In accordance with the above assertion, the offered differential equation by variable separation is P = 1/ (k*e^t +1).
What does a math differential equation mean?A differential equation in mathematics is one that has one or more negatively influencing variables. Dy/dx provides the function's derivative. The phrase describes an equation with several ways to connect the dependent variable to one or more regressors.
dP/dt = P - P^2
1/(P - P^2)dP = dt
∫1/(P - P^2)dP = ∫dt
t + c = 1/(P - P2)dP, where c would be a constant
Use the partial fractions method to calculate the integrated on the left. We wish to rewrite 1/(P-P2) in the pattern A/P+B/(1-P) for those constants A and B since P-P2 factors to P(1-P). We therefore have:
1/[P(1-P)] = A/P + B/(1-P)
A(1-P) + BP = 1
When P is 1, we have A(1-1)+B(1)=1, or B=1.
When P is 0, we have A(1-0)+B(0)=1, or A=1.
So, we can rewrite 1/(P-P^2) as 1/P+1/(1-P).
Whilst doing the entire on the ODE's left side, we have:
∫1/(P - P^2)dP
∫[1/P + 1/(1-P)]dP
∫(1/P)dP + ∫1/(1-P)dP
ln(P) + ∫1/(1-P)dP
Make a u-substitution to perform the second integral:
u = 1-P, du = -dP
ln(P) - ∫(1/u)du
ln(P) - ln(u)
ln(P) - ln(1-P)
ln[P/(1-P)]
Reconnecting that to the ODE yields the following:
ln[P/(1-P)] = t + c
e^ln[P/(1-P)] = e^(t + c)
P/(1-P) = e^t * e^c
P/(1-P) = ke^t, where k is a constant equal to e^c
P = (1-P)ke^t
P = ke^t - Pke^t
P + Pke^t = ke^t
P(1 + ke^t) = ke^t
P = ke^t / (1 + ke^t)
P = e^t / (1/k + e^t)
P = e^t / (d + e^t), where d is a constant equal to 1/k
So, the general solution to the ODE is P = e^t / (d + e^t), where d is a constant.
p*(1-p) = k*e^t ( we say that e^k is a constant)
1-p/p = k*e^t
P = 1/ (k*e^t +1)
To know more about Differential equation visit:
https://brainly.com/question/23802083
#SPJ4
The complete question is-
Solve the given differential equation by separation of variables.
dP/dt = P - P²
HELPPPPPPPPPPP
YALL AMAZING :))
Answer:
14.8%
Step-by-step explanation:
decrease = -100 * ((final - initial) / initial)
Answer:
14.8%
Step-by-step explanation:
Original fishing pole cost: $54
New fishing pole cost: $46
Using the percentage decrease formula:
[tex]\frac{Original Value - Final Value}{|Original Value|}[/tex] ×100%
Substitute
[tex]\frac{54-46}{|46|}[/tex] ×100%
From this, you should get 14.814814814814814...
Round to nearest tenths.
Final answer: 14.8%
Roxy is planning to move to Fort Lauderdale, Florida, and work as a nurse. She has one dog and no children. She uses public transportation and plans to rent an apartment when she moves. The new company she’ll work for pays employees bimonthly, which means twice a month. In this activity, you’ll help Roxy make a budget.
Part A
Roxy decides that she wants to set a financial goal of saving for an emergency fund. Write about some of the ways Roxy could make her financial goal a SMART goal.
Roxy can make her goal SMART by deciding an attainable amount of money, diving the total of money in paymets and using the money for emergencies only.
What is SMART?This is a technique to plan and achieve goals based on 5 characteristics:
S = Specific, which means the goal should not be too general.M = Measurable, which means you can measure your progress.A = Attainable or realistic.R = Relevant, which means achieving the goal has a positive impact.T = Time-based, which means it can be achieved in a specific period of time.How can Roxy make her goal SMART?S= Decide the amount of money for the saving fund, for example, $5000.M = Check month to month the amount of money she has saved.A = Divide the total in payments that fit her expenses.R = Make sure she will used the money only for emergencies.T = Complete the goal after 6 months.Learn more about money in: https://brainly.com/question/14253896
#SPJ1
If a road map has a scale of 3 in: 100 mi, find the following distances
How far is it between Cardwell and Claremont if they are 4.5 inches apart on the map?
The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
If a road map has a scale of 3 inches to 100 miles.
Then the scale factor is given as,
Sclar factor = 100 / 3
Sclar factor = 33.33 miles per inch
Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,
Distance = 33.33 x 4.5
Distance = 150 miles
The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ1
What is X= -5 graphed?…..?????????????
Answer:
see the picture attached
Step-by-step explanation:
To graph this, we will count to a negative five on the graph. This means that we will move to the left five spaces and plot a point at (-5,0). Now, we will create a vertical line at -5 to encapsulate all of the values found at x = -5. This is essentially an infinite line, but the picture I included shows it on a 10 x 10 plane. Hope this helps!
Answer:
What is X= -5 graphed
Step-by-step explanation:
Graph x=-5 x = −5 x = - 5 Since x = −5 x = - 5 is a vertical line, there is no y-intercept and the slope is undefined.
what is 6^-2 in a fraction form
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
For negative exponents, you get the original number and make it into its reciprocal, and then whatever power it is to, is the power the bottom number is to, so you get:
[tex]6^{-2} = \frac{1}{6^{2} }[/tex]
Which simplifies to:
[tex]\frac{1}{36}[/tex]
So, [tex]6^{-2}[/tex] in fraction form, is [tex]\frac{1}{36}[/tex].
Hope this helped!
Please give me brainliest if possible!
Find the area of the shaded triangle
The area of shaded triangle is 20 square feet
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area of triangle = 0.5*base*height
Area of whole triangle = 0.5*8*10 = 40 square feet
Area of unshaded triangle = 0.5*4*10 = 20 square feet
Area of shaded triangle
= Area of whole triangle - Area of unshaded triangle
= 40 - 20
= 20 square feet
Thus, the area of shaded triangle is 20 square feet
To learn more about the area from the given link
https://brainly.com/question/25292087
#SPJ1
Which point on the number line shows the position of square root 38
The point on the number line is between 6 and 7
How to determine the location of the pointFrom the question, we have the following parameters that can be used in our computation:
Number = square root 38
The square root of 38 is approximately 6.16441400296898.
This number is between 6 and 7 on the number line, closer to 6.
Also, it should be noted that
It's not a rational number so it's not on the number line with integers, but it can be represented as a decimal or as an irrational number.
Read more about number line at
https://brainly.com/question/12399107
#SPJ1
HELP ITS DUE IN 10 MINS
(05.01 MC)
An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles. Prove the diagonals of an isosceles trapezoid are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted. (10 points)
30 POINTS
Answer:
Step-by-step explanation:
To prove that the diagonals of an isosceles trapezoid are congruent, we will first define the terms and draw a diagram of the isosceles trapezoid.An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles.Let's call the isosceles trapezoid ABCD and let the parallel sides be AB and CD, and the congruent legs be AD and BC. Let the diagonals be AC and BD.Since, AD and BC are congruent legs, therefore ∠BAD = ∠CAD by the definition of congruent legs.And since ABCD is a trapezoid, therefore, AB || CD and therefore, ∠BAD = ∠CBD, due to alternate angles are congruent.Therefore, ∠CAD = ∠CBD, by CPCTC (corresponding parts of congruent triangles are congruent)AC = BD , since both are congruent by ASA (angle-side-angle) congruence.Thus, the diagonals of an isosceles trapezoid are congruent.
the population of the united states is aging. at right is the stemplot of the percentage of residents aged 65 and older in each of the 50 states, according to the 2010 census. there are three outliers: alaska has the lowest, utah has the second lowest, and florida has the highest. what is the percentage for utah?
The percentage for Utah is 9.0%.
The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
Thus, The percentage for Utah is 9.0%.
To know more about population and sample visit: brainly.com/question/15019364
#SPJ4
Use tracing paper to answer each of these questions for both sets of shapes below:
A
C
B
D
Which figure appears to be the exception?
What makes that shape different from the others?
●
What do the other three shapes have in common?
given rectangular grid nxm starting at position (x1,y1) you are trying to reach (x2,y2) return number of steps it takes to get there. code signal
Given an infinite grid, initial cell position (x, y) and a sequence of other cell position which needs to be covered in the given order.
The task is to find the minimum number of steps needed to travel to all those cells.
Note: Movement can be done in any of the eight possible directions from a given cell that is from cell (x, y) you can move to any of the following eight positions:(x-1, y+1), (x-1, y), (x-1, y-1), (x, y-1), (x+1, y-1), (x+1, y), (x+1, y+1), (x, y+1) is possible
Examples:
Input: points[] = [(0, 0), (1, 1), (1, 2)]
Output: 2
Move from (0, 0) to (1, 1) in 1 step(diagonal) and
then from (1, 1) to (1, 2) in 1 step (rightwards)
Input: points[] = [{4, 6}, {1, 2}, {4, 5}, {10, 12}]
Output: 14
Move from (4, 6) -> (3, 5) -> (2, 4) -> (1, 3) ->
(1, 2) -> (2, 3) -> (3, 4) ->
(4, 5) -> (5, 6) -> (6, 7) ->
(7, 8) -> (8, 9) -> (9, 10) -> (10, 11) -> (10, 12)
Since all the given points are to be covered in the specified order.
Find the minimum number of steps required to reach from a starting point to next point, then the sum of all such minimum steps for covering all the points would be the answer.
One way to reach from a point (x1, y1) to (x2, y2) is to move abs(x2-x1) steps in the horizontal direction and abs(y2-y1) steps in the vertical direction, but this is not the shortest path to reach (x2, y2).
The best way would be to cover the maximum possible distance in a diagonal direction and remaining in horizontal or vertical direction.
If we look closely this just reduces to the maximum of abs(x2-x1) and abs(y2-y1).
Traverse for all points and summation of all diagonal distance will be the answer.
To know more about rectangular grid visit brainly.com/question/12377139
#SPJ4
refer to exercise 50. how many axles would you need to sample if you wanted the standard deviation of the sampling distribution of x to be 0.0005 mm?
If the sample standard deviation from the sample distribution is 0.0005 mm, the sample should have 16 axes.
Given,
μ = 40.125 mm, σ = 0.002mm σ(x) = 0.0005mm
The standard deviation of the sampling distribution of the sample mean is the population standard deviation divided by the square root of the sample.
σ₁ = σ/√n
By multiplying both sides by √n
√nσ(x) = σ
By dividing both the side by σ₂
√n = σ / σ₁
By squaring both the sides
n = σ²/σ²(x)
Now,
Calculate the value of n
n = 0.002² / 0.0005²
= 16
Therefore,
If the sample's standard deviation of the sampling distribution is 0.0005mm, then the sample should be 16 axles.
Learn more about sample distribution:
https://brainly.com/question/29375938
#SPJ4
Express y in terms of x. 0.5y - 2 = 0.25x
Answer:
y = 0.5x + 4
Step-by-step explanation:
1. Move terms to one side of the equation
0.5y - 2= 0.25x +0
+2 +2
__________________
0.5y = 0.25x + 2
2. Divide the coefficient of y (0.5) to both sides of the equation
[tex]\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}[/tex]
3. Solve and simifpy
[tex]y = 0.5x +4[/tex]
act math scores are approximately normally distributed, with a mean of 21 and a standard deviation of 5.4. if eli decides to take the act exam, what would he need to score in order to be in the 85th percentile?
In order to be in the 85th percentile Eli would need to score 26.62.
What is called percentile?In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.
Given that act math scores are approximately normally distributed,
mean (μ) = 21 and a standard deviation (σ) = 5.4
percentile P(X>x) = 85 =0.85
P(z<x) = 0.85
z = 1.04
y the formula
z = (x - μ)/ σ
⇒ 1.04 = (x - 21)/5.4
⇒ 1.04*5.4 = x - 21
⇒ 5.616 = x - 21
⇒ x = 5.616 + 21
⇒ x = 26.62
To learn more about percentile visit:
brainly.com/question/1594020
#SPJ4
Yeah pls help been trying for tens of minutes
Answer:
34
Step-by-step explanation:
They gave us -3+5i.
The conjugate of -3+5i is
-3 - 5i
You use the same numbers -3 and 5i, but with a minus sign instead of a plus.
Then multiply them together.
(-3 + 5i)(-3 - 5i)
-3•-3 + 15i - 15i - 25i^2
= 9 - 25i^2
Remember i^2 is -1.
= 9 - 25(-1)
= 9 + 25
= 34
Shortcut version:
When you multiply a complex number and its conjugate, square both numbers and add them together.
3^2 + 5^2
= 9 + 25
= 34
7. When it is 9:00A.M. eastern standard time (EST)
in Pittsburgh, it is 6:00A.M. pacific standard time
(PST) in Los Angeles. A plane takes off from
Pittsburgh at 9:00 A.M. EST and arrives in Los
Angeles at 11:00 A.M. PST. If a second plane
were to leave Los Angeles at 10:00 A.M. PST and
take exactly the same amount of time for the trip,
what would be the plane's arrival time (EST) in
Pittsburgh?
A. 6:00 P.M. EST
B. 5:00 P.M. EST
C. 4:00 P.M. EST
D. 3:00 P.M. EST
Please guys I need this tomorrow help tysm I rlly appreciate it
Answer:
A, 6:00 P.M. EST
Step-by-step explanation:
The time difference between EST and PST is -3 hours
11 am - 9am = 2 hours
2 - (-3) = 2+3 = 5 hours
The flight time is 5 hours
Then:
The time difference between PST and EST is +3 hours
5 + 3 = 8
If the fly leaves Los Angeles at 10:00 AM PST
10 + 8 = 18
The plane will arrive at 6:00PM EST
I need explanation on these PLEASE
I'm struggling to understand how they got the answer!!!
Answer: The two problems aren't related
Step-by-step explanation:
The first problem has a 3 and a 9 but no 2, but the second problem does, which shows that these two problems are not related. Also, if you simplify the first one, you will get 27 [tex]\sqrt[4]{3}[/tex], which is not related to the second problem
Give me a list of integers
Answer: why is the question?
Step-by-step explanation: also the integer is the whole number whether if its negative or positive number e.g. -12 or 5
Integers = {...,−4, −3, −2, −1, 0, 1, 2, 3, 4, ... }
Negative Integers = { ..., −4, −3, −2, −1 }
Positive Integers = { 1, 2, 3, 4, ... }
hope it helps<3please answer my mock revision hw xx
Answer:
Step-by-step explanation:
AB = √36 = 6 cm
Area of semicircle πr²/2 or 9π/2
Area of 4 semicircles = 18 π
Total area = 36 + 18 π ≈ 92.5 cm²
A student is assessing the correlation between the average number of hours of internet browsing and the average score on a math test. The table below shows the data:
Number of hours of internet browsing
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Score on math test
(y) 95 94 93 92 91 90 89 88 87 86
Part A: Is there any correlation between the average number of hours of internet browsing and the average score on the math test? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What do the slope and y-intercept of the plot indicate? (3 points)
1. There is a correlation that exists between the average number of hours of internet browsing and the average score on the math test.
2. The function that best fits the data is: Y = f(X)
3. The slope and the intercept tells us that a student would be at their best in a test if they spent 0 hours browsing.
How to find the correlation in the data set1. The correlation that exists in this data set tells us that as a person spends more time on the computer, they would spend less time on their test preparation. This would eventually affect their score.
When the student did not browse the internet, they had their highest score in math. As they started to spend more time on the internet, the score started to drop.
2. The function is given as
math test score Y = function of X: hours spent browsing the internet
this is written mathematically as:
Y = f(X)
3. The Y intercept is at the point where the student spent 0 hours browsing. this is the point where they did their best in this test. This tells us that if a student spent 0 hours on the internet, they would do their best in the test.
Read more on correlation here; https://brainly.com/question/27902490
#SPJ1
Hey umm guys can anyone help
Graph h(x)=7sinx . Use 3.14 for π . Use the sine tool to graph the function. Graph the function by plotting two points. The first point must be on the midline and closest to the origin. The second point must be a maximum or minimum value on the graph closest to the first point.
The graph of the function h(x) = 7sin(x) is given by the image presented at the end of the answer.
How to define the sine function?The sine function is given as follows:
y = Asin(Bx) + C.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.From this problem, the amplitude is given as follows:
A = 7.
Hence:
The midline is at y = 0.The minimum value is of -7, as there is no vertical shift.The maximum value is of 7, as there is no vertical shift.As there is no phase shift, the minimum and maximum values have the x-coordinate given as follows:
Minimum: x = -π/2.Maximum: x = π/2.As the function has no phase shift, the period is given as follows:
2π.
More can be learned about trigonometric functions at brainly.com/question/21558626
#SPJ1
jason is a skilled rapper. he has already rapped a 40-word intro to a song and continues to rap 5 words per second
write an inequality to determine how many more seconds t he will rap to complete the song if the total song, including the intro, is at least 500 words.
drag each numbers or symbol into each box to correctly complete the inequality
hint
500
40
3
>
500
40
+
check
de toch
o
Answer:
500 > 40 + 5t
Step-by-step explanation:
At least 500
40 intro = initial, constant
t = time in seconds
5 words per second
Please mark as brainliest
If quadrilateral lmno is a parallelogram, what must the measure of angle lmn be? m∠lmn = °
The measure of angle ∠LMN = 105°
What is a parallelogram?
A parallelogram is a quadrilateral, which is a four-sided polygon, with opposite sides that are parallel. Additionally, opposite angles in a parallelogram are congruent (equal in measure). So, if a figure has parallel opposite sides and congruent opposite angles, then it is called a parallelogram.
In the given figure, quadrilateral LMNO is a parallelogram in which ∠L = 25x° and ∠MNO = (22x + 9)°
We have get the measurement of ∠LMN
Since in a parallelogram opposite angles are equal.
Therefore 25x = 22x + 9
25x - 22x = 9
3x = 9
x = 3
From another property of a parallelogram, we know that consecutive angles are supplementary.
∠LMN + ∠ONM = 180°
∠LMN = 180 - ∠OLM = 180 - (25x) = 180 - (25×3)
∠LMN = 180 - 75 = 105°
Hence, the measure of angle ∠LMN = 105°
To learn more about the parallelograms, visit:
https://brainly.com/question/970600
#SPJ4
(b) Using a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes Ox and Oy for -5≤x≤5 and -12 ≤ y ≤12
A graph will be drawn where a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes
What is called graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
What are the 6 types of graphs?Types of Graphs and Charts
Statistical Graphs (bar graph, pie graph, line graph, etc.)
Exponential Graphs.
Logarithmic Graphs.
Trigonometric Graphs.
Frequency Distribution Graph.
To learn more about graphs, click the following link:-
https://brainly.com/question/2264373
#SPJ1
Please help! Image below.
The hypotenuse side of the right triangle is 7 units.
The value of x in the triangle is 5.92 units.
How to find the side of a right triangle?A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The side of a right triangle can be found using Pythagoras's theorem as follows:
using Pythagoras's theorem,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
hypotenuse = 7
Let's find x.
7² - (√14)² = x²
49 - 14 = x²
x² = 35
square root both sides
x = √35
x = 5.9160797831
x = 5.92 units
learn more on right triangle here: https://brainly.com/question/28523734
#SPJ1
how do you think the cartesian product you read about is related to the cartesian coordinate system we use for graphing
The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.
The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.
When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.
In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.
To know more about cartesian products refer to:
brainly.com/question/29329368
#SPJ4
HELP!!! I GIVE 20 POINTS TO SOLVER!
QC ≅ Q'C' and ∠AQC is a right angle.
What is the transformation?
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or a geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Given: A reflection is a transformation that maps point Q in a figure over a line, AB, such that for point C at the intersection of AB and QQ'.
We know that reflection creates an image equidistant from the line of reflection.
Thus, QC ≅ Q'C'
Also in reflection, a line drawn from the point is perpendicular to the line of reflection.
Therefore, ∠AQC is a right angle.
To learn more about the transformation visit,
https://brainly.com/question/4289712
#SPJ1
3. Pencils are sold at a unit rate of 36 pencils per box.
Use the variables and number in the box to write an equation to
represent the proportional relationship. The letter b represents the
number of boxes, and p represents the total number of pencils.
Use the unit rate as the constant of proportionality.
Numbers and letters cannot be used more than once. Write
each number or letter in the appropriate box.
36
b
Р
HINT, H
The unit rates
constant of p
the equation
where m is th
proportional
The constant of proportionality for the proportional equation is 36.
Option A is the correct answer.
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 = 9 is an equation.
We have,
Box = b
Number of pencils in one box.
p = 36
Now,
The proportional equation for b and p.
p ∝ b
p = mb
where m is the constant of proportionality.
Now,
b = 1
p = 36
p = mb
36 = m x 1
m = 36
Thus,
The constant of proportionality is 36.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ1
Without graphing, determine whether the system of linear equations in two variables is consistent and dependent, consistent and independent, or inconsistent.
Answer:
Inconsistent as there are two same equations with different values.
So this doesn't make sense.
