Find an autonomous differential equation with all of the following properties:
equilibrium solutions at y=0 and y=5,
y′>0 for 0
y′<0 for −[infinity]
dydt=
Answers
An autonomous differential equation with all of the following properties is dy/dx = -y(y - 5).
Autonomous differential equation is a type of ordinary differential equation that does not depend on an independent variable.
It is an equation of the form dy/dx = f(y), where the right side of the equation does not depend on the independent variable x.
The differential equation should be:
dy/dx = f(x, y)
The differential equation is zero at equilibrium points, i.e., dy/dx = 0 at y = 0 and y = 5.
The differential equation is therefore
dy/dx = y(y - 5)
Given that y' > 0 for 0 < y < 5.
Replace y = 2 in dy/dx = y(y - 5) and then check the dy/dx sign.
dy/dx = (2)(2 - 5)
dy/dx = 2(-3)
dy/dx = -6 < 0 not satisfied the condition
Consequently, add -1 to the function f(x, y).
As a result, the necessary function is dy/dx = -y(y - 5).
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The complete question is:
Find an autonomous differential equation with all of the following properties:
equilibrium solutions at y = 0 and y = 5,
y' > 0 for 0 < y < 3 and
y' < 0 for -∞ < y < 0 and 5 < y < ∞
dy/dx =
Related Questions
complete and balance the following half-reaction: cr(oh)3(s)→cro2−4(aq) (basic solution)
Answers
The completed and balanced half-reaction in basic solution is, cr(oh)3(s) + 4OH− (aq) → cro2−4(aq) + 3H2O (l).
The half-reaction that is completed and balanced in basic solution for the reaction, cr(oh)3(s) → cro2−4(aq) is as follows:
Firstly, balance all of the atoms except H and OCr(OH)3 (s) → CrO42− (aq)
Now, add water to balance oxygen atoms
Cr(OH)3 (s) → CrO42− (aq) + 2H2O (l)
Then, balance the charge by adding OH− ionsCr(OH)3 (s) + 4OH− (aq) → CrO42− (aq) + 3H2O (l)
Thus, the completed and balanced half-reaction in basic solution is, cr(oh)3(s) + 4OH− (aq) → cro2−4(aq) + 3H2O (l).
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Please help me fast I need the answer rn
Answers
Answer: Rotation
Step-by-step explanation: The shape is not moving or reflecting in any way. It is just rotating.
find the area of the region bounded by the graphs of y = 32 / (x 2 17x 72), y = 0, x = 0, and x = 1.
Answers
To find the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1, we can use definite integration.
The area of the region bounded by the given graphs is approximately 25 square units.
To find the area, we need to integrate the given function over the interval [0, 1]. The integral represents the area under the curve between the limits of integration. Since the region is bounded by the x-axis, we integrate the function with respect to x.
∫[0, 1] (32 / (x² - 17x + 72)) dx
Evaluating this integral gives us the area of the region bounded by the graphs. Using numerical integration methods, we find that the area is approximately 25 square units.
The integral calculation involves finding the antiderivative of the function and then evaluating it at the upper and lower limits of integration. The resulting value represents the area between the curves and the x-axis within the specified interval.
Therefore, the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1 is approximately 25 square units.
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Remember what we know about vertical angles and solve for x.
Then tell me the measure of Angle R.
Answers
The value of x by using vertical angles is 4, and the measure of angle R is 34°
Vertical Angles.Vertical angles are angles that are formed and are opposite of each other when two lines intersect. Vertical angles are congruent angles, it implies that they exhibit the same angle measure. Vertical here refers to the fact that they have the same Vertex (corner point).
From the information given:
6x + 10 = 8x + 2
6x - 8x = 2 - 10
-2x = -8
x = -8/-2
x = 4
The measure of angle R = 6x + 10
= 6(4) + 10
= 24 + 10
= 34°
Therefore, we can conclude that the measure of angle R is 34°
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what is -(-4/9) * (-1/7)
Answers
Answer:
−4/63
Step-by-step explanation:
Solve the system using substitution or elimination:
8x - 3y = -13
-3x + 5y = 1
Make sure you answer is an ordered pair (x, y).
Answers
Answer:
{x = -2, y = -1
Step-by-step explanation:
Solve the following system:
{-3 y + 8 x = -13
5 y - 3 x = 1
Choose an equation and a variable to solve for.
In the first equation, look to solve for x:
{-3 y + 8 x = -13
5 y - 3 x = 1
Isolate terms with x to the left-hand side.
Add 3 y to both sides:
{8 x = 3 y - 13
5 y - 3 x = 1
Hint: | Solve for x.
Divide both sides by 8:
{x = (3 y)/8 - 13/8
5 y - 3 x = 1
Perform a substitution.
Substitute x = (3 y)/8 - 13/8 into the second equation:
{x = (3 y)/8 - 13/8
5 y - 3 ((3 y)/8 - 13/8) = 1
Expand the left-hand side of the equation 5 y - 3 ((3 y)/8 - 13/8) = 1.
5 y - 3 ((3 y)/8 - 13/8) = 5 y + (-(9 y)/8 + 39/8) = (31 y)/8 + 39/8:
{x = (3 y)/8 - 13/8
((31 y)/8 + 39/8) = 1
Choose an equation and a variable to solve for.
In the second equation, look to solve for y:
{x = (3 y)/8 - 13/8
(31 y)/8 + 39/8 = 1
Isolate terms with y to the left-hand side.
Subtract 39/8 from both sides:
{x = (3 y)/8 - 13/8
(31 y)/8 = -31/8
Solve for y.
Multiply both sides by 8/31:
{x = (3 y)/8 - 13/8
y = -1
Hint: | Perform a back substitution.
Substitute y = -1 into the first equation:
Answer: {x = -2, y = -1
8. H={all numbers of the form 3n+1, for n a natural number} under multiplication?
9. J={all numbers of the form 3n+2, for n a natural number under multiplication?
10. K={perfect squares of integers) under addition?
11. L={perfect squares of integers under multiplication?
12. M = {all numbers of the form 2", for n a natural number) under addition
pol
13. N= {all numbers of the form 2", for n a natural number under multiplication?
TIMBER
Answers
Answer and Step-by-step explanation:
H= {all numbers of the form 3n+1, for n natural number} under multiplication:
Sol: all number of the form 3n+1, for n natural number so, put n=2, 3(2) +1 = 7, which is a natural number. A natural number under multiplication does not form a group because its inverse does not exist.
J= {all number of the form 3n+2, for n natural number} under multiplication:
Sol: all the number of the form 3n+2, n is the natural number does not form a group under multiplication because the identity element does not form in this set, and inverse does not exist.
K= {perfect squares of integers} under addition:
Sol: perfect square of integers under addition does not form a group because the inverse does not exist. For example, for any element x, inverse (-x) does not exist because of a square integer.
L= {perfect squares of integers} under multiplication:
Sol: a set of the perfect square of integers under multiplication is not a set, because it does not have the inverse property
M= {all numbers of the form 2, for n natural number} under addition:
Sol: natural number in the form of 2n, n is a natural number under addition is not a group as it does not have identity property. Identity property, under addition, is zero.
N= {all number of the form 2n, n is natural number} under multiplication:
All number of the form 2n, n is the natural number under multiplication is not a group. Because its inverse does not exist. For example, an element x belongs to a natural number; its inverse (1/x) does not exist in this set.
Marcus is using a plant food to fertilize his garden his garden is a rectangle Marcus uses 1 cup of plant food for every square yard of his garden. There are 4 cups in 1 quart one quart of plant food weights 28 ounces what is the total weight in ounces of the plant food Marcus uses to fertilize his garden?
Answers
Marcus is using a plant food to fertilize his garden his garden is a rectangle Marcus uses 1 cup of plant food for every square yard of his garden.
To solve it, we need to first find the area of Marcus's garden in square yards, and then multiply it by 1 cup of plant food per square yard. Finally, we need to convert the total cups to ounces using the given conversion rate.
Let the length of Marcus's garden is l yards and the width is w yards. Then the area of his garden in square yards is
A = lw.
If Marcus uses 1 cup of plant food per square yard, then he will use A cups of plant food in total.
To convert cups to ounces, we can use the given conversion rate of 4 cups per 28 ounces.
1 cup = 28/4 ounces
Therefore, the total weight of plant food Marcus uses in ounces is
Total weight = A * (28/4) ounces
By substituting A = lw, we get
Total weight = lw * (28/4) ounces
Total weight = 7lw ounces
Hence, the total weight of plant food Marcus uses to fertilize his garden is 7 times the product of the length and width of his garden, measured in yards.
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PLEASE HELP ASAPPP!!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
Answers
Answer:
f(x)= -x^2-6x+7
Step-by-step explanation:
Since the graph opens downward the function for the parabola is going to be negative. This leaves us with two answers.
Now use the remaining possible equations and solve for the vertex.
Using x= -b/2a to solve for the x value of the vertex plug in the values to solve.
a= -1 b= -6 c=7 so, since -6 is already negative plugging it in makes it positive -(-6)/2(-1) = 6/-2 = -3. So x equals negative 3.
Then plug in -3 into the equation to get the y-value.
- (-3)^2 - 6(-3) + 7 = -9 + 18 + 7 = 16 so this confirms the vertex for this equation is (-3,16) so the answer is -x^2-6x+7.
Hope this helped! :)
$89.75 scooter ; 7.25% tax
Answers
Answer: $96.25
Step-by-step explanation:
Take 89.75 divided by 100% = 0.8975
Then times 7.25% = $6.5
Total is 89.75 + 6.5 = $96.25
Which of the following is a run on sentence
Answers
Answer:
It is defiantly either C or D.
Step-by-step explanation:
It's not A because it has a period with means there is 2 sentences and not 1.
It's not B because it does not have multiple commas.
It might most likely be C because it has the most amount of commas.
If I'm wrong about C, than try D.
T/F two lines either intersect or are parallel.
Answers
The given statement is True.
What are parallel lines?
Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
True. Two lines either intersect or are parallel.
This means that there are only two possibilities for the relationship between two lines: they either meet at a single point, in which case they are said to intersect, or they never meet, in which case they are said to be parallel.
If two lines are intersecting, then they are not parallel, and if two lines are parallel, then they do not intersect.
Hence, The given statement is True.
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In the rhombus ABCD, ĐDAE = 30°. Which is ĐABC?
309
D
C
A.
30°
OB.
60°
c.
120°
OD.
150°
Answers
Answer:
C. 120 deg
Step-by-step explanation:
All sides of a rhombus are congruent.
That means that triangle ADC is an isosceles triangle with AD = CD, so angles DAE and DCE are congruent.
m<DAE + m<DCE + m<ADC = 180
30 + 30 + m<ADC = 180
m<ADC = 120
Opposite angles of a rhombus are congruent, so
m<ABC = m<ADC = 120
if a humane society has 73 dogs and cats to be adopted. the number of cats is 10 more than twice the number of dogs. how many of each animal is up for adoption
Answers
D + C = 73
C = 2D + 10
Substituting the second equation into the first equation, we get:
D + 2D + 10 = 73
3D + 10 = 73
3D = 63
D = 21
Substituting this back into the second equation, we find that C = 2 * 21 + 10 = 52.
Therefore, there are 21 dogs and 52 cats up for adoption.
I need help on this question
Answers
Answer:
Diego: y = 11 + 5 x
Emilia: y = 60 - 2 x
Step-by-step explanation:
y for saving and x for weeks
Diego: y = 11 + 5 x
Emilia: y = 60 - 2 x
Which graph has a correlation coefficient, r, closest to 0.95
Answers
Answer:
A correlation coeff close to +1 would have a positive slope, and all dots representing the data set would be quite close to the regression line.
Correlation is a measure of association between two variables. IF there is a perfect linear association then correlation would be nearer to 1.
Correlation always lies between -1 and +1.
If between-1 and 0 we say there is a negative correlation.
If nearer to 1 than to 0 then we say strong correlation
Here given correlation is 0.95 i.e. positive and have almost perfect linear relation.
Hence we see that Graph C shows almost linear relationship with slope positive
So option C is answer
answer for p=2l+2w for l
Answers
Answer:
\(I=\frac{p-2w}{2}\)
Step-by-step explanation:
\(p=2I+2w\\\\p-2w=2I+2w-2w\\\\p-2w=2I\\\\\frac{p-2w}{2}= I\)
What is the greatest common factor of 8, 28, and 48?
Answers
\( \: \: \: \: \: \: \: \)
the GCF of 28,48 are GCF OF 281 , 2, 4, 7, 14, 28GCF OF 48
1 , 2, 3, 4, 6, 8, 12, 16, 24, 48 hope it helpsThe greatest common factor of 8, 28, and 48 is 4.
Greatest Common FactorThe largest common factor out of all the numbers in the given set is known as Greatest Common Factor.
How to evaluate Greatest Common Factor?Factors of 8, \(8=2\times 2\times 2\)
Factors of 28, \(28=2\times 2\times 7\)
Factors of 48, \(48=2\times 2\times 2\times 2\times 3\)
The common factors in the above set of numbers are 2and 2.
So, the Greatest Common Factor of 8, 28, and 48 is \(2\times 2=4\).
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Gavin combines Thirty-two and two-fifths ounces of water and 7.15 ounces of lemon juice in a pitcher to make lemonade. Which is the most reasonable estimate for the amount of liquid in the pitcher? 39 ounces 42 ounces 45 ounces 47 ounces
Answers
Answer:
OPTION A is correct
39 ounces
Step-by-step explanation:
Given:
The amount of water in the pitcher= 32 ounces
The amount of lemon juice in the pitcher = 7.15 ounces
We were to calculate the most reasonable estimate for the amount of liquid in the pitcher
To do this we need to sum up the Amount of water and Amount of lemon juice in the pitcher because the water is a liquid as well as the lemon juice which is
32 ounces + 7.15 ounces
=39.15 ounces
Therefore, the Estimated amount of liquid in the pitcher is approximately 39 ounces
find the surface area of the triangular prism.
i chose 608 for the first one and it was wrong.
Answers
Answer:
I think the answer is either c or d
Step-by-step explanation:
sorry that i dont know (-_-”)
3n + 9 = 11n -23 Please
Answers
Answer: N=4
Step-by-step explanation:
Answer: n = 4
Step-by-step explanation:
subtract 9 from both sides simplify subtract 11n from both sides then combine like terms, simplify, divide both sides by the same factor, then simplify then boom :)
the lines below are parallel if the slope of the green line is -2 what is the slope of the red line?
a)-1/2
b)1/2
c)2
d)-2
Answers
Answer:
D
Step-by-step explanation:
Remember that parallel lines have equal slopes.
So, if the green line is parallel to the red line, and the slope of the green line is -2, this means that the slope of the red line must also be -2!
So, our answer is D.
And we're done!
Answer: D
Step-by-step explanation:
If the slope of The green line is -2 and it is parallel to the red line, the slope of the red line must also be -2
If f(x) = x and g(x) = X + 2, which statement about the graphs of the functions is true?
A. g is a translation of f 2 units down.
B. g is a translation of f 2 units to the right.
C. g is a translation of f 2 units to the left and 2 units down.
D. g is a translation of f 2 units up.
PLEASE HELP ME DUE IN 10 minutes!!!
Answers
Answer: D
Step-by-step explanation: +2 would be an upwards translation
a) Agora é com você! Complete a tabela abaixo determinando os valores de y = f (x) e os respec- tivos pontos de coordenadas (x, y) do gráfico da função f.
Answers
Answer:
Im sorry! can you please translate this?
Step-by-step explanation:
Molly is making a punch for the school picnic. The recipe calls for 3/4 quart of lemonade, 3 cups of cranberry juice, 4 cans of orange juice concentrate, and 5 cups of water. If Molly uses 1(2/5) quarts of lemonade, how many cups of cranberry juice will she need?
Answers
She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
To make the recipe,
3/4 quart of lemonade and 3 cups of cranberry juice
The ratio of cranberry juice to a quart of lemonade
⇒ 3/(3/4) = 4
To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.
So,
4 = cranberry juice / 1(2/5)
(5/7) × cranberry juice = 4
Cranberry juice = 28/5 ⇒ 5 (3/5).
Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".
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What’s the area of the shape
Answers
21.2 because you use the area of a circle formula which is pi times r squared and divide it by four to get each quarter and then multiply by three because there are 3 quarters of the circle.
�
=
5
9
(
�
−
32
)
The equation above shows how temperature
�
, measured in degrees Fahrenheit, relates to a temperature
�
, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
Answers
For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.
What is meant by temperature?
Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.
The given equation is:
\(C = \frac{5}{9} (F- 32)\)
where C = temperature in Celsius
F = temperature in Fahrenheit
The above equation can be rewritten as:
C = 5/9F - 160/9
Now, this is an equation of a straight line with a formula,
y = mx + c
Comparing,
m = 5/9 which is the slope of the equation.
This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.
So the option I is true.
Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.
So option II is true.
Option III is not true as is discussed above.
Therefore for the given equation of temperature, the correct option is Option D.
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Answer:
D
Step-by-step explanation:
I have nothing else to say- lol
PLS ANSWER!!!!!!!!!!!!!!!
Answers
Answer:
m
Step-by-step explanation:
It is closest to being a vertical line.
the picture is a model of a barn that is being built the bottom is a perfect cube with a square pyramid sitting on top the architect wants to paint the whole outside of the model (including the bottom) red, how much red paint will he need?
Answers
Explanation
Step 1
to find the total area divide the figure
\(\begin{gathered} \text{Area}=4\text{ squares+4 triangles} \\ \end{gathered}\)now, we need to find the area of the triangle
so, we need to find the hypotenuse of the triangle
\(\begin{gathered} \text{hyp}^2=3^2+4^2 \\ \text{hyp}^2=9+16 \\ \text{hyp}^2=25 \\ \sqrt[]{\text{hyp}^2}=\sqrt[]{25} \\ \text{hyp}=5 \end{gathered}\)so, the height of the triangle is 5 cm
Step 2
let
side of the square=6
heigth of the triangle=5
base of the triangle=6
\(\begin{gathered} \text{Area}=4\text{ squares+4 triangles} \\ \text{Area}=4(side^2)\text{+4 }(\frac{b\cdot h}{3}) \\ \text{replace} \\ \text{Area}=4(6^2)\text{+4 }(\frac{6\cdot5}{3}) \\ \text{area}=4(36)+4(10) \\ \text{area}=144+40 \\ \text{area}=184\text{ square cm} \end{gathered}\)I hope this helps you
Kelly deposited $4,205 in an account for 3.5 years. She earned $662.29 in interest. What interest rate did the bank pay her?
Answers
Answer:
r = 4.5%
Step-by-step explanation:
Formula:
I = Prt
r = I/(Pt)
Given:
I = 662.29
P = 4205
t = 3.5
Work:
r = I/(Pt)
r = 662.29/(4205 * 3.5)
r = 662.29/14717.5
r = 0.045
r = 4.5%