 + 140 = 309
Therefore, the answer is B. 309.
Answer:B.309 I hope this helps you
Step-by-step explanation:
7x^2-13x-5=0
Identify the coefficients , and of the quadratic equation
something like this
a=7 b=-13, c=-5
Evaluate the discriminant by substituting a=7, b=-13 and c=-5 into the expression b^2-4ac
Something like this
(-13)^2-4 time 7( -5)
Simplify the expression then you get your answer
309
Please helpp find the perimeter of CDEF !!!!!
Answer:
p= 77
Step-by-step explanation:
√3x+4 = 1+√3x-11 When both sides of the equation are squared, the resulting equation is
The resulting equation is 14√3x - 47 = 0.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
√3x + 4 = 1 + √3x -11
√3x + 4 = √3x - 10
Squaring both sides
(√3x + 4)² = (√3x - 10)²
3x² + 16 + 8√3x = 3x² - 20√3x + 100
16 - 100 + 8√3x + 20√3x = 0
28√3x - 94 = 0
2(14√3x - 47) = 0
14√3x - 47 = 0
Thus,
14√3x - 47 = 0 is the resulting equation.
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When both sides of the given equation are squared, the resulting equation is x = 20.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question, as follows:
√(3x+4) = 1+√(3x-11)
Squaring both sides of the equation:
3x + 4 = (1 + √(3x - 11))²
Expanding the square on the right side:
3x + 4 = 1 + 2√(3x - 11) + (3x - 11)
Simplifying the above equation, we get
196 = 12x - 44
12x = 196 + 44
12x = 240
x = 20
So the value of x that satisfies the equation is 20.
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cost price of a torchlight is rs.1400 its mp is 40% more than cost price if the shopkeeper sells it at 20% discount what is marked price of the torch
Answer:
The marked price of the torchlight is Rs. 1960.
Step-by-step explanation:
The marked price (MP) of a torchlight is 40% more than the cost price (CP), so we can calculate the MP using the formula:
MP = CP + (CP x 40%)
The cost price of the torchlight is Rs. 1400, so the marked price is:
MP = 1400 + (1400 x 40%) = 1400 + 560 = 1960
The shopkeeper is selling the torchlight at a 20% discount, so we can calculate the selling price (SP) using the formula:
SP = MP - (MP x 20%)
The marked price of the torchlight is Rs. 1960, so the selling price is:
SP = 1960 - (1960 x 20%) = 1960 - 392 = 1568
So the marked price of the torchlight is Rs. 1960.
question content area top part 1 what is a closed question? what is an open question? discuss the advantages and disadvantages of each type of question.
A Closed Question is a type of question which has fixed choices for answers, whereas an Open Question is a free response question.
The Open Questions are questions that allow for a free-flowing response, they often starting with "what," "how," "why," etc. They encourage the elaboration and provide deeper insights about topic .
The Closed Questions are questions which can be answered with a simple "yes" or "no" or a specific piece of information. They are good for quickly gathering specific information.
For Open Questions :
⇒ Advantages : Encourages elaboration and deeper insights , Builds rapport and relationship , Promotes active listening and understanding .
⇒ Disadvantages : Can be time-consuming and harder to analyze , May lead to vague or irrelevant responses
For Closed Questions :
⇒ Advantages : Quick and easy to answer , Facilitates efficient information gathering , Good for verifying information
⇒ Disadvantages : May limit information obtained , Can come across as rigid and uninterested .
The given question is incomplete , the complete question is
What is an Open and Closed Question ; discuss the advantages and disadvantages of each type of question .
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11. At 2 weeks old, baby Nellie weighed 9 pounds. When she was 8 weeks old, she weighed 12
pounds. Let x represent how old the baby is in weeks and y represent the baby's weight in
pounds. Find the equation of the line that goes through these two points.
From given data, equation of line will be x - 2y = -16.
Find the equation of the line that goes through these two points?To find points on the line y = mx + b, choose x and solve the equation for y, or. choose y and solve for x.
The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .
It's called this because it clearly identifies the slope and the y-intercept in the equation. The slope is the number written before the x. The y-intercept is the constant written at the end. Let's look at an example: y = 3x + 2.
Given,
x represent how old the baby is in weeks
y represent the baby's weight in pounds.
At 2 weeks old, baby Nellie weighed 9 pounds. When she was 8 weeks old, she weighed 12 pounds.
⇒ (2,9)
⇒ (8,12)
Equation of line will be = y - yo = m (x - xo)
= y - 9 = 1/2 (x - 2)
= 2y - 18 = x - 2
= x - 2y = -16
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a data analyst creates a scatter plot in tableau and notices an outlier. what should they do next? 1 point investigate the outlier to determine if it can lead to any important observations shift the outlier to the center of the other data points for conformity use a filter to highlight the outlier, as it is more important than the rest of the data remove the outlier, as it is unlikely to lead to any important observations
The data analyst should a)investigate the outlier to determine if it can lead to any important observations and b)use a filter to highlight the outlier, as it is more important than the rest of the data.
When analyzing data, it is important to look at outliers as they can provide valuable information. Outliers can point to an unexpected correlation or reveal a hidden trend that could be missed if they were removed. By investigating the outlier, a data analyst can look for any important observations the outlier might reveal.
Additionally, using a filter to highlight the outlier allows the analyst to focus on the outlier and compare it to the other data points. This can help the analyst to understand how the outlier differs from the rest of the data and draw any relevant conclusions.
Removing the outlier should be avoided as it can lead to data bias and remove important information from the analysis.
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The function A() given by A()=0. 24551 can be ued to etimate the average age of employee of a company in the year 1981 to 2009. Let A() be the average age of an employee, and be the number of year ince 1981; that i, =0 for 1981 and =9 for 1990. What wa the average age of the employee in 2003 and in 2009?
The the function to estimate the average age of employee of a company is A(s)=0.285s + 59 , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98
To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22 ;
because the number of years between 2003 and 1981 is = 22 years ;
So , A(22) = 0.285×22 + 59 = 65.27 ;
The average age of an employee in 2003 is approximately 65.27.
To estimate the average age of an employee in 2009,
we need to find the value of A(s) when s = 28
because the number of years between 2009 and 1981 is = 28 years ;
So , A(28) = 0.285×28 + 59 = 66.98 ;
The Average age of employee in 2009 is approximately 71.48.
The given question is incomplete , the complete question is
The function A(s) given by A(s)=0.285s + 59 can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let A(s) be the average age of an employee, and "s" be the number of year since 1981; that is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in 2009 ?
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Solve the equation
( attached an image of the problem)
Answer:
B
Step-by-step explanation:
[tex]x = \frac{2}{3}\pi r^{3}[/tex]
The objective is to isolate r and make r the subject of the equation:
Cross-multiplication is applied:
[tex]= 2\pi r^{3}= 3x[/tex]
The variables and number multiplied with [tex]r^{3}[/tex] are transferred to the other side of the equation:
[tex]= \pi r^{3} = \frac{3x}{2}[/tex]
[tex]= r^{3} = \frac{3x}{2\pi}[/tex]
Cube root is applied to both sides of the equation to get rid of the cube:
[tex]= \sqrt[3]{r^{3}} = \sqrt[3]{\frac{3x}{2\pi}}[/tex]
[tex]r = \sqrt[3]{\frac{3x}{2\pi}}[/tex]
what is an example of a pure exact number
An example of a pure exact number is "3".
In mathematics, pure exact numbers are also known as mathematical constants or closed-form numbers. Unlike approximations, such as those obtained through measurement or estimation, exact numbers have a fixed and well-defined value.
A pure exact number is a number that has a fixed, precise value and is not subject to any estimation or measurement error.
Examples of pure exact numbers include integers (e.g. 3, 42), rational numbers (e.g. 1/2, -3/7), and some real numbers that can be expressed as a ratio of integers (e.g. pi, e).
These numbers have a definite value and do not change, regardless of the measurement or calculation method used.
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because averages are less variable than individual outcomes what is true
The averages are less variable as compare to the individual outcomes is a true statement as individual value spread in wide range.
The averages are less variable compare to individual values.
It is a true statement.Average is the representation of the sum of all the individuals outcomes divided by number of individuals.Average is quiet near to all the individual values.Range of individual values to individual values is quiet wide compare to average to individual value.Spreading of data is more in individual values.Range of average is less than than individuals outcomes.Therefore, the individual values are more variable than averages is a true statement.
The given question is incomplete, I answer the question in general according to my knowledge:
Averages are less variable than individual outcomes is a true statement ? Give reason?
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Two friends shop for fresh fruit. Elaine buys a watermelon for 6.30$ and pounds of cherries. Elena buys a pineapple for $4.15 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more spent.
Step-by-step explanation:
Elaine spent 6.30 + px dollars on her purchase and Elena spent 4.15 + 4p dollars on her purchase. To find how much more Elaine spent, we can subtract Elena's total cost from Elaine's total cost: (6.30 + px) - (4.15 + 4p) = (6.30 - 4.15) + (px - 4p) = 2.15 + (px - 4p) = 2.15 + p*x - 4p. This is the simplified expression for how much more Elaine spent than Elena.
# Find the unknown sizes of angles. x-10°+ 2x-50° +3xº.
in a lab experiment, a population of 300 bacteria is able to double every hour. which equation matches the number of bacteria in the population after 2 hours
The equation that matches the number of bacteria in the population after 2 hours is [tex]y = 300 * 2^2[/tex], where y is the number of bacteria and [tex]2^2[/tex] is the exponential term representing the doubling of the bacteria every hour.
In the lab experiment, the population of bacteria is doubling every hour, so after 2 hours, the number of bacteria will be 2 times the initial number of bacteria for each of the 2 hours, or [tex]2^2[/tex] times the initial number of bacteria.
So, the equation for the number of bacteria after 2 hours is [tex]y = 300 * 2^2[/tex], where y is the number of bacteria and 300 is the initial number of bacteria. This equation calculates the number of bacteria in the population after 2 hours by multiplying the initial number of bacteria by 2 raised to the power of the number of hours the bacteria has been doubling, or [tex]2^2[/tex] in this case.
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4x+y is less than 8, x-y is greater than 3. graph the solution set of the given system of linear inequalities. (and fill in)
The required solution for the given inequalities has been shown in the graph.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
4x + y < 8
x - y > 3
Illustrate the graph of the inequality, the overlapped region on the graph is the solution of a system of inequalities.
Thus, the required solution for the given inequalities has been shown in the graph.
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Help me pls I don’t understand
Answer:
Table C
Step-by-step explanation:
This is a problem that is just process of elimination. The first step here is to organize all the x values (in each table) by value (lowest to highest). Luckily this has already been done for us. The next step is to establish slope. We can do this from any two points in the table. You find the difference between the y-values (y2-y1), then the x values (x2-x1) (where the points are (x1,y1) (x2,y2)). Now we just need to make sure the rest of the points obey that same slope.
For Example, take table A. The first two points are (1,-1) and (3,1) so using what was said before, the change in the x values is +2, and the change in the y values is +2 as well. Now applying that to the last two points, (5,3) and (8,5) we can see the slope is not the same. The change is x is +3 and the change in y is +2. Therefore we know that Table A does not represent a linear function.
The only table that has a constant slope is Table C with a change in x of +3, and a change in y of +2.
Use the Binomial Theorem and substitution to expand each Binomial. Show your step.
A) (3x+y)^4
B) (x-2y)^6
Answer:
A) (3x + y)^4:
The Binomial Theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n is given by the sum of n terms of the form:
C(n,k)a^(n-k)b^k
where C(n,k) is the binomial coefficient (n choose k).
So, expanding (3x + y)^4:
(3x + y)^4 = C(4,0)(3x)^4(y)^0 + C(4,1)(3x)^3(y)^1 + C(4,2)(3x)^2(y)^2 + C(4,3)(3x)^1(y)^3 + C(4,4)(3x)^0(y)^4
Using the binomial coefficients:
C(4,0) = 1, C(4,1) = 4, C(4,2) = 6, C(4,3) = 4, C(4,4) = 1
Expanding the terms:
(3x + y)^4 = 1(3x)^4(y)^0 + 4(3x)^3(y) + 6(3x)^2(y)^2 + 4(3x)(y)^3 + 1(y)^4
= 1(81x^4) + 4(27x^3y) + 6(9x^2y^2) + 4(3xy^3) + 1(y^4)
= 81x^4 + 108x^3y + 54x^2y^2 + 12xy^3 + y^4
B)
The Binomial Theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:
(a + b)^n = C(n, 0)a^n * b^0 + C(n, 1)a^(n-1) * b^1 + C(n, 2)a^(n-2) * b^2 + ... + C(n, n-1)a^1 * b^(n-1) + C(n, n)a^0 * b^n
where C(n, k) represents the binomial coefficient, which can be calculated as n! / (k! (n - k)!).
Applying this to (x - 2y)^6, we get:
(x - 2y)^6 = C(6, 0)x^6 * (-2y)^0 + C(6, 1)x^5 * (-2y)^1 + C(6, 2)x^4 * (-2y)^2 + ... + C(6, 5)x^1 * (-2y)^5 + C(6, 6)x^0 * (-2y)^6
Expanding each term:
C(6, 0) = 6! / (0! 6!) = 1
C(6, 1) = 6! / (1! 5!) = 6
C(6, 2) = 6! / (2! 4!) = 15
C(6, 3) = 6! / (3! 3!) = 20
C(6, 4) = 6! / (4! 2!) = 15
C(6, 5) = 6! / (5! 1!) = 6
C(6, 6) = 6! / (6! 0!) = 1
Now we can substitute each value into the equation:
(x - 2y)^6 = 1x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + 1 * (-2y)^6
Answer:
(x - 2y)^6 = x^6 - 12x^5 * 2y + 90x^4 * (-2y)^2 - 360x^3 * (-2y)^3 + 720x^2 * (-2y)^4 - 720x * (-2y)^5 + (-2y)^6.
the world record for the fastest spinning on ice skates is 1848 degress of rotation per seconds. describe this rate of revolutions per minute
step by step please
Answer: The rate of revolutions per minute is 308.8 revolutions per minute.
Step-by-step explanation: To find the rate of revolutions per minute, we need to convert the number of degrees of rotation per second to the equivalent number of full rotations per minute.
First, divide the number of degrees of rotation per second by 360, which is the number of degrees in one full rotation:
1848 / 360 = 5.13
Next, multiply the number of full rotations by 60 to get the number of rotations per minute:
5.13 * 60 = 308.8
So, the rate of revolutions per minute is 308.8 revolutions per minute.
