To predict the behavior of the autonomous differential equation as t -> infinity, analyze the phase portrait of the system. The behavior of X(t) as t approaches infinity depends on the initial conditions. Verify the explicit solution of the DE when k=1 and a=B. Graph the solutions and observe their behavior as t-> infinity.
Explanation:To predict the behavior of the autonomous differential equation dX/dt = k(a-X)(B-X) as t -> infinity, we can analyze the phase portrait of the system. The phase portrait will show the equilibrium points and the direction of the solutions as time increases. In this case, there will be two equilibrium points, one at X = a and one at X = B, assuming a < B. The behavior of X(t) as t approaches infinity depends on the initial conditions. If X(0) < a, the solution will approach X = a, and if X(0) > a, the solution will approach X = B.
To verify the explicit solution of the differential equation when k=1 and a=B, we substitute these values into the equation: X(t) = a - 1/(t+c). For the solution that satisfies X(0) = a/2, we substitute t=0 and X(0) = a/2 into the equation and solve for c. Similarly, for the solution that satisfies X(0) = 2a, we substitute t=0 and X(0) = 2a into the equation and solve for c. We can then graph these two solutions and observe that as t approaches infinity, X(t) approaches a for both solutions, which confirms our analysis from part (b).
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HURRY ILL PICK BRAINLIEST!!!!!!!
Melinda and Paul shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway. 30x + 30y = 450 20x + 25y = 345 How much more can Paul shovel in 1 minute than Melinda? 3 square feet per minute 6 square feet per minute 9 square feet per minute 15 square feet per minute
Carmen needs at least 86 points to pass Karissa's score. Karissa has 631 points. How many points does Carmen have?
HELP PLEASE IS URGENT NEED TO PASS CLASS
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0
The equation of this circle in standard form is
A. (x - 2)^2 + (y + 3)^2 = 5
B. (x - 2)^2 + (y + 3)^2 = 18
C. (x - 4)^2 + (y + 6)^2 = 24
D. (x + 4)^2 + (y - 6)^2 = 24
E. (x + 2)^2 + (y - 3)^2 = 35
The center of the circle is at the point __
A. (-14,21)
B. (-2,3)
C. (2,-3)
D. (-4,6)
E. (4,-6)
And it's radius is ___ units.
A. 5 1/2
B. 3(2 1/2)
C. 2(6 1/2)
D. 35 1/2
Answer:
The standard form equation is B.
The centre of the circle is B
The radius is B.
Step-by-step explanation:
Firstly, the equation can all be divided by 7:
(7x² + 7y²− 28x + 42y − 35) ÷ 7 =
x² + y² - 4x + 6y - 5 = 0
x² - 4x + y² + 6y - 5 = 0
Now add [tex]\frac{1}{2}* b[/tex]
0.5 * 4 = 2, 2² = 4 so 4
0.5 * 6 = 3. 3² = 9 so 9
(x² - 4x + 4) + (y² + 6y + 9) - 4 - 9 - 5 = 0
As the standard form of a circle is (x - a)² + (y - b)²= r² , we need to change this to this. Simply find a number that multiplies to 4 and adds to -4 ( -2 ) and a number that multitplies to 9 and adds to 6 (3):
(x - 2)² + (y + 3)²
Also, we need to subtract the square of the number inside the brackets, as this is completing the square:
-2 * -2 = 4
3 * 3 = 9
So we need to subtract 4 and 9, and 5 as that was in the original:
(x - 2)² + (y + 3)² - 4 - 9 - 5 = 0
To find the radius, we need to move this numbers over to the other side making them positives:
(x - 2)² + (y + 3)² = 4 + 9 + 5
(x - 2)² + (y + 3)² = 18
So the equation is B.The centre of the circle in (x - a)² + (y - b)² is [tex]a[/tex] and [tex]b[/tex]
So in this equation the centre is -2, 3. Which is B.The radius is the square root of whatever (x - a)² + (y - b)² equals, so the square root of 18 is the radius:
√18 = √9√2
= 3√2
= [tex]3 * (2x^{\frac{1}{2} } )[/tex]
So your answer is B.Assume that 2 cards are drawn in succession and without replacement from an ordinary deck of 52 cards. Find the probability that the following occurs.
1 diamond and 1 jack other than the jack of diamonds (in that order) are drawn
Help me please ASAP need to get this done.
Answer:
39 mph
15 mph and 28 mph
Median
Median
It shows the median speed.
Step-by-step explanation:
calculate the area of the circle , round your answer to the nearest hundredth
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP
Describe or show two ways to find the following product: 3 x 3/4 .
A person who is 5.8 feet tall is standing in a pool. The top of the person's head is 1.6 feet above the surface of the water. How deep is the pool? Write your answer as a decimal.
Each month, a retail store awards a blue ribbon to its employee of the month. The probability that Chloe is the employee of the month is 29% in January and 49% in February. What is the probability that she is awarded a blue ribbon in both January and February?
14.21%
19.51%
10.00%
21.81%
Answer:
Option A. 14.21%
Step-by-step explanation:
The probability that Chloe is awarded the employee of the month in January
= 29% P (J) = 0.29
The probability that Chloe is awarded the employee of the month in February = 49% P (F) = 0.49
As we know that both events are independent so
P ( J & F ) = P (J) × P (F)
P = 0.29 × 0.49 = 0.1421 or 14.21%
Therefore the probability that she is awarded a blue ribbon in both January and February 14.21%
3× 1,250 in expanded form and use distributive property
Hasan has 18 3/4 yards of fabric. It takes 3 1/6 yards to make a pillowcase. Hasan plans to make as many pillow cases as he can. How many yards of fabric is left over?
Answer:
[tex]\frac{35}{38}[/tex] yards of fabric is left over.
Step-by-step explanation:
Hasan has the total length of fabric = [tex]18\frac{3}{4}[/tex] yards
= [tex]\frac{75}{4}[/tex] yards
Hasan plans to make as many pillow cases as he can.
To make one pillow case the fabric will be needed = [tex]3\frac{1}{6}[/tex] yards = [tex]\frac{19}{6}[/tex] yards
Hasan can make the total number of pillowcases = [tex]\frac{\frac{75}{4} }{\frac{19}{6} }[/tex]
= [tex]\frac{75}{4}[/tex] × [tex]\frac{6}{19}[/tex]
= [tex]\frac{75}{2}[/tex] × [tex]\frac{3}{19}[/tex]
= [tex]\frac{225}{38}[/tex]
= [tex]5\frac{35}{38}[/tex]
He can make 5 pillow cases and [tex]\frac{35}{38}[/tex] yards of fabric would be left over.
If you need to be at the party in 2.5 hours, how fast would you need to drive to get there?
The answer would be 60 km/h. :D
Find the percent of a standard normal model found in the given region
6.2 * 10 to the third power equals
The interior angles formed by the sides of a quadrilateral have measures that sum to 360°. What is the value of x? Enter your answer in the box. x =
The value of x is equal to 59°.
In Mathematics and Euclidean Geometry, a quadrilateral is a type of polygon that has four (4) sides, four (4) vertices, four (4) edges and four (4) angles.
Generally, the sum of the interior angles of any quadrilateral is equal to 360 degrees. In this context, we can logically deduce the following;
2x + 3 + x + 2x + 3 + x = 360°
6x + 6 = 360°
6x = 360° - 6
6x = 354°
x = 354/6
x = 59°.
Last year there were 380 students at Woodland middle school this year the student population will increase by 5% what will be the schools increased student population?
The area of a rectangle mirror is 11 11/16 Square feet. The width of the mirror is 2 3/4 feet. If there is a 5 foot tall space on the wall to hang the mirror, will it fit?
Answer:
Love
Step-by-step explanation:
Thanks for the help.
The local park has 4 bike racks . Each bike rack can hold 15 bikes . There are 16 bikes in the bike racks.What expression shows the total number of empty spaces in the bike racks ?
the cost of an item is 100% of its price. what number goes in place of ? in the addition problem?
The answer is 100 thats all you have to put trust me.
Find the 80th percentile of the distribution of the average of 49 fly balls.
The 80th percentile of the distribution of the average of 49 fly balls is approximately 254.2 feet
The 80th percentile of the distribution of the average of 49 fly balls can be found using the formula for the sample mean and the Z-score. Given that the mean distance of fly balls hit is 250 feet, the standard deviation is 50 feet, and the sample size is 49, we can calculate the 80th percentile as follows:
Calculate the Z-score corresponding to the 80th percentile, which is 0.842
Use the Z-score formula to find the sample mean:
Sample Mean=Population Mean + Z × Standard Deviation/ Sample Size
Sample Mean=250+0.842× 50/ √49
Sample Mean=250+0.842×5
Sample Mean=250+4.2
Sample Mean=254.2
Therefore, the 80th percentile of the distribution of the average of 49 fly balls is approximately 254.2 feet
Complete question:
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. Find the 80th percentile of the distribution of the average of 49 fly balls.
Does the absolute value determine direction which the graph opens
solving a mathematical problem without the use of paper and pencil,calculator, or computer is called using _________ math
PLEASE HELP!!!!!!!!
A business reports a net income of −$5,040 over a 9-month period.
What is the average income per month for that period? −$45,360
−$560
$560
$45,360
On the coldest night in Vostok Station, Antarctica, the temperature dropped from 0°C to −24°C in 4 hours.
What is the average temperature change per hour?
Answer 2 and 4 please
In the 1939 movie The Wizard of Oz, when the brainless Scarecrow is given the confidence to think by the Wizard(by merely handing him a diploma, by the way), the first words the Scarecrow utters are, “The sum of the square roots of any two side of an isosceles triangle is equal to the square root of the remaining side.” An isosceles right triangle is just a right triangle having both legs the same length. Supposed that an isosceles right triangle has legs each length of 3. What is the length of the hypotenuse? Is the Scarecrow’s assertion valid? This question illustrated the true value of a diploma without studying.
The equation that the scarecrow uttered can be expressed mathematically as:
sqrt (C) = sqrt (A) + sqrt (B)
where A, B, and C are the sides of the triangle
Since the triangle is an isosceles, therefore A = B and
sqrt (C) = 2 sqrt (A)
given that the measure of the leg is 3, A = 3, C is:
sqrt C = 2 sqrt (3)
sqrt C = 3.464
C = 12
In a any triangle, the sum of two sides must be greater than the third side, since in this case C > A + B therefore the Scarecrow is not correct because the correct relationship should be A + B > C.
To find the correct hypotenuse, we start with the Pythagorean equation:
C^2 = A^2 + B^2
So what the scarecrow mistakenly did was to ignore the “+” symbol during the square root. Taking the square root on both sides, the correct equation is:
C = sqrt (A^2 + B^2)
Calculate for C, since A = B = 3:
C = sqrt (3^2 + 3^2)
C = 4.24
So now A + B > C and this is now correct.
Geometry.
In circle F, what is the measure of arc CB?
A) 60°
B) 70°
C) 17.5°
D) 35°
The measure of arc CB, <CFB = 70°.
What is Arc?A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of a circle.
Given:
First, Draw segment FC.
Measure of arc CB = ∠CFB
As, ∠CFB is complementary to ∠CFA
So, ∠CFB = 180° - ∠CFA
We have Δ CFA is isosceles then
∠ FAC = ∠ FCA = 35°
∠CFA +∠ FAC + ∠ FCA = 180°
∠CFA = 180° - 70°
∠CFB = 180° - (180° - 70°)
<CFB = 70°
Thus, the Measure of arc CB is 70°.
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Which of the following is less than 6.5 x 10^-5.
A. 1.4 x 10^-3
B. 2.5 x 10^-4
C. 7.8 x 10^-5
D. 4.6 x 10^-6
[tex]4.6\times10^{-6}[/tex] is less than [tex]6.5\times10^{-5}[/tex]. Therefore, option D is the correct answer.
Given that, [tex]6.5\times10^{-5}[/tex].
We need to find which is less than [tex]6.5\times10^{-5}[/tex].
What is scientific notation?The scientific notation helps us to represent the numbers that are very huge or very tiny in a form of multiplication of single-digit numbers and 10 raised to the power of the respective exponent. The exponent is positive if the number is very large and it is negative if the number is very small.
Now, [tex]6.5\times10^{-5}[/tex] =0.000065
[tex]1.4\times10^{-3}[/tex] =0.0014
[tex]2.5\times10^{-4}[/tex] =0.00025
[tex]7.8\times10^{-5}[/tex] =0.000078
[tex]4.6\times10^{-6}[/tex] =0.0000046
[tex]4.6\times10^{-6}[/tex] is less than [tex]6.5\times10^{-5}[/tex]. Therefore, option D is the correct answer.
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write a measurement division story problem for 6 divided by 3/4
Mira has 6 pieces of wood, and she wants to divide them into equal parts of 3/4. Then in total how many pieces of wood she has?
What is division?Division is the process of splitting a number or an amount into equal parts
Here, we have,
6÷ 3/4
=6×4/3
=8
The required story may be:
Mira has 6 pieces of wood, and she wants to divide them into equal parts of 3/4. Then in total how many pieces of wood she has?
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