3x + 1 is called the Collatz problem.
Describe Collatz problem."The 3x+1 problem, often referred to as the Syracuse problem, Collatz problem, Kakutani's problem, Hasse's algorithm, and Ulam's problem, concerns the behaviour of the iterates of the function that takes odd numbers n to 3n+1 and even integers n to n/2. One of the most well-known unsolved mathematical puzzles is the Collatz conjecture. The conjecture asks if every positive integer will eventually become 1 if two basic arithmetic processes are repeated.
Given
3x + 1 is called the Collatz problem.
"The 3x+1 problem, often referred to as the Syracuse problem, Collatz problem, Kakutani's problem, Hasse's algorithm, and Ulam's problem, concerns the behaviour of the iterates of the function that takes odd numbers n to 3n+1 and even integers n to n/2.
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ROLLER COASTERS The height of a roller coaster is 157.5 feet. If the roller
coaster's shadow is 60 feet long, how long will a person's shadow be if the
person is 5 feet 3 inches tall?
Answer:
2 feet
Step-by-step explanation:
(60 / 157.5) * 63 inches = 24 inches = 2 feet
because the population distribution is skewed, the principal is considering using the median number of absences last month instead of the mean number of absences to summarize the distribution. describe how the principal could use a simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50
The simulation to estimate the standard deviation of the sampling distribution of the sample median for random samples of size 50 is given as follows:
A for loop with 50 iterations.For each iteration, a sample is selected, then the median is computed and stored in an array.After the 50 iterations, the mean of these medians is computed.After computing the mean, the standard deviation is computed.What is sampling?Sampling is a technique for when a group of elements from a population is taken to represent the entire population.
Hence, for this problem, multiple samples of 50 students are taken, and for each sample, the median is computed and then stored in a list, according to the procedure described at the beginning of the answer.
Then, after the entire procedure runs, we will have a sample of 50 values, which represent the median for each sample. Then the standard deviation is calculated as the square root of the sum of the difference squared between each of these observations and the mean of all these observations, divided by 50, which is the cardinality of the data-set.
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The table represents a quadratic function. Write an equation of the function in standard form.
The function's standard form equation is equivalent to [tex]\frac{-x^2}{4}+1=0[/tex].
A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.
The standard form of a quadratic equation in mathematics is given by;
[tex]ax^2+bx+c=0\\y=f(x)=ax^2+bx+c[/tex]
Next, using the information in the previous table, we would create the following system of equations:
[tex]-3=a(-4)^2+b(-4)+c\\-3=16a-4b+c[/tex].......equation (i)
[tex]0=a(-2)^2+b(-2)+c\\0= 4a-2b+c[/tex]........equation(ii)
[tex]1=a(0)^2+b(0)+c\\1=c[/tex].........equation (iii)
Inputting the value of c into equations 1 and 2 results in:
[tex]-4=16a-4b[/tex]......ewuation(iv)
[tex]-1=4a-2b[/tex]......equation(v)
Equation 5 is multiplied by two and solved concurrently to yield:
[tex]-2=8a\\a=\frac{-2}{8} \\a=\frac{-1}{4}[/tex]
What we have for b's value is:
[tex]-1=4a-2b\\-1=4(\frac{-1}{4})-2b\\ -1=-1-2b\\2b=0\\b=0[/tex]
Inputting the values of a, b, and c into a quadratic equation in standard form:
[tex]ax^2+bx+c=0\\\frac{-1}{4}x^2+(0)x+1=0\\ \frac{-x^2}{4} +1=0[/tex]
When x equals 2, we get:
[tex]\frac{-x^2}{4} +1=0\\\frac{-2^2}{4}+1=0\\ \frac{-4}{4}+1=0\\ -1+1=0[/tex]
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Solve the equation with the help of laplace transform (d^2y+dx=2 ,when x(0)=3, x’(0)=1, where d=d/█(dtà)
Correct Question:-
Solve the following differential equation using Laplace transformation.
[tex]\rm{x''(t)+x'(t)=2,\quad x(0)=3,\quad x'(0)=1}[/tex]
where [tex]\rm{x'(t)=\dfrac{dx}{dt},\quad x''(t)=\dfrac{d^2x}{dt^2}.}[/tex]
[tex]\quad[/tex]
Solution:-
Let,
[tex]\cal{L}\{\rm{x(t)}\}=X(s)[/tex]
[tex]\cal{L}^{\rm{-1}}\{\rm{X(s)}\}=x(t)[/tex]
Given,
[tex]\longrightarrow\rm{x''(t)+x'(t)=2}[/tex]
We take Laplace transformation of both sides of the equation.
[tex]\longrightarrow\cal{L}\{\rm{x''(t)+x'(t)}\}=\cal{L}\{\rm{2}\}[/tex]
[tex]\longrightarrow\cal{L}\{\rm{x''(t)}\}+\cal{L}\{\rm{x'(t)}\}=\cal{L}\{\rm{2}\}[/tex]
We have,
[tex]\cal{L}\{\rm{x''(t)}\}=\rm{s^2\,X(s)-s\,x(0)-x'(0)}[/tex]
[tex]\cal{L}\{\rm{x'(t)}\}=\rm{s\,X(s)-\,x(0)}[/tex]
[tex]\cal{L}\{\rm{2}\}=\rm{\dfrac{2}{s}}[/tex]
Then,
[tex]\small\text{$\longrightarrow\rm{\big[s^2\,X(s)-s\,x(0)-x'(0)\big]+\big[s\,X(s)-x(0)\big]=\dfrac{2}{s}}$}[/tex]
[tex]\longrightarrow\rm{s(s+1)\,X(s)-(s+1)\,x(0)-x'(0)=\dfrac{2}{s}}[/tex]
Given that [tex]\rm{x(0)=3}[/tex] and [tex]\rm{x'(0)=1.}[/tex] Then,
[tex]\longrightarrow\rm{s(s+1)\,X(s)-3(s+1)-1=\dfrac{2}{s}}[/tex]
[tex]\longrightarrow\rm{s(s+1)\,X(s)-3s-4=\dfrac{2}{s}}[/tex]
[tex]\longrightarrow\rm{s(s+1)\,X(s)=\dfrac{2}{s}+3s+4}[/tex]
[tex]\longrightarrow\rm{X(s)=\dfrac{2}{s^2(s+1)}+\dfrac{3s+4}{s(s+1)}}[/tex]
[tex]\longrightarrow\rm{X(s)=\dfrac{3s^2+4s+2}{s^2(s+1)}\quad\dots(1)}[/tex]
We will factorise this expression by partial fractions.
Assume,
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{As+B}{s^2}+\dfrac{C}{s+1}}[/tex]
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{(As+B)(s+1)+Cs^2}{s^2(s+1)}}[/tex]
[tex]\longrightarrow\rm{3s^2+4s+2=(As+B)(s+1)+Cs^2}[/tex]
[tex]\longrightarrow\rm{3s^2+4s+2=(A+C)s^2+(A+B)s+B}[/tex]
Equating corresponding coefficients,
[tex]\rm{A+C=3}[/tex]
[tex]\rm{A+B=4}[/tex]
[tex]\rm{B=2}[/tex]
Solving each equation we get,
[tex]\rm{A=2}[/tex]
[tex]\rm{B=2}[/tex]
[tex]\rm{C=1}[/tex]
Therefore,
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{2s+2}{s^2}+\dfrac{1}{s+1}}[/tex]
[tex]\longrightarrow\rm{\dfrac{3s^2+4s+2}{s^2(s+1)}=\dfrac{2}{s}+\dfrac{2}{s^2}+\dfrac{1}{s+1}}[/tex]
Then (1) becomes,
[tex]\longrightarrow\rm{X(s)=\dfrac{2}{s}+\dfrac{2}{s^2}+\dfrac{1}{s+1}}[/tex]
Now we will inverse Laplace transformation to obtain the solution.
[tex]\longrightarrow\cal{L}^{\rm{-1}}\{\rm{X(s)}\}=\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{2}{s}+\dfrac{2}{s^2}+\dfrac{1}{s+1}}\right\}[/tex]
[tex]\small\text{$\longrightarrow\rm{x(t)}=\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s}}\right\}+\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s^2}}\right\}+\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s+1}}\right\}$}[/tex]
[tex]\small\text{$\longrightarrow\rm{x(t)}=\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s}}\right\}+\rm{2}\,\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1!}{s^{1+1}}}\right\}+\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s-(-1)}}\right\}$}[/tex]
We have,
[tex]\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s}}\right\}=\rm{1}[/tex]
[tex]\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1!}{s^{1+1}}}\right\}=\rm{t}[/tex]
[tex]\cal{L}^{\rm{-1}}\left\{\rm{\dfrac{1}{s-(-1)}}\right\}=\rm{e^{-t}=\dfrac{1}{e^t}}[/tex]
Hence,
[tex]\longrightarrow\rm{\underline{\underline{x(t)=2+2t+\dfrac{1}{e^t}}}}[/tex]
This is the solution to our differential equation.
[tex]\quad[/tex]
Some results of Laplace Transformation:-
[tex]\boxed{\begin{array}{c|c}&\\\rm{x(t)}=\cal{L}^{\rm{-1}}\{\rm{X(s)}\}&\rm{X(s)}=\cal{L}\{\rm{x(t)}\}\\\\=============&==================\\\\\rm{\dfrac{d^nx}{dt^n}}&\rm{s^n\,X(s)}-\displaystyle\sum_{\rm{r=0}}^{\rm{n-1}}\rm{s^{n-r-1}\,\dfrac{d^rx}{dt^r}(t=0)}\\\\----------&--------------\\\\\rm{x'(t)}&\rm{s\,X(s)-x(0)}\\\\----------&--------------\\\\\rm{x''(t)}&\rm{s^2\,X(s)-s\,x(0)-x'(0)}\\\\----------&--------------\\\\\rm{a}&\rm{\dfrac{a}{s}}\\\\----------&--------------\\\\\rm{t^n,\ n}\in\mathbb{N}&\rm{\dfrac{n!}{s^{n+1}}}\\\\----------&--------------\\\\\rm{e^{at}}&\rm{\dfrac{1}{s-a}}\\&\end{array}}[/tex]
select all the true statements. if vertical angles are congruent, then two lines cut by a transversal are parallel. if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints. points on a perpendicular bisector of a line segment are never equidistant from the segment’s endpoints.
Answer:
if two parallel lines are cut by a transversal, then corresponding angles are congruent. if two parallel lines are cut by a transversal, then alternate interior angles are congruent. points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.Step-by-step explanation:
You want to identify the true statements regarding angles at a transversal crossing parallel lines, and perpendicular bisectors.
AnglesThe Corresponding Angles theorem tells you that corresponding angles are congruent where a transversal crosses parallel lines. Since vertical angles are congruent, and angles congruent to the same angle are congruent to each other, this also means that alternate interior angles are congruent.
Perpendicular bisectorA bisector of a segment passes through its midpoint, a point that is equidistant from the end points. When the bisector is perpendicular to the segment, all points on the perpendicular bisector are equidistant from the segment's endpoints.
The following chart shows the number of days a book is overdue and the fines for that book. Find an equation that defines the fines with respect to the number of days overdue. EXPLAIN your steps.Explain what the values in your final equation mean.
The equation that defines the fines with respect to the number of days overdue is written as: y = 0.1x + 1.
How to Write a Linear Equation?The equation that defines the fines with respect to the number of days overdue can be written as a linear equation that is expressed in slope-intercept form as y = mx + b, where the slope or unit rate is m, while the y-intercept or initial value is b.
Using two points from the chart, (2, 1.20) and (5, 1.50), find the slope or unit rate:
Slope / unit rate (m) = change in y / change in x = (1.50 - 1.20) / (5 - 2)
m = 0.3 / 3
m = 0.1
Find the y-intercept by substituting m = 0.1 and (x, y) = (2, 1.20) into y = mx + b:
1.20 = 0.1(2) + b
1.20 = 0.2 + b
1.20 - 0.2 = b
1 = b
To write the equation, substitute m = 0.1 and b = 1 into y = mx + b:
y = 0.1x + 1
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What is an example of an inverse relationship in math?
An inverse relationship in math is a relationship between two quantities where one quantity increases as the other decreases and vice versa.
An example of an inverse relationship is the relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.
The relationship between temperature in degrees Celsius (C) and temperature in degrees Fahrenheit (F) is defined by the following equation:
F = (9/5)C + 32
This equation shows that as the temperature in degrees Celsius increases, the temperature in degrees Fahrenheit decreases. For example, if the temperature in degrees Celsius is 20, the temperature in degrees Fahrenheit is 68. If the temperature in degrees Celsius is 40, the temperature in degrees Fahrenheit is 104.
Therefore, the relationship between temperature in degrees Celsius and temperature in degrees Fahrenheit is an inverse relationship.
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If a₁ = 4 and an = -4an-1 +5 then find the value of a5
If a₁ = 4 and an = -4an-1 +5 then the value of a5 is 72, in the given sequence.
What is sequence?A group of enumerated objects where repetitions are allowed and order is crucial is referred to as a sequence in mathematics. Similar to a set, it has members. The sequence's length is expressed in terms of its number of elements.
Given that, sequence
[tex]a_1=4, a_n=4 a_{n-1}+5[/tex]
Now
[tex]a_2=4 a_1+5[/tex]
[tex]a_2=4 \times 4+5[/tex]
[tex]a_2=21[/tex]
[tex]a_2=4 \times 4+5[/tex]
[tex]a_2=21[/tex]
And the common difference d = 21 - 4 = 17
Therefore [tex]a_5=a_1+4 d[/tex]
[tex]a_5=4+4 \times 17[/tex]
[tex]a_5=4+68[/tex]
[tex]a_5=72[/tex]
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If one science book has a mass of 2 kilograms, what is the mass of 4 science books?
A) 2 kilograms
B) 4 kilograms
C) 6 kilograms
D) 8 kilograms
Answer:
D) 8 kilograms
Step-by-step explanation:
If one science book has a mass of 2 kilograms, then 4 science books would have a mass of 2 x 4 = 8 kilograms.
What is 25x+1 = 125x-1?
Answer:
x= 1/50 or 0.02, or x=50^-1
Answer:
[tex]x=\frac{1}{50}[/tex]
Step-by-step explanation:
If you would like to see the steps here they are.
What is the formula for calculating half-life?
The formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]
What is Half-life?The half-life is the amount of time required for a quantity (of substance) to reduce to half of its initial value.
The expression is commonly used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.
Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay).
For instance, the medical sciences may refer to the biological half-life of drugs and other substances in the human body.
Time doubles in proportion to life's exponential expansion.
The formula to calculate half-life: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]
Where N(t) is the quantity of the substance remaining, N₀ is the initial quantity of the substance, t is the time elapsed and t₁₎₂ is the half-life of the substance.
Therefore, the formula that can be used to calculate the half-life is: [tex]N(t)=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1 / 2}}}[/tex]
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help me pleaseee! asap would be lovely :)
Answer:
x = - 28/101
Step-by-step explanation:
Answer:
x=-42
Step-by-step explanation:
[tex]-3x-28=98\\(-3x-28)+28=(98)+28\\-3x=126\\\frac{-3x}{-3}=\frac{126}{-3}\\x=-42[/tex]
PLEASE HELP! Thank you
Answer:
1. 7
2. 5/3
3. 2.6
Step-by-step explanation:
The "+" or "-" sign of a number is disregarded in this operation since distance in mathematics is never negative. You can tell what a number's absolute value is by putting it between two vertical bars known as absolute value brackets.
Answer:
1. 7
2. 5/3
3. 2.6
Step-by-step explanation:
The absolute value is the distance between a number and zero
1. We see the distance is 7, so the answer is 7
2. We see the distance as 5/3, so the answer is 5/3
3. We see the distance is 2.6, so the answer is 2.6
How do you graph 4 lines?
To graph four lines, you will need to plot at least four points for each line and then draw a line through these points.
A general procedure you can use is as follows:
Identify the equation of each line. You will need the equation of each line in slope-intercept form (y = mx + b) to graph the line.Choose at least four points to plot on each line. You can choose these points based on the x-values you want to use or by substituting different values for x into the equation of the line and solving for y.Plot the points on the graph. Use a ruler to draw a line through the points for each line.Give the graph a title and identify its axes. Make sure to include units of measurement on the axes if necessary.It can be helpful to use a different color or style (such as a solid line or a dotted line) for each line to make it easier to tell them apart.
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Is the equation 3x² 7y 13 a linear equation in 2variables?
This is not a two-variable linear equation.
If an equation is written in the form axe + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., When both a and b, in turn, do not equal zero, an equation with two variables is said to be linear. Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation.
Given equation,
[tex]3x^{2} -7y=13[/tex]
In this case, the variable x's degree is 2.
Hence, this is not a two-variable linear equation.
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15 m
50 m
B
X
A
30 m
Ra
KY
18 m
Assuming that figure A is the original figure,
state the scale factor. Write your answer as
a simplified fraction.
Answer:
5/3
Step-by-step explanation:
The scale factor is the ratio of the side length of the image to the corresponding side in the preimage.
So, the scale factor is [tex]\frac{50}{30}=\frac{5}{3}[/tex].
5(?+3)+?(6 + 3)=108.
Answer:?=93/14
Step-by-step explanation:
the ? is the variable in this equation so we have to solve for it
1. distributive property ->
5(?+3) = 5?+15
?(6+3) = 9?
so 5?+15+9?=108 -> 14?+15=108
2. then solve,
14? -15 = 108 -15
14?=93
?=93/14
I need help with this
The correct equation that represents the inequality is f(x) > √1 - x.
What is the inequality equation?
To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
An inequality is a mathematical relationship between two expressions and is represented using one of the following: ≤: "less than or equal to" <: "less than" ≠: "not equal to"
We have given the graph that represents the inequality equation,
and the inequality equations:
f(x) > √1 - x
f(x) ≤ √1 - x
f(x) ≥ √1 - x
f(x) < √1 - x
Hence, the correct equation that represents the inequality is f(x) > √1 - x.
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How do you find the sum of numbers from 1 to 100 in Java?
The sum of all natural numbers from 1 to 100 is 5050. The total number of natural numbers in this range is 100. So, by applying this value in the formula: S = n/2[2a + (n − 1) × d], we get S=5050.
In Java, finding the sum of two or more numbers is very easy. First, declare and initialize two variables to be added. Another variable to store the sum of numbers. Apply mathematical operator (+) between the declared variable and store the result. So you simply make this: sum=sum+num; for the cycle. For example sum is 0, then you add 5 and it becomes sum=0+5 , then you add 6 and it becomes sum = 5 + 6 and so on.
Thus, the sum of all natural numbers 1 to 10 can be calculated using the formula, S= n/2[2a + (n − 1) × d], where, a is the first term, d is the difference between the two consecutive terms, and n is the total number of natural numbers from 1 to 10. Therefore, the sum of the first ten natural numbers is 55.
public class T35{
public static void main(String[] args) {
int nmb;
for(nmb= 1; nmb<= 100; nmb++){
System.out.println(nmb);
}
}
}
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Someone help meeeee. I do not understand this work
Answer:
Step-by-step explanation:
i belive it would be 500 divided by 20m
complete the following statement of congruence?
What type of function is f/x )= sinx?
f(x) = sinx is an trigonometric function.
A trigonometric function is a type of mathematical function that is defined in terms of the angles of a right triangle. The most common trigonometric functions are sine, cosine, and tangent. The function f(x) = sinx is a sine function, which is defined as the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse. The sine function can be used to calculate the angles of a triangle when the lengths of two sides are known. It is also useful for modeling many real-world phenomena such as the motion of waves and the oscillations of pendulums.
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Amadou misses 2% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 32?
The total free throws Amadou attempts, if Amadou misses 2% of the free throws he attempts in a season, he missed 32, is 1600.
What is the percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
Amadou misses 2% of the free throws he attempts in a season, he missed 32,
Calculate the total number of throws as shown below,
2% of x = 32
Here, x is the total number of throws,
0.02 × x = 32
x = 32 / 0.02
x = 1600
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Graph the image of the triangle using the transformation given.
What number makes the expressions equivalent? −1.1 −1.4m + 0.4 = ? − 1.4m
Answer: -0.7
Step-by-step explanation:
-1.1 - 1.4m + 0.4 = ? - 1.4m
-1.1 + 0.4 = -0.7
-0.7 - 1.4m = -0.7 - 1.4m
find f. f ''(x) = x−2, x > 0, f(1) = 0, f(6) = 0
The resulting value of the equation after performing integration is , f(x) = -log(x) + log(1) - log(4).
Integrating on both the sides with respect to x.
⇒ ∫ f''(x)dx= ∫x-2dx
⇒ ∫ f''(x) dx = (x-2 + 1)/(-2 + 1) + C1
⇒ f'(x) = x-1/(-1) + C1
Then again performing integration ,
∫ f'(x) dx = -log(x) + C1 + x + C2
f(x) = -log(x) + C1 + x + C2
Now, since we know that f(1) =0
when x = 1 then f(1) =0
0 = -log(1) + C1 + C2
it is also given that ,f(4) = 0
0 = -log(4) + 4C1+ C2
We will subtract these two equations in order to get C1 and C2.
0 = -log(1) + log(4) - 3C1
3c1 = -log(1) + log(4)
= log(4/1) {since log(a) - log(b)
= log(a/b)}
C1 = log(4)/3
C1 = log(4)/3 and (2)
0 = -log(1) +(4/3)log(4) + C2
log(1) - (4/3)log(4) = C2
Therefore, the equation becomes
f(x) = -log(x) + [log(4)]/3 + log(1) - (4/3)log(4)
f(x) = -log(x) + log(1) - log(4)
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whats 78,563 divided by 98
Ty for whoever helps me <3
Answer:
801.66
Step-by-step explanation:
calculator
Answer:
801.6632653061
Step-by-step explanation:
.......
How do you do linear graphs in math?
Linear graph equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
How do one express the standard form of a linear equation?A linear equation has the following standard form: ax + by + c = 0.
Here, variables x and y and constants a, b, and c are used.
Also, a ≠ 0, and b ≠ 0.
For linear equations, the slope-intercept formula is: y=mx+b
Where m stands for the line's slope and b represents the y-intercept.
The three types of linear equations are point-slope, slope-intercept, and standard form.
When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.
Steps of drawing linear graphs are described below:
Step 1: Using the provided linear equation, determine the value of y with respect to x.
Step 2: Arrange these data in a table format.
Step 3: Create a graph using the points from the database.
Step 4: Connect the points to form a straight line.
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What is the formula for calculating the slope m of a line?
The formula or equation used to determine the slope of a straight line is as follows:
m = (Y₂-Y₁)/(X₂-X₁)
What is an equation?An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.
Equations can be graphed, they are used to model many problems and theories.
The straight lines are characterized by a finite succession of points, when they have an inclination they adopt a slope value different from 0, and to determine that slope it is necessary to know two points of the line and use the following equation:
m = (Y₂-Y₁)/(X₂-X₁)
Where the points are:
P₁ = (X₁,Y₁)P₂ = (X₂,Y₂)Learn more about equations at:
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in this 10 digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3 what is the value of A + B + C
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The value of A + B + C based on the information is A. 5.
How to illustrate the information?From the information, we have digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3.
It should be noted that all multiple of 8 have it's digits add up to a multiple of 9. This can be illustrated as:
4 + A + B + C + 2 + 3 + 9 + 0 + 4 + 0
= 22 + A + B + C
This will be equated to 27 which is the nearest multiple of 9
22 + A + B + C = 27
A + B + C = 27 - 22
A + B + C = 5
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Complete question
In this 10 digit number 4,ABC,239,040 A B and C are digits. if the number is the product of 6 consecutive positive multiples of 3 what is the value of A + B + C?
A 5
B 6
C 7
D 8