The solution to the given initial value problem [tex]cos2x sin x dy + (cos?x)y = 5, 7(7/3) = 4 dx[/tex] is [tex]y(x) = (5/6) * (cos^2(x) - 1) + (28/9) * sin(x) + (40/9) * cos(x)[/tex].
To solve the initial value problem, we can use the method of integrating factors. The integrating factor is found by taking the exponential of the integral of the coefficient of y with respect to x. In this case, the coefficient is cos(x). So, the integrating factor is [tex]e^(^\int ^{ cos(x)} \, ^d^x^) = e^s^i^n^(^x^))[/tex].
Multiplying the given differential equation by the integrating factor, we obtain:
[tex]e^{sin(x)} * [cos^{2x} sin(x) dy + cos(x) y] = 5e^{sin(x)} dx[/tex]
By using the product rule and simplifying, we have:
[tex]d/dx [e^{sin(x)} * y * cos^{2x}] = 5e^{sin(x)}[/tex]
Integrating both sides with respect to x, we get:
[tex]e^{sin(x)} * y * cos^{2(x)} = \int {5e^{sin(x)}} \, dx = 5e^{sin(x)} + C,[/tex]
where C is the constant of integration.
Simplifying and solving for y, we obtain:
[tex]y(x) = [(5/6) * (cos^{2x} - 1) + (28/9) * sin(x) + (40/9) * cos(x)] / (e^{sin(x)} * cos^{2(x)} + Ce^{-sin(x)},[/tex]
where C is the constant of integration.
To find the value of C, we can use the initial condition y(7/3) = 4. Substituting this into the equation and solving for C, we can determine the specific solution.
In conclusion, the solution to the given initial value problem is [tex]y(x) = (5/6) * (cos^{2x} - 1) + (28/9) * sin(x) + (40/9) * cos(x)[/tex], subject to the specified initial condition.
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2000 x 0.045 x 7 =
5000 x 0.07 x 20 =
28000 x 0.09 x 1 =
7500 x 0.035 x 2 =
4000 x 0.045 x 2.5 =
Answer:
639.8
7000
2520
525
450
..........
Question 7: The red line has an equation of y = -1/2 x + 2. The blue line is perpendicular to the red line. Write the equation for the blue line. EXPLAIN PLS
Answer:y=2+2x
Step-by-step explanation:
Perpendicular means the slope is the opposite reciprocal of the red line’s. Opposite reciprocal means that if the red line has a negative slope the blue line will have a positive one, and you flip the fraction of the red line from 1/2 to 2. The y intercept is at 2 so that’s why there is a +2
Streaming movies from Company A costs $3 per month per movie plus a monthly fee of $9. Streaming movies from Company Bcost $4 per movie with no monthly fee. The monthly cost to stream depends on the number of movies, m streamed. Which inequality represents the situation when the montly cost at Company A is less than the montly cost at Company B.
Which ordered pair is a solution of 9(x – 2)2 – 4(y + 5)2 ≥ 36?
(2, –3.5)
(2, 5.5)
(–7.5, –5)
(1.5, –5)
Answer:
its c kiddos
Step-by-step explanation:
The required ordered pair for the solution of an equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).
An ordered pair from the options is the solution of the equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] to be determined.
An ordered pair is defined as the coordinates when put into the equation giving the solution of the equation.
While plotting the curve of the given equation on the graph and also plotting the ordered pair on the graph. It is seen that points (2, –3.5), (2, 5.5), and (1.5, –5) lie on the unshaded portion. While ordered pair (-7.5, -5) lies on the shaded portion.
Thus, the required ordered pair for the solution of an equation [tex]9(x - 2)^2 - 4(y + 5)^2\geq 36[/tex] is (-7.5,-5).
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The table gives the number of yeast cells in a new laboratory culture.
Time(hours) Yeast cells Time(hours) Yeast cells
0 18 10 509
2 39 12 597
4 80 14 640
6 171 16 664
8 336 18 672
(a) Plot the data and use the plot to estimate the carrying capacity for the yeast population. (Round the answer to the nearest ten.)
K = ___680_________ (from multiple choice)
(b) Use the data to estimate the initial relative growth rate. (Use the first two points of the data.)
___________________
(c) Find an exponential model for these data.
P(t) =___________________________
(d) Find a logistic model for these data.
P(t) =__________________
(e) Use your logistic model to estimate the number of yeast cells after 5 hours. (Round the answer to the nearest whole number.)
________________________ yeast cells
The carrying capacity for the yeast population, estimated from the plot, is 680 cells. The initial relative growth rate can be determined using the first two points of the data.
(a) From the plot of the data, we observe that the yeast population levels off or stabilizes around the value of 680 cells. This value represents the carrying capacity of the yeast population in the laboratory culture. (b) To estimate the initial relative growth rate, we use the first two points of the data: (0, 18) and (2, 39). The relative growth rate can be calculated by dividing the change in the number of yeast cells by the change in time. In this case, the change in cells is 39 - 18 = 21, and the change in time is 2 - 0 = 2. Therefore, the initial relative growth rate is 21 / 2 = 10.5 cells per hour.
(c) An exponential model for the data can be determined by fitting an exponential function to the data points. Using the initial point (0, 18) as the initial condition, we can write the exponential model as P(t) = P₀e^(kt), where P(t) represents the number of yeast cells at time t, P₀ is the initial number of cells, k is the growth rate constant, and e is the base of the natural logarithm. Substituting the given data, we can solve for the values of P₀ and k. The exponential model for these data is P(t) = 17.08e^(0.189t).
(d) A logistic model accounts for the carrying capacity of the yeast population. It is given by the formula P(t) = K / (1 + ae^(-kt)), where K represents the carrying capacity, a is a constant related to the initial condition, and k is the growth rate constant. Using the given data, we can solve for the values of K, a, and k. The logistic model for these data is P(t) = 680 / (1 + 4.126e^(-0.189t)).(e) Using the logistic model obtained in part (d), we can estimate the number of yeast cells after 5 hours by substituting t = 5 into the equation. Thus, P(5) = 680 / (1 + 4.126e^(-0.189(5))). Calculating this expression yields approximately 231 yeast cells after 5 hours.
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simply this number 15min :3hours
Answer:
1 min : 12 min
Step-by-step explanation:
To simplify the given ratio, convert both to the same unit of time.
1 hour = 60 minutes
3 hours = 3 x 60 minutes
= 180 minutes
So that,
15 min : 3 hours = 15 min : 180 min
divide through by 15 to have;
15 min : 180 min = 1 min : 12 min
Thus the simplified form of the number give is 1 min : 12 min.
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.1 million cells per microliter and a standard deviation of 0.4 million cells per microliter. (a) What is the minimum red blood cell count that can be in the top 26% of counts? (b) What is the maximum red blood cell count that can be in the bottom 16% of counts? (a) The minimum red blood cell count is million cells per microliter. (Round to two decimal places as needed.)
The minimum red blood cell count that can be in the top 26% of counts is approximately 5.37 million cells per microliter. The maximum red blood cell count that can be in the bottom 16% of counts is approximately 4.602 million cells per microliter.
(a) The minimum red blood cell count that can be in the top 26% of counts can be found by calculating the z-score corresponding to the cumulative probability of 0.26.
Using the standard normal distribution table or a calculator, we find that the z-score is approximately 0.675.
We can then use the z-score formula to find the corresponding value in the original distribution: minimum red blood cell count = mean + (z-score * standard deviation) = 5.1 + (0.675 * 0.4) = 5.37 million cells per microliter.
(b) The maximum red blood cell count that can be in the bottom 16% of counts can be found by calculating the z-score corresponding to the cumulative probability of 0.16.
Using the standard normal distribution table or a calculator, we find that the z-score is approximately -0.994.
Using the z-score formula, we can find the corresponding value in the original distribution: maximum red blood cell count = mean + (z-score * standard deviation) = 5.1 + (-0.994 * 0.4) = 4.602 million cells per microliter.
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Please help me with the questions please ASAP ASAP please please ASAP please please help please I’m begging please please
Answer:
3/2
Step-by-step explanation:
The ratio of perimeters of similar polygons is the same as the ratio of the lengths of corresponding sides.
WX/AB = 12/8 = 3/2
Quadrilateral PQRS is a rectangle. Describe the error in finding the value of x
Answer:
∠PSR=90°
m∠QSR= 90-m∠QSP
x= 90-58=32°
Step-by-step explanation:
The actual value of the x is 32°.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
Given quadrilateral is a rectangle.
All the four interior angles of a rectangle is perpendicular angle or is 90 degrees.
So measure of ∠PSR = 90°
m ∠QSR + m ∠QSP = 90°
Given that m ∠QSP = 58°
Substituting,
m ∠QSR + 58° = 90°
m ∠QSR = 90° - 58°
= 32°
So x° = 32°
Hence the error is that both the angles are made to be equal instead of making the sum of the angles equal to 90°.
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Find the real potential, Φ(x,y), and the complex potential, (F(z), between the parallel plates at y = x and y = x+k, which have potentials of 0 V and 300 V, respectively.
The real potential, between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation in two dimensions. The first paragraph provides a summary of the answer, followed by an explanation in the second paragraph.
The real potential, Φ(x, y), is given by the equation Φ(x, y) = C1x + C2y, where C1 and C2 are constants determined by the boundary conditions. In this case, the boundary conditions are Φ(x, x) = 0 V and Φ(x, x + k) = 300 V. By substituting these conditions into the equation, we can solve for the constants C1 and C2 and obtain the real potential Φ(x, y) between the plates.
The complex potential, F(z), is related to the real potential by the equation F(z) = Φ(x, y) + iψ(x, y), where ψ(x, y) is the stream function. The stream function can be determined by solving the equation ∇²ψ = 0, subject to the same boundary conditions as the real potential. Once the stream function is obtained, the complex potential F(z) can be calculated.
In conclusion, the real potential, Φ(x, y), and the complex potential, F(z), between the parallel plates at y = x and y = x + k can be determined by solving the Laplace equation and using the appropriate boundary conditions. The real potential is given by Φ(x, y) = C1x + C2y, where the constants C1 and C2 are determined by the given potential values on the plates. The complex potential is obtained by combining the real potential with the stream function, which is determined by solving the Laplace equation for the stream function with the same boundary conditions.
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I need help with surface area
Answer:
Surface Area varies by object/shape.
Ask your teacher/learning helper for those formulas of surface area
Step-by-step explanation:
Surface area is the sum of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.
What are they coordinates
Answer:
let ABC be a right-angled triangle, where A is the right angle (left to right)
the original coordinates:
A (-8, 8)
B (-1, 8)
C (-8, 5)
by changing the coordinates from (x, y) to (-y, x)
A (-8, -8)
B (-8, -1)
C (-5, -8)
look attachment
Solve the equations for points!!
(Only 3)
Answer:
-2 , -10 & -99
Step-by-step explanation:
1)
⇒ x + 6 = 4
⇒ x = 4-6
⇒ x = (-2)
2)
⇒x - (-4) = -6
⇒ x + 4 = -6
⇒ x = -6-4
⇒ x = -10
3)
⇒2(x-1) = -200
⇒ x - 1 = -200/2
⇒ x - 1 = -100
⇒ x = 1 - 100
⇒ x = (-99)
Answer:
1. x= -2 2. ×= -10 3. x= -99
Step-by-step explanation:
1. x+6 = 4
x = 4-6
x = -2
2. x-(-4) = -6
x+4 = -6
x = -6 - 4
x = -10
3. 2(x-1) = -200
2x - 2 = -200
2x = -200 +2
2x = -198
x = -99
What is the length of the terrace?
Answer:
A) 12 feet or d) 10 feet..
What does this mean in discrete Math?
L(C) = L(R) ∩ L(S) and there is an underline in the top of L(S)__L(S)
can you please translate this to english?
In discrete mathematics, the expression "L(C) = L(R) ∩ L(S)" means that the language generated by the grammar or automaton represented by C is equal to the intersection of the languages generated by the grammars or automata represented by R and S.
The term "L(C)" refers to the language generated by C, which represents the set of all valid strings or sequences that can be produced by the grammar or automaton C. Similarly, "L(R)" and "L(S)" represent the languages generated by R and S, respectively.
The intersection (∩) symbol signifies the common elements or strings that are present in both L(R) and L(S). In other words, it represents the set of strings that can be generated by both R and S.
As for the underline symbol in the expression "L(S)__L(S)", it is commonly used to denote the closure or complement of a language. However, without additional context or information, it is difficult to determine the exact meaning in this case. It could indicate a specific operation or property related to the language L(S), which would require further clarification.
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Please help with numbers 7 and 8.
Answer:
Below
Step-by-step explanation:
Every triangle should add up to 180 degrees,
This is a right triangle because it has the square in the corner meaning it is 90 degrees.
39 + 90 = 129
180 - 129 = 51 degrees
A: 51 degrees
C: 90 degrees
Answer:
a. 51 degrees
c. 90 degrees
I think
what is x - (14x-4) + 12 = 6x + 32
Answer:
x= -16/19
Step-by-step explanation:
x−14x+4+12=6x+32
−13x+16=6x+32
16=6x+32+13x
16=19x+32
16−32=19x
−16=19x
-16/19=x
one number added to twice another number is 23. Four times the first number added to twice the other number is 38. What are the numbers?
Answer:
x =5 & y =9
Step-by-step explanation:
let anumber x & y
-(x + 2y = 23)
4x + 2y = 38
-x -2y = -23
4x + 2y = 38
-x + 4x + 2y - 2y = 38-23
3x+0 = 15
3x /3 = 15/3
x = 5 then
5 + 2y = 23
2y = 23-5
2y/2 = 18/2
y = 9
therefore y =18 and x = 5
What is the value called that is small enough that anything
equal to or below it will allow you to rule out chance as the most
likely explanation? What are its typical values?
The value that is small enough to rule out chance as the most likely explanation is called the p-value. Typical p-values considered as statistically significant are 0.05 or lower.
The p-value is a measure of the strength of evidence against the null hypothesis in statistical hypothesis testing. It represents the probability of obtaining the observed data or more extreme results, assuming that the null hypothesis is true. If the p-value is below a predetermined significance level (often 0.05), it is considered statistically significant.
This means that the observed data is unlikely to have occurred by chance alone, providing evidence to reject the null hypothesis in favor of an alternative hypothesis. Lower p-values indicate stronger evidence against the null hypothesis.
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25 POINTS - Need ASAP . Answer word problem attached.
If you answer just for points I won’t hesitate to report so don’t try pls!
Answer:
0.82
Step-by-step explanation:
82/100 as a fraction is equal to 0.82
. A rectangle's length is 1 feet shorter than 3 times its width. If we use w to
represent the rectangle's width, use a polynomial to represent the
rectangle's area in expanded form.
area =
square feet
Answer:
Step-by-step explanation:
w is the width of the rectangle, then the length would be 3w - 1.
A = lw
A = w(3w - 1)
A = 3w² - w
somebody help I don't understand this stuff.
Answer:
Dena's answer
14ft^2
Step-by-step explanation:
Her answer is correct because area of triangle is base times height divided by two. Base is 7 and height is 4
From there, you can find the area which is 14.
hope this is correct
How do I do this one?
Step-by-step explanation:
[tex]16 {x}^{2} - 25 = 0 \\ 16 {x}^{2} = 0 + 25 \\ 16 {x}^{2} = 25 \\ {x}^{2} = \frac{25}{16} \\ x = \sqrt{ \frac{25}{16} } \\ = 1.25 \: or \frac{5}{4} \: or1 \frac{1}{4} [/tex]
Do note that this question might have two answers as Square roots will actually give you a positive and negative solution. Clarify with your teacher about this.
Answer:
x=0.09765625 or rounded up as 0.1
Step-by-step explanation:
first you have to add 25 to the 0 and subtract it from the sid it is on. making it look like this
16x²=25
256x=25
now divide both sides by 256 and you get
x=0.09765625 or rounded up as 0.1
a) Work out the size of angle x.
100
B
b) Give reasons for your answer.
co-exterior angle
to
F
Н
G
Answer:
100°= angle b(VERTICAL OPPOSITE ANGLE)
100°+x°=180°[co interior angle]
x=180°-100°
x=80°
The Measure for angle x is 80 degree.
What is Vertical Angle?When two straight lines cross, they generate a pair of non-adjacent angles known as vertical angles. In the corners of the "X" created by two straight lines, or to put it another way, vertical angles are situated opposite one another. Due to their position opposite one another, they are also known as vertically opposite angles.
Given:
<CBD = 100 degree.
So, <ABF = <CBD (Vertical Opposite Angle)
<CBD = 100 degree.
Now, <ABF + <BFE = 180 (Angle on same side of Transversal)
<ABF + 100 = 180
<ABF = 180-100
x= 80 degree.
Hence, the measure for x is 80 degree.
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what are remainder theorem
Answer:
Step-by-step explanation:
When doing synthetic division, if the remainder is zero, we know that the divisor is a root of the polynomial. If the remainder is not zero, the remainder is the function vaue for that divisor.
Celiac disease is a digestive disease that damages the small intestine and affects the absorption of food. People who have this disease cannot tolerate gluten, which is a protein found in many grain products such as wheat, barley, and rye. In recent years, the incidence of diagnosed cases of this disease has risen dramatically. The following data has been collected on the incidence of celiac disease since 1950. Years Since 1950 0 8 16 24 32 40 48 52 56 60 Diagnosed Cases of 10 11 14 13 11 9 12 18 31 Celiac x 1000 a. Create a scatter plot of this data. Answer: b. What regression model would best fit this model? Answer: c. Find an appropriate equation for the curve of best fit. Answer: d. Using your model, how many cases of celiac disease may be diagnosed in 2020?
a. The scatter plot of the data shows the incidence of diagnosed cases of celiac disease since 1950.
b. A linear regression model would best fit this data.
c. The equation for the curve of best fit is y = 0.603x + 8.821, where y represents the number of diagnosed cases of celiac disease (per 1000) and x represents the years since 1950.
d. Using the regression model, approximately 10.835 cases of celiac disease may be diagnosed in 2020.
a. To create a scatter plot of the data, we plot the number of diagnosed cases of celiac disease (y-axis) against the years since 1950 (x-axis). Each data point represents a pair of (x, y) values. For example, the first data point would be (0, 10), the second (8, 11), and so on.
b. In this case, a linear regression model would best fit the data because the scatter plot suggests a roughly linear relationship between the years since 1950 and the number of diagnosed cases of celiac disease.
c. To find the equation for the curve of best fit, we can use linear regression. We calculate the slope and intercept of the line that minimizes the sum of squared distances between the data points and the line. The equation of a line is y = mx + b, where m is the slope and b is the intercept. By performing linear regression on the given data points, we obtain the equation y = 0.603x + 8.821.
d. To estimate the number of diagnosed cases of celiac disease in 2020, we substitute x = 70 (since 2020 is 70 years since 1950) into the equation y = 0.603x + 8.821. Solving the equation, we find that y is approximately equal to 10.835. Therefore, using the regression model, around 10.835 cases of celiac disease may be diagnosed in 2020.
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Does the figure below have rotational symmetry? Explain.
A.)Yes; it can be rotated 360° or less and match the original figure.
B.)Yes; it can be rotated 180° or less and match the original figure.
C.)No; it does not match the original figure after any rotation of 180° or less.
D.)No; it does not match the original figure after any rotation of 360° or less.
Answer:
B.) Yes; it can be rotated 180° or less and match the original figure.
Step-by-step explanation:
You have to trust me its b I did the quiz on Pearson Conexus. I would show a picture but I'm on pc and don't know how to .
My answer will help.
Anyways, have a great day/night !! <3
Step-by-step explanation:
Does the figure below have rotational symmetry? Explain.
A.)Yes; it can be rotated 360° or less and match the original figure.
B.)Yes; it can be rotated 180° or less and match the original figure.
C.)No; it does not match the original figure after any rotation of 180° or less.
D.)No; it does not match the original figure after any rotation of 360° or less.
How hot is the air in the top (crown) of a hot air balloon? Information from Ballooning: The Complete Guide to Riding the Winds, by Wirth and Young (Random House), claims that the air in the crown should be an average of 100°C for a balloon to be in a state of equilibrium. However, the temperature does not need to be exactly 100°C. What is a reasonable and safe range of temperatures? This range may vary with the size and (decorative) shape of the balloon. All balloons have a temperature gauge in the crown. Suppose that 59 readings (for a balloon in equilibrium) gave a mean temperature of x = 97°C. For this balloon, ≈21°C.
ompute a 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium. (Round your answers to one decimal place.)
lower limit
°C
upper limit
°C
The 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).
The 95% confidence interval (CI) for the mean temperature in the crown of the balloon is calculated as follows. We first assume that the population distribution is normal with a standard deviation (SD) of σ = 6°C as per the given data. We will then use the z-distribution to calculate the required confidence interval.
The formula for calculating the 95% confidence interval is given by
CI (mean) = x ± z × (σ/√n)
Where 'x' is the mean, 'z' is the z-score associated with the 95% CI, 'σ' is the standard deviation, and 'n' is the number of samples taken.
For the given data the confidence interval is calculated as:
CI (Mean) = 97 ± 1.96 × (6/√59)
CI (Mean) = 97 ± 1.22
Therefore, the 95% confidence interval for the average temperature at which this balloon will be in a steady-state equilibrium is (95.78°C, 98.22°C).
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what is x over 3 less than or equal to 7
Answer:
x≤21
Step-by-step explanation:
x/3≤7
Multiply both sides by 3
3x/3≤7×3
Simplify
x≤21
Hope this helped!!!
The box plots compare the weekly earnings of two groups of salespeople from different clothing stores. Find and compare the IQRs of the box plots. Group A IQR = $ . Group B IQR = $ . Group A's IQR is Group B's IQR, so the salaries in the middle 50% for Group A are spread out as those for Group B.
Answer:
Group A, IQR = 700
GROUP B, IQR =.450
Group A's IQR is greater
The values in the middle 50%.of Group A are more spread out Than those of Group B.
Step-by-step explanation:
Data for.each group :
The IQR = Q3 - Q1
From the boxplot :
Group A:
Q1 = 1100 ; Q3 = 1800
IQR = 1800 - 1100 = 700
Group B:
Q1 = 1400; Q3 = 1850
IQR = 1850 - 1400 = 450
Greater IQR = Group A
The values in the middle 50%.of Group A are more spread out Than those of Group B.