Find the general solution of the differential equation. (enter your solution as an equation.) (8 + x)y' = 3y
Answers
Final answer:
The general solution to the differential equation (8 + x)y' = 3y is y = C(8+x)³, where C is a constant and can be found by integrating and rearranging the separated variables.
Explanation:
To find the general solution of the differential equation (8 + x)y' = 3y, we can separate variables and integrate both sides. First, we divide both sides by (8 + x) and then by y to get [tex]\frac{ y'}{y} = \frac{3}{8 + x}[/tex]
Next, we integrate both sides:
Integrate LHS: [tex]\int \frac{dy}{y} = ln|y| + C_1[/tex]
Integrate RHS: [tex]\int \frac{3dx}{8 + x} = 3ln|8+x| + C_2[/tex]
Now, we can combine the two constants (C₁ and C₂) into a single constant C by writing C = C₂ - C₁. So our solution looks like ln|y| = 3ln|8+x| + C. We can exponentiate both sides to solve for y:
[tex]y = e^{3ln|8+x|+C}[/tex]
Remembering that [tex]e^{ln|a|} = a[/tex], we can simplify this to:
y = C(8+x)³ where C is a constant.
This is the general solution to the differential equation.
Related Questions
Mama Mia restaurant used start fraction, 1, divided by, 2, end fraction of their mozzarella cheese making pizza and the remaining 646464 ounces making pasta.
How many pounds of mozzarella cheese did Mama Mia start with?
Answers
Mama Mia restaurant used start fraction, 1, divided by, 2, end fraction of their mozzarella cheese making pizza and the remaining 64 ounces making pasta.
How many pounds of mozzarella cheese did Mama Mia start with?
Let
x---------------> total ounces of mozzarella
we know that
making pizza-----------> (1/2)*x------> x/2
therefore
making pasta-------> [x-x/2]--------> (2x-x)/2-----> x/2
making pizza=making pasta=x/2
(x/2)=64---------------> x=64*2-----------> x=128 ounces
remember that
1 ounces----------------> 0.0625 pounds
then
128 ounces*0.0625=8 pounds
the answer is 8 pounds
write an expression that is equivalent to 5 cubed
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5^3 is three 5s multiplied together.
Can you share 35 equally?
Answers
Meis mothers is 4 times as old as mei. Mei’s mother is twice as old as mei’s mother.the sum of the three ages of 117. How old is mei, her mother, and her grandmother?
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Final answer:
Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old, determined by defining variables for their ages and solving the equation based on their age relationships and the given total sum of their ages.
Explanation:
To solve the problem regarding the ages of Mei, her mother, and her grandmother, we can use a system of equations based on the information given. Let's define Mei's age as m, her mother's age as 4m (since her mother is 4 times Mei's age), and her grandmother's age as 8m (since the grandmother is twice as old as Mei's mother).
According to the problem, the sum of their ages is 117 years:
m + 4m + 8m = 117
Simplifying this equation gives us:
13m = 117
Next, we divide both sides by 13 to find m:
m = 117 / 13
m = 9
Now that we have Mei's age, we can easily calculate her mother's and grandmother's ages:
Mei's mother: 4m = 4(9) = 36 years oldMei's grandmother: 8m = 8(9) = 72 years oldTherefore, Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old.
A pound of popcorn is popped for a class party. The popped corn is put into small popcorn boxes that each hold 130 popped kernels. There are 1,450 kernels in a pound of unpopped popcorn. If all the boxes are filled except for the last box, how many boxes are needed and how many popped kernels are in the last box? Please explain how you get the answer
Answers
1450/130 is 11.15 so You round up and need 12 boxes (because you can’t have .15 of a box) so you get the 11 boxes and multiply by how much it can hold (130) and get 1430 which is 20 short of 1450 so 20 would be in the last box .
12 boxes are needed in all.
Last box will contain only 20 kernels.
Step-by-step explanation:Given is :
The popped corn is put into small popcorn boxes that each hold 130 popped kernels.
There are 1450 kernels in a pound of un popped popcorn.
If all the boxes are filled except for the last box, then how many boxes are needed?
Number of boxes = Total number of kernels/Number of kernel in each box
=> [tex]\frac{1450}{130}= 11.15[/tex]
Therefore, a total of 11+1 = 12 boxes are needed as 11.15 is more than 11.
And the last box will contain = [tex]1450-1430=20[/tex] kernels.
Therefore, the last box will have 20 kernels.
(30 points)
What are genes?
A. The ovservable characteristic.
B. The expressed trait.
C. The basic unit of inheritance.
D. The measurable factor.
Answers
Genes can be inherited by offspring from parent. They can determine a characteristic/trait, but usually many genes influence each. Genes can't be "measured" with a unit.
1 What is the solution to the system of equations?
3x-4y=16
2x+3y=5
A (–4, 1)
B(4, –1)
C(–4, –1)
D (4, 1)
2 what is the solution to the system of equations?
7x-2y=-24
5x+5y=15
A (2, –5)
B (–2, 5)
C (–2, –5)
D (2, 5)
Answers
2. The answer is B (-2, 5)
Answer:
The answer for the first question would be B: (4, –1)
Step-by-step explanation:
Imagine that you are pouring cement into cinder blocks to build a very sturdy wall. Each cinder block is 1.3 feet long, 0.67 feet high, and 0.67 feet wide. If 1 bag of cement is equivalent to 5 cubic feet, what is the number of bags of cement that you will need to fill the entire wall? Show the work
Answers
To find out how many cement bags are needed, calculate the volume of one cinder block and see how many such blocks fit in a cement bag. Then, divide the total number of cinder blocks by the number of blocks one bag can fill and round up to the nearest whole number.
To determine the number of cement bags needed to fill a cinder block wall with the given measurements, first calculate the volume of one cinder block. Then, figure out how many cinder blocks fit into one bag of cement.
The volume of one cinder block is:
V = length × height × width
V = 1.3 ft × 0.67 ft × 0.67 ft
V [tex]\approx[/tex] 0.5809 cubic feet
Now, since one bag of cement is equivalent to 5 cubic feet, determine how many cinder blocks one bag can fill:
Number of blocks per bag = 5 cubic feet / 0.5809 cubic feet per block
Number of blocks per bag [tex]\approx[/tex] 8.61 blocks
We need the total number of cinder blocks for the entire wall. Assuming we know the total wall dimensions, let's say we have a total of 100 blocks (for example purposes).
Total number of bags = Total number of blocks / Number of blocks per bag
Total number of bags = 100 / 8.61
Total number of bags [tex]\approx[/tex] 11.62
Since you can't buy a fraction of a bag, you would need to round up to the next whole number, so you would need 12 bags of cement to fill the wall.
X^3-64=0
Solve the equation
Answers
We want to solve for x. Start by getting x by itself on one side.
We can do this by adding 64 to both sides of the equation.
x^3 = 64
Now, to get rid of the 3rd power that x is raised to, we can raise both sides to the 1/3 power
(x^3)^1/3 = 64^1/3
(x^3)^1/3 is the same as x
So x = 64^(1/3) and 64^(1/3) = 4
So x = 4 :)
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The table below shows the number of marbles of different colors in a bag: Color of Marbles Number of Marbles Pink 5 Blue 2 Green 3 Ursula draws a marble from the bag randomly without looking. She then draws another marble from the bag without replacing the first one. Which expression shows the probability of drawing green marbles in both the trials? 3 over 10 multiplied by 2 over 9 3 over 10 multiplied by 2 over 10 3 over 10 added to 2 over 9 3 over 10 added to 2 over 10
Answers
Answer:
3/10 * 2/9
Step-by-step explanation:
the ratio of cookies to glasses of milk is 3:1 if there are 25 glasses of milk how many cookies are there
Answers
For the graph x = -3 find the slope of a line that is parallel to it.
-3
-1/3
0
undefined
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the slope of the line that is parallel to x=-3 is classified as undefined.
let's check the answer
1) take any two points of the line x = -3
point A (-3,0) point B (-3,5)
2) find the slope of the line x=-3
m=(5-0)/(-3+3)=5/0----------> is undefined
the answer is the option undefined
Answer:
undefined
Step-by-step explanation:
A square is ____ a parallelogram. always sometimes never submit
Answers
You bought the meat for Saturdays cookout. A package of hot dogs cost $1.60 and a package of hamburgers cost $5. You bought a total of 8 packages of meat and you spent $23. How many packages of hamburger meat did you buy?
Answers
The number of hamburger meat he bought is 3.
How to find the number of hamburger meat bought?A package of hot dogs cost $1.60 and a package of hamburgers cost $5.
You bought a total of 8 packages of meat and you spent $23.
Therefore,
let
x = number of package of hot dogs
y = number of package of hamburger
Hence,
x + y = 8
1.60x + 5y = 23
multiply equation(i) by 5
5x + 5y = 40
1.60x + 5y = 23
Subtract equation(ii) from equation(i)
3.4x = 17
x = 17 / 3.4
x = 5
y = 8 - 5
y = 3
Therefore, the number of hamburger meat he bought is 3.
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If given f(x) = x + 4 and g(x) = –2x2 + 3x – 1, what is (f – g)(x)?
A.
(f – g)(x) = –2x2 + 4x – 3
B.
(f – g)(x) = –2x2 – 2x + 5
C.
(f – g)(x) = 2x2 + 2x + 5
D.
(f – g)(x) = 2x2 – 2x + 5
Answers
5a - {3b - 5[a - (b + -4a)]}
Answers
Start at the very right and keep on removing brackets and collecting like terms.
5a - {3b - 5[a - (b - 4a)]} I just changed the sign on the right bracket.
5a - {3b - 5[a - b + 4a]}
5a - {3b - 5[5a - b]} Now deal with []. You are still on the right.
5a - {3b - 25a + 5b}
5a - {8b - 25a} Finally remove {}
5a - 8b + 25a
30a - 8b
If you can solve another like this, you are well on your way to being good in computer science.
5 is one-fourth of a number c.
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The value of number c is 20
5 as one-fourth of a number c is represented using the following equation
[tex]5 = \frac 14 \times c[/tex]Multiply both sides of the above equation by 4
[tex]4\times 5 = \frac 14 \times c \times 4[/tex]Evaluate the products
[tex]20 = c[/tex]Rewrite the above equation as
[tex]c = 20[/tex]Hence, the value of number c is 20
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Answers
5x + 25 < 85
5x < 85 - 25
5x < 60
x < 60 ÷ 5
x < 12
x < 12
Explanation:
To solve this, we will need to isolate the x on one side of the inequality as follows:
5(x+5) < 85
x+5 < 85/5
x+5 < 17
x+5-5 < 17-5
x < 12
Hope this helps :)
The formula for the area, A, of a circle is A = πr2 , where r is the circle’s radius, and the formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter. Which statement is correct?
Answers
Answer:
The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Step-by-step explanation:
For a circulus with radius r, we have that:
The area of the circulus is:
[tex]A = \pi r^{2}[/tex]
That is, the radius is squared, not multiplied by 2, so the first statement is incorrect.
The circumference of the circulus is:
The derivative of the area, so
[tex]C = 2\pi r[/tex]
However
The radius if half the diameter. So
[tex]C = 2\pi \frac{d}{2}[/tex]
[tex]C = \pi d[/tex]
So the correct statement is:
The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Both statements are correct. The formula for the area of a circle is A = πr², where r is the radius, and the formula for the circumference of a circle is C = πd, where d is the diameter.
The formula for the area of a circle is given by A = πr², where A represents the area and r represents the radius of the circle. In this formula, the radius is squared and then multiplied by the mathematical constant π (pi) to calculate the area enclosed by the circle.
On the other hand, the formula for the circumference of a circle is given by C = πd, where C represents the circumference and d represents the diameter of the circle. In this formula, the diameter is multiplied by the mathematical constant π to calculate the total distance around the circle.
These formulas are derived from the properties of circles. The radius is the distance from the center of the circle to any point on its edge, while the diameter is the distance across the circle passing through its center. The circumference represents the boundary or perimeter of the circle, while the area represents the space enclosed by the circle.
It's important to note that the relationship between the radius and diameter is given by the equation d = 2r, where d represents the diameter and r represents the radius. This relationship allows us to interchangeably use the radius or diameter in the formulas for the area and circumference of a circle.
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Complete Question:
1. The formula for the area, A, of a circle is A = [tex]\pi r^2[/tex] , where r is the circle’s radius.
2. The formula for the circumference, C, of a circle is C = πd , where d is the circle’s diameter.
Which of the above statements is correct?
Given: segment AB || segment DE, C is the midpoint of segment DB. Prove: ΔACB ≅ ΔECD Fill in the missing reason for the proof. A) definition of midpoint B) vertical angles are congruent C) all right angles are congruent D) supplementary angles are congruent
Answers
Answer:
Given: Segment AB || segment DE, C is the midpoint of segment DB.
Prove: ΔA CB ≅ ΔE CD
Proof: In ΔA CB and ΔE CD
C is the Mid point of B D.
BC=C D→ definition of midpoint
∠A CB= ∠ EC D→→vertical angles are congruent
∠BAC=∠DEC→→[AB║DE,so alternate angles are equal]
→→ΔA CB ≅ ΔE CD[A AS or A SA]
Option B: vertical angles are congruent
Answer:
The answer is A) Definition of midpoint
Step-by-step explanation:
Answer B is wrong. I just did the test
I need help I would really thank wheeler answers this for me
Answers
a. |-15| + |-26|
15 + 26
41
b. -|-40|
-40
c. |0.5| + |-1 1/2|
0.5 + 1 1/2
0.5 = 1/2
1/2 + 1 1/2
2
Describe the vector as an ordered pair. Round the coordinates to the nearest tenth. The diagram is not drawn to scale.
Answers
ANSWER
[tex]
\angle19.4,50.4 \: > [/tex]
EXPLANATION
The given vector has magnitude 54 units.
The vector is making an angle of 69° with the x-axis.
The horizontal component of the vector is
[tex] = 54 \cos(69) [/tex]
[tex] = 19.35[/tex]
To the nearest tenth, we have,
[tex] = 19.4[/tex]
The vertical component is
[tex] = 54 \sin(69 \degree) [/tex]
[tex] = 50.41[/tex]
[tex] = 50.4[/tex]
to the nearest tenth.
The required vector is
[tex]
\angle19.4,50.4 \: > [/tex]
The components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.
What is a vector?A vector is a quantity that has both magnitude and direction. It has two components a vertical component(Sine) and a horizontal component(Cosine). The component of a vector can be written as,
Vertical component, [tex]V_y = \vec V\ Sin(\theta)[/tex]
Horizontal component, [tex]V_x = \vec V\ Cos(\theta)[/tex]
We know that a vector can be divided into two components a horizontal component and a vertical component, therefore, the vector components can be written as,
[tex]V_y = \vec V Sin\theta\\\\V_y = 54\ Sin(69^o)\\\\V_y = 50.4133[/tex]
[tex]V_x = \vec V Cos\theta\\\\V_x = 54\ Cos(69^o)\\\\V_x = 19.3519[/tex]
Hence, the components of the vector with magnitude 54 and the angle of 69° from the horizontal can be written as <19.3519, 50.4133>.
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Angles C and D are complementary. The measure of angle D is 25 degrees greater than the measure of angle C. What is the measure of each angle?
Answers
Angle C measures 32.5 degrees and angle D measures 57.5 degrees.
Explanation:Let's represent the measure of angle C as x. Angle D is 25 degrees greater than angle C, so we can represent the measure of angle D as x + 25.
We know that angles C and D are complementary, so their measures must add up to 90 degrees.
Therefore, we can set up the equation:
x + (x + 25) = 90
Combining like terms, we get:
2x + 25 = 90
Subtracting 25 from both sides, we get:
2x = 65
Dividing both sides by 2, we get:
x = 32.5
So, the measure of angle C is 32.5 degrees, and the measure of angle D is 57.5 degrees.
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What is the better estimate for the height of a desk,1 meter or 1 kilometer
Answers
The best estimate for the height of a desk is a meter. One kilometer is equal to 1,000 metres. A desk is obviously not 1,000 metres high because, well, our roofs wouldn't be that high!
Asha and Jamal are selling plants to raise money for their soccer team. They started out with 45 plants. They sold some plants and now they have 21 plants left. Asha wrote the equation 45 – p = 21 to find the number of plants they sold. Jamal wrote the equation 21 + p = 45 to find the number of plants sold. Whose equation will find the number of plants sold? A. Asha’s equation. B. Jamal’s equation. C. Both equations will find the correct solution. D. Neither equation will find the correct solution.
Answers
C. Both equations will find the correct solution.
EXPLANATION
It was given in the question that, Asha and Jamal started with 45 plants.
We were told that, they sold some plants and now they have 21 plants left.
Let
[tex]p[/tex]
represent the number of plants sold.
Then when we add the number of plants sold and the number left, we should get 45.
This implies that,
[tex]21 + p = 45[/tex]
This is Jamal's equation.
On the other hand, if we subtract the number of plants sold from the total number of plants, we should get 21. Thus,
[tex]45 - p = 21[/tex]
This is Asha's equation.
The two equations are therefore equivalent.
They will give the same solution.
The correct answer is C.
Answer:
C. Both equations will find the correct solution.
Step-by-step explanation:
What is a counterexample for the conjecture? Any number that is divisible by four is also divisible by eight
Answers
To find other examples, add 8 to 12 to get 20. Then add on 8 more to get 28. This pattern continues on forever.
Example: y = -2x and y = x + 3
does the point (0,4) make either equation true? substitute it in and find out
Answers
x = 0
y = 4
Substitute x with 0 in the equations and evaluate if it would make 4 as the result of y.
First equation
y = -2x
y = -2 × 0
y = 0
The result is not 4, therefore point (0,4) doesn't make the first equation true.
Second equation
y = x + 3
y = 0 + 3
y = 3
The result is not 4, therefore (0,4) doesn't make the second equation true.
The first class had a kids in it, the second had b kids in it, and the third class had c kids in it. Kids from all three classes were equally divided between two buses. How many kids were on each bus?
Answers
(a*b*c)/2
A class contains 3 female and 9 male students. Find the probability that a student chosen at random is a male, and then a second student chosen at random from the remaining students is also male.
a). 9/16
b). none
c). 1/2
d).6/11
e).3/4
HELPP today plzzz!!!
Answers
9 are male
1st = 9/12 = 3/4
2nd = 8/11
3/4 * 8/11 = 6/11
Answer = D) 6/11
The probability that two student chosen at random is a male is 6/11.
What is the Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Here, Class contains 3 females and 9 males it means total 12 students.
Probability for having 1st student male = 9/12 = 3/4
Probability for having 2nd student is also male = 8/11
Overall Probability = [tex]\frac{3}{4} X \frac{8}{11}[/tex]
= 6/11
Thus, the probability that two student chosen at random is a male is 6/11.
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Elliot buys a 5 pound package of ground beef for 12.50. At the same unit price, how much would 8 pounds of ground beef cost
Answers
So 8*2.5=20
It should be 20 dollars
2.5 x 8 = 20
8 pounds of ground beef would cost $20.