[tex]e^y-e^{-y}=x\implies e^y-\cfrac{1}{e^y}=x\implies \cfrac{(e^y)^2-1}{e^y}=x \\\\\\ e^{2y}-1=xe^y \implies e^{2y}-xe^y=1[/tex]
now, we're going to do some "completing the square" on the left-side, that is, we'll make it a perfect square trinomial by using our very good friend Mr Zero, 0.
[tex]2\cdot n\cdot e^y=xe^y\implies n=\cfrac{xe^y}{2e^y}\implies n=\cfrac{x}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]e^{2y}-xe^y=1\implies e^{2y}-xe^y + n^2 - n^2=1\implies e^{2y}-xe^y+n^2=1+n^2 \\\\\\ (e^y)^2-xe^y+\left( \cfrac{x}{2} \right)^2=1+\cfrac{x^2}{4}\implies \left( e^y -\cfrac{x}{2} \right)^2=1+\cfrac{x^2}{4} \\\\\\ e^y -\cfrac{x}{2}=\sqrt{1+\cfrac{x^2}{4}}\implies e^y =\sqrt{1+\cfrac{x^2}{4}}+\cfrac{x}{2} \\\\\\ \ln(e^y)= \ln\left(\cfrac{x}{2}+ \sqrt{1+\cfrac{x^2}{4}} \right)\implies {\Large \begin{array}{llll} y=\ln\left(\cfrac{x}{2}+ \sqrt{1+\cfrac{x^2}{4}} \right) \end{array}}[/tex]
Lara is a wildlife researcher. They were analyzing the mean and median lengths of
7
77 fish their team had observed. The fish all had different lengths between
15
cm
15cm15, start text, c, m, end text and
33
cm
33cm33, start text, c, m, end text.
Lara found out that they were misreading the longest length. It was actually
88
cm
88cm88, start text, c, m, end text, not
33
cm
33cm33, start text, c, m, end text.
How will this length increasing affect the mean and median?
Using their concepts, we have that the mean will be increased and the median will remain constant.
What is the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile, which is the middle value of the distribution.
The largest value is the 7th observation, therefore it will be included in the calculation of the mean.
Since this observation have an increased value, the sum of all observations will be increased while the number of observations remains constant,
So the mean will be increased.
Hence, for a distribution of 7 observations, we have that:
The first three observations are the first half.
The 4th observation is the median.
The last three observations are the second half.
Here only the last observation changes, not the fourth, hence the median remains constant.
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PLEASE ANSWER
Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day. How many miles can the business person travel on the $110?
Using the permitted $110 for travel, the businessperson can cover 291 miles.
How is this determined?We need to deduct the daily rate of $37.33 from the permitted money, then divide the sum by the per-mile rate of 25 cents to get how many miles a businessperson can travel with $110.
$110 - $37.33 = $72.67
$72.67 ÷ $0.25 = 291 miles
It's crucial to remember that, regardless of how many kilometres the businessperson drives, the daily charge includes a fixed sum for the rental automobile. Each mile driven results in an additional fee known as the per-mile tariff. We may calculate the maximum number of miles the business person can travel without incurring additional costs by subtracting the daily rate from the permitted amount and dividing by the per-mile rate.
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Given the following information, determine which lines , if any , are parallel.State the converse that justifies your answer.
Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.
Why do parallel angles exist?j and k angles.The Converse of Corresponding Angles Postulate leads to the expression j || k.
2Angles 2 and 5 make up the alternating inner angles of the lines j and k.Angle 2 equals Angle 5 if
Reversed Alternate Interior Angles.The theorem states that j || k.
J and K converse different internal angles.
3. Angle 3 also equals Angle 10.
The exterior angles of the lines l and m are, respectively, Angle 3 and
Angle 10.
The Converse of Alternate Exterior Angles Theorem states that angle 3 equals angle 10, so l || m.
Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.
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During her first week of work, a physical therapist estimated that therapy sessions would
last about 30 minutes each. However, the sessions take longer than expected. On one
day, the sessions lasted for 47 minutes, 53 minutes, 32 minutes, 50 minutes, and 45
minutes. How long should the physical therapist expect to spend at a therapy session?
Round to the nearest whole number.
If during her first week of work, a physical therapist estimated that therapy sessions would last about 30 minutes each. The time the physical therapist expect to spend at a therapy session is: about 45 minutes.
How to find the mean ?In order to find the expected duration of a therapy session, you can calculate the mean (average) of the durations for the five sessions.
The mean is calculated by adding the durations of all the sessions and then dividing by the number of sessions.
Mean = (47+53+32+50+45) / 5
Mean = 227/5
Mean = 45 minutes
Therefore the physical therapist should expect to spend about 45 minutes on average for each therapy session.
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Consider the graph , thanks
Answer:
Step-by-step explanation: it just graph of y=-x
y+x=
4x+4y4y=
2x-y≤-3
graph the inequality
Therefore , the solution of the given problem of inequality graph comes out to be the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane
What do you mean by inequality graph?An inequality graph is a graph that represents the solution set of an inequality, showing the values of the independent variable (usually represented on the x-axis) for which the inequality is true.
Here,
An inequality can be represented graphically by shading the region on a coordinate plane that satisfies the inequality. The direction of shading (above or below the line) depends on the inequality symbol.
The graph of the inequality 2x - y ≤ -3 in the x-y plane can be plotted by finding the boundary line for the inequality and shading the region that satisfies the inequality. To do this, we can start by setting the equation 2x - y = -3 and finding the x- and y-coordinates of the points on the line. Then we can plot these points and draw the line that connects them.
Next, we will determine which side of the line represents the solution set. To do this, we can pick a point that is not on the line and substitute its x- and y-coordinates into the inequality. If the inequality is true for the point, we shade the region that contains the point. If the inequality is false, we shade the region that does not contain the point.
So the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane and is shaded on one side. The shaded region represents all the x- and y-coordinates that satisfy the inequality.
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Find the volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis.
y=e^(x-9)
y=0, x=9, x= 10
According to the problem the volume of the solid generated by revolving the region is .
What is volume?The amount of space a thing occupies is its volume, which is expressed in cubic units. It is a three-dimensional measure of an object's size, as opposed to its length and width, which are considered two-dimensional measures. Volume is commonly used to measure the capacity of containers, such as barrels, tanks, and boxes.
This is a solid of revolution generated by revolving the region bounded by the curves y=[tex]e^{(x-9)}[/tex] and y=0 and the lines x=9 and x=10 about the x-axis. To find the volume of this solid, we can use the method of washers.
The formula for the volume of a solid of revolution generated by revolving a region bounded by two curves about the x-axis is given by:
V = π∫[tex]b a [((f(x))^{2} - (g(x))^{2}] dx[/tex]
In this problem, f(x) = [tex]e^{(x-9)}[/tex] and g(x) = 0. Thus,
V = π∫10 9 [tex]e^{(2x-18)} dx[/tex]
Integrating, we get
V = π [tex][\frac{e^{(2x-18)}}{2}] 10^{9}[/tex]
V = π(157.087 - 1.1102)/2
V = 78.488π [tex]cm^{3}[/tex] equal to the integral of the area of the region over the interval [9, 10] with respect to x.
The area of the region is equal to the integral of y from 9 to 10. Thus, the volume of the solid generated by revolving the region is equal to the double integral:
V = ∫[tex]9^{10}[/tex] ∫[tex]0^{e^{(x-9)} } dy dx[/tex]
Evaluating the integral yields:
V =∫ [tex]9^{10} e^{(x-9)} dx[/tex]
[tex]= \frac{e^{(x-9)} }{9^{10} }\\ =e^{1} -1\\ =2.718-1 =1.718[/tex]
Therefore, the volume of the solid generated by revolving the region is 1.718.
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write down the measure summary of cadbury report?
The Cadbury Report is a document that was produced by "The Committee on the Financial Aspects of Corporate Governance
What is the Cadbury Report?The Cadbury Report, also known as Financial Aspects of Corporate Governance, is a document that was produced by "The Committee on the Financial Aspects of Corporate Governance," which was led by Sir Adrian Cadbury, the chairman of Cadbury.
It contains recommendations on how company boards and accounting systems should be set up to reduce the risks and failures associated with poor corporate governance. The Cadbury committee was established by the London Stock Exchange in 1991, and a draft of the report was released in May 1992. In December of that same year, it was released in its altered and complete form.
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IREADY MATH AREA QUESTIONS PLS HELP TTYYY!!
A circle has a diameter of 10 cm. A rectangle has a length of 10 cm and a width of 5 cm.
Determine how the areas of the circle and the rectangle are related.
Use the drop-down menus to describe how the areas are related.
Area of circle: A = r²
1) The rectangle's length is equal to ______of the circle,
THIS BLANKS OPTION CHOICE:
A) the radius
B) the diameter
C) the circumference
D) half the circumference
E) twice the circumference
2) while the The rectangle's length is equal to rectangle's width is equal to _______. the circle.
THE BLANKS OPTION:
A) the radius
B) the diameter
C) the circumference
D) half the circumference
E) twice the circumference
3) So, the area of the circle is _______ of the Pick of area of the rectangle.
THE BLANK ANSWER CHOICES:
A) one fifth
B) two fifths
C) one half
D) twice
Answer:
The rectangle's length is equal to the diameter of the circle.while the rectangle's width is equal to half the circumference.So, the area of the circle is approximately two times the area of the rectangle.The following expression gives an approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995. 410t+5690 Use this expression to predict what the total average credit card debt was or will be in the year 1998. answer: in the year 1998, the total average credit card debt for a u.s. household will be (or was) ______dollars.
In the year 1998, the total average credit card debt for a U.S. household was approximately 6920 dollars.
As per the data given in the questions,
We have,
The expression for calculating the approximate value of the total average credit card debt in a u.s. household (in dollars) t years after 1995 is: 410t+5690
So, first we will calculate the value of t
As we have in the year 1998, t = 1998 - 1995 = 3.
So, for determining the value of the total average credit card debt in a u.s. household, we will simply plug in this value into the expression,
Thus, will get it as
410 * 3 + 5690
= 1230 + 5690
= 6920
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PLEASE ANSWER
Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day. How many miles can the business person travel on the $110?
The number of miles that the business person can travel on the $110 is; 290.68 miles
How to solve Linear Equation word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The daily rate of $37.33 can be said to be the y-intercept.
While 25 cents or $0.25 can be said to be the slope.
Thus, the equation of the line formed is;
y = 0.25x + 37.33
At a cost of $110, the number of miles is;
110 = 0.25x + 37.33
0.25x = 110 - 37.33
0.25x = 72.67
x = 72.67/0.25
x = 290.68 miles
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Find the error and describe it
Answer:
Step-by-step explanation:
the error, based on the question, the eqution has 4 solution for the X
listed as (4, -4, -3, 1)
as X solution in verticial , put all the X value into the F(x) to find the Y valuein horizontal value
Please help me with this question.
The value of vector (2u + v) is -5i +8k +5j and the value of u.v is -7.
What is a vector?Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude.
As a result, vectors are depicted as arrows and have starting and ending points.
The value of the vector (2u + v) is calculated as:-
E = (2u + v)
E = 2 ( -i + 5k) +( -3i + 5j -2k)
E = -2i +10k -3i +5j -2k
E = -5i + 5j + 8k
The value of u.v will be:-
u.v = ( -i +oj + 5k).(-3i +5j -2k)
u.v = 3 - 10
u.v = -7
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The graph of a sinusoidal function has a minimum point at (0, 3) and then intersects its midline
at (5,5).
Write the formula of the function, where x is entered in radians.
f(x) =
The formula is: f(x) = 2 * sin(x * 5 / 2π) + 5
How did we arrive at the formula?A = 5 - 3 = 2, the amplitude of the function.
Since (0,3) is the minimum, the midline is at y = 3 + 2 = 5, the average value of the maximum and minimum.
Let "c" be the shift, so the equation of the midline is y = 5 + c.
At x = 5, the function intersects its midline, so 5 = 5 + c.
Therefore, c = 0.
The period of the function is 2π / b, where b is the number of radians for one complete cycle.
Since the function intersects its midline at (5,5), b = 5.
Therefore, the period of the function is 2π / 5.
The formula of the sinusoidal function is:
f(x) = A * sin(b * (x - c)) + d,
where d = 5, the equation of the midline.
Therefore, the formula is:
f(x) = 2 * sin(x * 5 / 2π) + 5
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The rate at which people enter an amusement park on a given day is modeled by the function E defined by
E(t) = 15600/(t^2 - 24t + 160)
The rate at which people leave the same amusement park on the same day is modeled by the function L defined by
L(t) = 9890/(t^2 - 38t + 370)
Both E(t) and L(t) are measured in people per hour and time I is measured in hours after midnight. These functions are valid for q < t ≤ 23 the hours during which the park is open. At time t = 9 the are no people in the park.
(a) How many people have entered the park by 5:00 P.M. (t = 17)? Round your answer to the nearest whole number.
(b) The price of admission to the park is $15 until 5:00 P.M. (t = 17) After 5:00 P.M., the price of admission to the park is $11. How many dollars are collected from admissions to the park on the given day? Round your answer to the nearest whole number.
(c) Let H(t) = ∫1 to 9 (E(x) - L(x)) dx from 0 to t for 9 <= t <= 23 The value of H(17) to the nearest whole number is 3725. Find the value of H^ prime (17) , and explain the meaning of H(17) and H’(17) in the context of the amusement park.
(d) At what time t, for 9 ≤ t ≤ 23 does the model predict that the number of people in the park is a maximum?
The value of H^ prime (17) will be 17
At H'(t) = 0 time t, for 9 ≤ t ≤ 23, the model predicts that the number of people in the park is a maximum.
a) To find the number of people who have entered the park by 5:00 P.M. (t = 17),
we need to find the definite integral of the function E(t) from 0 to 17.
b) The total amount of money collected from admissions to the park on the given day is the sum of the money collected before 5:00 P.M. and the money collected after 5:00 P.M.
We can find this by finding the definite integral of the function 15600/(t^2 - 24t + 160) for t from 0 to 17,
Now finding the definite integral of the function
11*9890/(t^2 - 38t + 370) for t from 17 to 23.
c) H(t) represents the number of people in the park at time t. H'(t) represents the rate at which the number of people in the park is changing at time t.
H(17) = 3725 means that at 5:00 P.M. there are 3725 people in the park.
H'(17) can be found by finding the derivative of the function H(t) at t = 17.
d) To find the time t at which the model predicts that the number of people in the park is a maximum, we need to find the maximum value of H(t) for 9 ≤ t ≤ 23.
This can be done by finding the derivative of H(t), setting it equal to 0, and solving for t.
The value of t at which H'(t) = 0 will correspond to the maximum value of H(t).
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21. Probability. is a measure of the ___________________ that a specific event will occur
Probability is a measure of the likelihood that a specific event will occur in a random experiment.
What is the Probability?
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
In other words, the probability is a number that represents the chance or chance of an event occurring out of all possible outcomes.
It is expressed as a fraction, decimal, or percentage.
For example, if there is a 50% chance of rain, this means that the probability of rain is 0.5 or 1/2.
Probability is important in decision-making, risk assessment, and mathematical modeling. It helps to quantify uncertainty and provides a way to assess the likelihood of different outcomes.
Hence, Probability is a measure of the likelihood that a specific event will occur in a random experiment.
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kendra has $7.35 in her purse. she needs at least $2.87 more to buy a special bead. what is the total amount, x, she needs for the bead? which inequalities can be used to represent the situation? select all that apply.
Answer:
$10.22
Step-by-step explanation:
The total amount Kendra needs for the bead is $2.87 more than the amount she currently has in her purse, which is $7.35. Therefore, x = $7.35 + $2.87 = $10.22.
The inequality that represents this situation is:
x ≥ $7.35 + $2.87
x ≥ $10.22
Another way to represent this would be:
x - $7.35 ≥ $2.87
x ≥ $10.22
Both of these inequalities represent the same thing, that x (the total amount Kendra needs for the bead) must be greater than or equal to $10.22.
if i have two cat and my cat has two more how many do i have
Answer: 4
Step-by-step explanation:
For the given decision algorithm, find how many outcomes are possible.
Step 1
Alternative 1: 1 outcome
Alternative 2: 5 outcomes
Step 2
Alternative 1: 4 outcomes
Alternative 2: 3 outcomes
Alternative 3: 1 outcome
The total number of outcomes that are possible are given as follows:
48 outcomes.
How to obtain the number of outcomes?The number of outcomes for each case is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.
The number of outcomes in each step is given as follows:
Step 1: 1 + 5 = 6 outcomes.Step 2: 4 + 3 + 1 = 8 outcomes.Hence the total number of outcomes that are possible are obtained as follows:
N = 6 x 8
N = 48.
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Original discount price of a puppy $169.95. Discount 45%. Tax 6%.
Answer:
99.08
Step-by-step explanation:
169.95*(1-45%)*(1+6%) = 99.08
Answer:
400.33
Step-by-step explanation:
haul price= 377.67
tax=22.66
377.67+22.66=400.33
The price for peaches at Smith’s Grocery is usually $3.60 per pound. This week, the peaches are on sale and the price for peaches is 20% less than usual. What is the price per pound of peaches this week?
Answer:
$2.88
Step-by-step explanation:
formula → 3.6 × (1 - 20%)
→ 3.6 × (1 - 0.2)
calculate sum or difference
→ 3.6 × 0.8
→ = 2.88
what is the area of a square with the length of 20 and the width of 15
Answer:
300
Step-by-step explanation:
do 20 times 15 and you get 300 length times width = area
Answer:
300
Step-by-step explanation:
First of all, a square's side lengths must be the same for it to be correctly labeled as a square.
The quadrilateral we need to find the area for here is a rectangle.
The area of a rectangle is defined as length × width. So, to answer this question, all we need to do is multiply the given dimensions.
20 × 15
= (2 + 10) × 15
= (2 × 15) + (10 × 15)
= 30 + 150
= 300
 When solving equations - or "undoing" the operations to get "x" by itself on one side of the equation - we use INVERSE OPERATIONS.
Match the operation with its inverse operation.
Column A
2
Addition
Multiplication
Square
Cube
Column B
a. Divide by 3
b. Cube root
Divide by 2
d. Square root
Subtraction
f.
Division
For given arithmetic operations, matching is as:
Addition - Subtraction
Multiplication - Division
Square - Square root
Cube - Cube root
What are arithmetic operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
As, inverse operations inverses the actual value
Addition - Subtraction
Multiplication - Division
Square - Square root
Cube - Cube root
hence, they will be matched accordingly.
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Hamza found a pattern with some division expressions.
1. Calculate each quotient. (I already did this.)
2. Describe a pattern you see. (I can't find anything :)
The pattern in the following expressions is of square of numbers.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
In given expressions, In divisor the numerator and denominator are square of numerator and denominator in the dividend.
e.g. in (3/5)/(9/25) 9=3^2 and 25=^2
Hence,
The pattern in the following expressions is of square of numbers.
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Find the measure of angle x in the figure below: angle x⁰ angle 75⁰ 75⁰
a) 15⁰
b) 25⁰
c) 30⁰
d) 60⁰
the measure of the angle x is c)30°
Answer:
30 degrees
Step-by-step explanation:
In the bottom triangle,
Both angles are 75 degrees, so their sum is 75 + 75 = 150 degrees
The remaining angle is 180 - (sum of the two other angles)
= 180 - ( 75 + 75)
= 30 degrees
As this angle is a the vertically opposite angle to x, it will be equal to x
∴ x = 30 degrees
A stuntman jumped from a helicopter and opened his parachute. His height (in feet) at
time t seconds is given by the equation h (t) = -2t² 1000t+25000. What is his acceleration in ft/sec²?
Answer: The acceleration of the stuntman is given by the second derivative of the height function, which is:
h''(t) = d²h/dt² = (-2 * 2 * t * 1000 + 1000 * -2) = -4000t + 1000
So, the acceleration is -4000t + 1000 ft/sec².
Step-by-step explanation:
4 In the beginning of 2072 B.S. the populations growth Take 10%, what will be the populations of the town at the end of 2074 B.S. 7 find it.
At the beginning of 2072 B.S., the population of the town was X.
What will be the populations of the town at the end of 2074 B.S. 7?Assuming the population growth rate is 10%, the population at the end of 2074 B.S. will be (X + 10% of X) + (X + 10% of X + 10% of X) = 1.1X + 1.1(1.1X) = 2.21X.
Therefore, the population of the town at the end of 2074 B.S. will be 2.21X. This is based on a linear population growth rate of 10% over two years. It is possible that the growth rate may not be constant, so the actual population may be slightly different.
In order to get a better estimate of the population at the end of 2074 B.S., it is important to consider other factors such as birth and death rates, migration, and economic and social factors.
For example, if the town is experiencing an influx of migrants, then the population growth rate may be higher than the estimated 10%. On the other hand, if the town faces an economic recession or job losses, then the population growth rate may be lower than the estimated 10%.
Overall, the population of the town at the end of 2074 B.S. is estimated to be 2.21X, based on a linear population growth rate of 10% over two years. However, this estimate may be slightly different depending on the other factors mentioned above.
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What’s the measure of AC?
What’s the measure of AC’
What’s the measure of C’B
The measure of AC is 12 units.
The measure of AC' is 6 units
The measure of C'B' is 10.5 units.
How to find the measure of a triangle?The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle. Therefore, the segment is parallel to the third side and half of it.
Therefore, applying mid segment principle,
C'B' = 1 / 2 (21)
C'B' = 21 / 2
C'B' = 10.5 units
Hence, using mid segment principle
AC' = CC' = 6
Therefore,
AC = 6 + 6 = 12 units
using mid segment principle,
AC' = 6 units
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Can someone help me with question number 3 and 4 please?
3) The components of composition between two functions are [tex]f(n) = n^{2}+ 5^{n}[/tex] and g(n) = n² + 1.
4) The composition between functions g(n) = √(4 + n + √n) and h(n) = n⁴ + 8 is the function (g ° h)(n) = √[4 + n⁴ + 8 + √(n⁴ + 8)].
How to apply composition between functions
In this problem we find two cases of composition between functions, that is, a operation between two functions, so that the input of the first function (f(x)) is substituted by the entire second function (g(x)), that is:
f ° g(x) = f [g(x)]
Case 3 - If we know that [tex](f\,\circ \,g) (n) = (n^{2}+1)^{2}+5^{n^{2}+1}[/tex], then the components of the composition of functions are:
[tex]f(n) = n^{2}+ 5^{n}[/tex]
g(n) = n² + 1
Case 4 - If we know that g(n) = √(4 + n + √n) and h(n) = n⁴ + 8, then the composition between the two functions is:
(g ° h)(n) = √[4 + n⁴ + 8 + √(n⁴ + 8)]
To learn more on composition of functions: https://brainly.com/question/17427409
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I bet no one can do this. Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100
Answer:
It is a well-known fact that for any natural number k, there are no non-zero integers x, y, and z that satisfy x^3 + y^3 + z^3 = k, unless k = 1 or k = 8. This is known as Fermat's Last Theorem.
However, for k = 1, we have the solution (x, y, z) = (1, 0, 0) and for k = 8, we have the solution (x, y, z) = (2, −1, 1)
It's important to note that this problem is a complex mathematical problem, which was solved only by Andrew Wiles in 1994 using advanced mathematical theories such as Iwasawa theory and Galois representations.
