Differential equation is a way to represents the relation between the functions and their variables. The solution to the differential equation given in the question is,
[tex]y=\dfrac{3}{15x-1}[/tex]
Given-
The equation in the question is,
[tex]{dy\times {dx}=5y^2[/tex]
What is differential equation?Differential equation is a way to represents the relation between the functions and their variables.
Rewrite the equation,
[tex]\dfrac{dy}{5y^2} =dx[/tex]
Integration both sides,
[tex]-\dfrac{1}{5y} =x+c[/tex]
Here, c is the integrating constant.
Now the given initial condition is,
[tex]y(0)=3[/tex]
Use this for the integrated function to find the value of the constant,
[tex]-\dfrac{1}{5\times 3} =c[/tex]
[tex]c=-\dfrac{1}{15}[/tex]
Put this value in equation we get,
[tex]-\dfrac{1}{5y} =x-\dfrac{1}{15}[/tex]
[tex]y=\dfrac{3}{15x-1}[/tex]
Hence the solution to the differential equation given in the question is,[tex]y=\dfrac{3}{15x-1}[/tex]
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To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, use separation of variables and integration. Substitute the initial condition to find the specific solution.
Explanation:To solve the differential equation dy/dx = 5y^2 with the initial condition y(0) = 3, we can use separation of variables.
First, rewrite the equation as dy/y^2 = 5dx. Integrate both sides: ∫1/y^2 dy = ∫5 dx. This simplifies to -1/y = 5x + C.
Next, apply the initial condition y(0) = 3: -1/3 = 0 + C. Therefore, C = -1/3.
Substitute C back into the equation: -1/y = 5x -1/3. Solve for y: y = -1/(5x -1/3).
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A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag.
The probibly of not drawing a black marhle is_
The probability of drawing a red marble is_
Answer:
Question 1: 4/5 or %80
Question 2: 7/10 or %70
Step-by-step explanation:
Step 1: Find the total amount of marbles
5 + 2 + 3
10
Step 2: Find the probability of not drawing a black marble
Add the total amount of marbles that are not black
5 + 3
8
Now find the probability:
8/10
4/5 or %80
Answer: 4/5 or %80
Step 3: Find the probability of not drawing a red marble
Add the total amount of marbles that are not red
5 + 2
7
Now find the probability:
7/10 or %70
Answer: 7/10 or %70
Answer: its 4/81
Step-by-step explanation:
i just did it
What are the solutions of each equation? Use a graph of the related function. a. x2 + 4 = 4 b. x2 + 16 = 0 c. x2 − 49 = 0
The solutions to the equations are: a) x = 0, b) No real solutions, c) x = 7, -7.
Explanation:In order to find the solutions to each equation, we can use a graph of the related function. Let's go through each equation:
a. x² + 4 = 4
Subtracting 4 from both sides of the equation, we get x² = 0. This means x = 0 is the only solution.
b. x² + 16 = 0
Subtracting 16 from both sides gives us x² = -16. Since the square of a real number cannot be negative, there are no real solutions to this equation.
c. x² - 49 = 0
Adding 49 to both sides yields x² = 49. Taking the square root of both sides gives x = ±7. So the solutions to this equation are x = 7 and x = -7.
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What does the value of x have to be so that
(x, -7) and (-1,4) have a slope of 11 between them?
Answer:
x= -2
Step-by-step explanation:
Please see attached picture for full solution.
What is the least common multiple of 18, 16, and 9?
A.
48
B.
144
C.
288
D.
2,592
Answer:
The correct answer is B. 144
Can you show me a workout
Answer:
d
Step-by-step explanation:
Suppose you filled the ice-cream cone shown with your favorite ice-cream. Which measurement BEST describes the
amount of ice-cream in the cone? (round to the nearest tenth)
Amount of ice-cream in the cone = 6.3 in³
Solution:
Given data:
Diameter of the cone = 2 in
Radius of the cone = 2 ÷ 2 = 1 in
Height of the cone = 6 in
The value of π = 3.14
Volume of the cone = [tex]\frac{1}{3} \pi r^2 h[/tex]
[tex]$=\frac{1}{3}\times 3.14\times 1^2\times 6[/tex]
= 6.3
Volume of the cone = 6.3 in³
Amount of ice-cream in the cone = 6.3 in³
Answer:
6.3 in ^3
Step-by-step explanation:
Trust me ;)
If y varies inversely with the square of r, what is the constant of proportionality when y - 10 and 1 = 5?
Question:
If y varies inversely with the square of r, what is the constant of proportionality when y =10 and r = 5?
Answer:
The constant of proportionality is 250
Solution:
Given that,
y varies inversely with the square of r
Which means,
[tex]y \propto \frac{1}{r^2}\\\\y = k \times \frac{1}{r^2}[/tex]
Where, "k" is constant of proportionality
Subtitute y = 10 and r = 5
[tex]10 = k \times \frac{1}{5^2}\\\\10 = k \times \frac{1}{25}\\\\k = 10 \times 25\\\\k = 250[/tex]
Thus the constant of proportionality is 250
9. Seven more than the quotient of a number b
and 45 is greater than 5.
which of these rational numbers are also an integer?
a.2/4
b.0.24
c.4/2
d.2.4
Answer:
D.2.4
Step-by-step explanation:
Because it's a fraction and can be written in fraction as 240/100
Answer:
answer is C
Step-by-step explanation:
4/2 : rational
4/2 = 2 : integer
and When you simplify 4/2 you get 2, 2 is an integer.
Solve 3x - 9x + 7 - 3 = -8.
6
-6
2
-2
Answer:
x=2
Step-by-step explanation:
add like terms (3x-9x= -6x, 7-3= 4)then move the constant to the right (-8+4=-12)finally divide it by 6 which gives you "x"Answer:
x=2
Step-by-step explanation:
3x - 9x + 7 - 3 = -8
Combine like terms
-6x +4 = -8
Subtract 4 from each side
-6x +4-4 = -8-4
-6x = -12
Divide each side by -6
-6x/-6 = -12/-6
x = 2
As part of summer camp, Henry goes on a treasure hunt. He starts at the base of a tree and walks 189 ft due north. He then Turns and walks 89 ft due east. He turns again and walks 89 ft due south. How far is Henry from the tree?
Answer:
133.87 ft
Step-by-step explanation:
Patrick spins both spinners below. What is the probability the hw spins green on both spinners?
Answer:
4/12 or 2/6 or 1/3
Step-by-step explanation:
Liszt had test scores of : 72, 94, 108, 60
what is the range for her test scores
Answer: 48
Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 108 - 60 or 48. So the range of this data set is 48.
A cube has an edge length of 8 meters. What is its volume, in cubic meters?
Answer:
[tex]512\ m^{3}[/tex]
Step-by-step explanation:
Volume of any cube equals a product of all the edge lengths. Since there are 3 edges:
[tex]V = a^{3} = 8^{3} = 512\ m^{3}[/tex]
The required area of the cube with an edge length of 8 meters is 512 cubic meters.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
A cube has an edge length of 8 meters.
The volume of the cube = a³
The volume of the cube = 8³ = 512 cubic meters
Thus, the required area of the cube with an edge length of 8 meters is 512 cubic meters.
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The point (4,5) is translated two units down. What is the y-coordinate of the image?
Answer:
(4,3), y-coordinate is 3
Step-by-step explanation:
If we're translating down, that means we are subtracting however many units we go down by the y-coordinate.
So 5-2=3, and the new y-coordinate is 3
Answer is (4,3)
Step-by-step explanation:
So you need to this...
(x), (y-2)
Now you need to leave the x because It won't do nothing but the y yes because it said bring 2 units down so its (y-2) because its going negative. Now subtract the number you have given.
Now replace y with 5 and subtract 2.
Now you will be given the answer (4,3)
Hope this helps you :)
A group of 5 friends are going to a concert and equally share the cost. If the total for the tickets is N, and each person paid less than 12 dollars, write an inequality to show the possible solutions for n, the total amount of the bill?
Answer:
They each used 60 dollars in total
Step-by-step explanation:
They each brought 12 dollars and if you multiply it by 5 that's how much they spent in total
Zhen and Justin made two different
number patterns that each started
at 0. Zhen wrote terms using the rule
"add 18." Justin wrote terms using the
rule "add 6." What is the relationship
between the two patterns?
Zhen pattern will be
[tex]0, 18, 36, 54, 72, 90,\ldots[/tex]
Justin pattern will be
[tex]0, 6, 12, 18, 24, 30,\ldots[/tex]
Since Zhen always add 18 and Justin always adds 6, and 6 is one third of 18, the n-th element of Zhen's pattern will always be three times the n-th element of Justin's pattern.
5) through (-2, -3) and (0,1)
Slope-Intercept:
Standard Form:
Answer:
Slope = 2
y-intercept = 1
x-intercept = -0.5
Standard Form ⇒ y - 2x = 1
Step-by-step explanation:
write the equation of the line through (-2 , -3) and (0,1)
The general form of the line is y = mx + c
Where m is the slope and c is the y-intercept
The slope m = (y₂ - y₁)/(x₂ - x₁) = (1 - [-3])/(0 - [-2]) = 4/2 = 2
∴ y = 2x + c
By substitution with the point (0,1) to find c
1 = 2 *0 + c
c = 1
∴ y = 2x + 1
Or y - 2x = 1 ⇒Standard Form
Also,
See the attached figure which represents the graph of the line y - 2x = 1
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut point with the y axis
We have the following points:
[tex](x_ {1}, y_ {1}): (0,1)\\(x_ {2}, y_ {2}): (-2, -3)[/tex]
We find the slope:[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-3-1} {- 2-0} = \frac {-4} {- 2} = 2[/tex]
Thus, the equation is of the form:
[tex]y = 2x + b[/tex]
We substitute a point and find b:
[tex]1 = 2 (0) + b\\b = 1[/tex]
Finally, we have:
[tex]y = 2x + 1[/tex]
On the other hand, the equation in the standard form is given by:
[tex]ax + by = c[/tex]
So, according to the slope-intersection equation we have:
[tex]2x-y = -1[/tex]
Answer:
[tex]y=2x+1\\2x-y=-1[/tex]
The table below shows an inequality and a number by which to divide both sides. Inequality Divide each side by Negative 125 greater-than-or-equal-to negative 135 Negative 5 What is the resulting true inequality? Negative 25 less-than-or-equal-to negative 27 Negative 25 greater-than-or-equal-to negative 27 25 greater-than-or-equal-to 27 25 less-than-or-equal-to 27
Answer:
[tex]25\leq 27[/tex]
Explanation:
1. Starting inequality:
[tex]-125\geq -135[/tex]
2. Divide both sides by [tex]-5[/tex]
3. Rule
When you divide an inequality by a negative number, the inequality symbol has to be changed:
> changes to << changes to >≤ changes to ≥≥ changes to ≤4. Solution
Thus, when dividing by -5 change the inequality symbol ≤ to ≤
[tex]\dfrac{-125}{-5}\leq \dfrac{-135}{-5}\\\\\\25\leq 27[/tex]
Use the rational root theorem to list all possible rational roots for each equation. Then find any actual rational roots. X^3-4x+1=0
Answer:
[tex] \pm1[/tex]
Step-by-step explanation:
The given equation is
[tex] {x}^{3} - 4x + 1 = 0[/tex]
According to the rational roots theorem, the possible rational roots are all factors of the constant term, expressed over all
factors of the leading coefficient.
The factors of the leading term, 1 are:
±1
The factors of the leading coefficient are:
±1
The possible rational roots are:
[tex] \pm1[/tex]
Justin and TJ are servers at a local restaurant. The table below shows the tips they earned.
Which student has a higher median tip for the week and by how much?
Answer:
1. For the median (as per the question posted): the median of Justin's earnings is more than the median of TJ's earnings
Difference = $3
2. For the mean (as per the requirement in the image): the mean of TJ's earnings is more than the mean of Justin's earnings
Difference = $4
Explanation:
The complete question is shown in the attached image
1. The median:
It is defined as the value found in the middle of a set of arranged data/numbersIf the set has odd number of data, then the median is simply the middle valueIf the set has even number of data, then the median is the average of the two middle valuesTo get the median, we need to first arrange the given dataa. For Justin:
He earned the following: $32, $45, $50, $33 and $50
Arranging the data: $32, $33, $45, $50 and $50
The middle value is: $45
The median is: $45
b. For TJ:
He earned the following: $58, $48, $40, $42 and $42
Arranging the data: $40, $42, $42, $48 and $58
The middle value is: $42
The median is: $42
c. Comparing the medians:
From the above, we can conclude that the median of Justin's earnings is more than the median of TJ's earnings
Difference = $45 - $42 = $3
2. The mean:
It is defined as the average value of a set of dataIt is calculated by summing the values in the set and then dividing this sum by the number of vales in the seta. For Justin:
He earned the following: $32, $45, $50, $33 and $50
Summing the data: $32 + $33 + $45 + $50 + $50 = 210
Number of values in the data= 5
The mean is: [tex]\frac{210}{5}=42[/tex]
b. For TJ:
He earned the following: $58, $48, $40, $42 and $42
Summing the data: $40 + $42 + $42 + $48 + $58 = $230
Number of values in the data: 5
The mean is: [tex]\frac{230}{5} = 46[/tex]
c. Comparing the values:
From the above, we can conclude that the mean of TJ's earnings is more than the mean of Justin's earnings
Difference = 46 - 42 = $4
Hope this helps :)
PLEASE I NEED HELP!!!
A. The perimeter of quadrilaterals are same when x=2.
B. The area of quadrilaterals are same when x=4.6
Step-by-step explanation:
A. Perimeter of the quadrilaterals must be equal.
Perimeter of square is 4a.where, a = 6Perimeter of rectangle is 2(l+b).where, l = 2 and b = (3x+4)Perimeter of square = Perimeter of rectangle
4(6) = 2(2+3x+4)
⇒ 24 = 2(3x+6)
⇒ 24 = 6x + 12
⇒ 6x = 12
⇒ x = 12/6
x = 2
For x=2, the perimeters of both the quadrilaterals are same.
B. Area of the quadrilaterals must be equal.
Area of square is a².where, a = 6.Area of rectangle is l[tex]\times[/tex]b.where, l = 2 and b = (3x+4)Area of square = Area of rectangle
(6)² = 2(3x+4)
36 = 6x+8
6x = 28
x = 28/6
x = 4.6
For x=4.6, the area of both the quadrilaterals are same.
Which of the following is defined by a line divides two sides of a triangle
proportionally, then it is parallel to the third?
O
A. Converse of the Triangle Proportionality Theorem
O
B. Triangle Midsegment Theorem
O
C. Triangle Proportionality Theorem
) D. Converse of the Triangle Midsegment Theorem
Answer: A
Step-by-step explanation:
Triangle Proportionality Theorem Converse states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side.
what is the difference between the points (-3,4) and (5,4)
Answer:
That 1st one will be in the negatine seconw one will de positive
You cut a sheet of paper along its diagonal, as shown. What is the length of the diagonal? Round your answer to the nearest tenth. HOW MANY INCHES?
Answer:
14.4
Step-by-step explanation:
Use the Pythagorean Theorem: a^2 + b^2 = c^2
Answer:
14.4
Step-by-step explanation:
90 in terms of pi please help
Answer:
90 degrees pi/2 radians
I think so but i dont know
Step-by-step explanation:
What is the mean of: 9.6, 2, 4.1, 8, 5.9, 2, 3.7, 6, 7.6?
Answer: 5.43
Step-by-step explanation:
To find the Mean, sum the values and divide by the number of values
=9.6 + 2 + 4.1 + 8 + 5.9 +2 + 3.7 + 6 + 7.6/9
= 48.9/9
=5.43
I hope this helps.
The scatter plot below shows the commute times of 25 different people and the number of stoplights they drive through on their way to work.
Which type of association best describes the relationship between the number of stoplights on a person's commute and that person's commute time?
A.
no association
B.
negative association
C.
positive and negative association
D.
positive association
Answer:
D. Positive association
Step-by-step explanation:
The line of best fit would have a positive slope
Whats is the product of 35×3/5=
Answer:
35.6
Step-by-step explanation:
35 * 3/5
35 * 5/5 + 3/5
175/5 + 3/5
178/5
35.6
Answer: 35.6
equation 5x + 3(X
= 10X - 2x - 37
Answer: there is no x
Step-by-step explanation:
5x + 3(×)= 10x -2x -37
Open the bracket
5x + 3×= 10x -2x -37
Combine like terms
8x= 8x-37
8x - 8x = -37
0 = -37