The general solution to the differential equation dy/dx = (x - 1)/(3y^2) for y > 0 is given implicitly by the equation y^3 = (x^2 - 2x + 2)/2 + C, where C is an arbitrary constant.
To find the general solution to the given differential equation, we can separate variables and integrate both sides.
Rearranging the equation, we have 3y^2 dy = (x - 1) dx.
Integrating both sides, we get ∫3y^2 dy = ∫(x - 1) dx.
The integral on the left side can be evaluated as y^3/3, and the integral on the right side is (x^2/2 - x) + K, where K is a constant of integration.
Thus, we have y^3/3 = (x^2/2 - x) + K.
Multiplying both sides by 3, we get
y^3 = (x^2 - 2x + 2)/2 + 3K.
We can combine 3K into a single constant C, so the general solution becomes y^3 = (x^2 - 2x + 2)/2 + C.
This equation represents the general solution to the given differential equation for y > 0, where C is an arbitrary constant.
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What does the factored form of a quadratic equation tell you?
What does factored form of an equation mean?Factored form, the result of combining two linear terms with a constant: or. The roots of the function are the parameters and (the x-intercepts of the graph ). The process of factoring involves reducing a quadratic function to its factored form. The polynomial can be expressed as the product of its linear elements by factoring quadratics. It is a method that enables us to locate the roots of quadratic expressions, simplify them, and solve equations. A parenthesized algebraic expression is a factored form. A factored form is essentially a sum of products of sums or a product of sums of products of sums. Any factored form can serve as a representation for any logic function, and every factored form serves as a representation for some logic function.
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the table below shows the number of cap and salmon in 3 different lakes. for each lake write the ratio of carp to salmon in the from 1:n. put the lakes in ascending order on the proportion of fish that sre salmon
carp | salmon
---------------------
lake a | 15 | 48
lake b| 35 | 7
lake c | 9 | 30
The ratio of carp to salmon for each lake is given as follows:
Lake a: 1 : 3.2.Lake b: 1 : 0.2.Lake c: 1: 3.33.
Then the ascending order on the proportion of fish that are salmon is given as follows:
Lake b, Lake c, Lake c.
How to obtain the ratios?The ratio of an amount A over an amount B is obtained applying the proportion of these amounts, that is, the division of A by B.
The ratios of carp to salmon, in the form 1:n, are obtained considering that n is the division of the number of salmon by the number of carp, hence:
Lake a: n = 48/15 = 3.2.Lake b: n = 7/35 = 0.2.Lake c: n = 30/9 = 3.33.The higher rates of salmon have the higher values of n, thus the ascending order of the proportion of fish that are salmon is given as follows:
Lake b, Lake c, Lake c.
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Rewrite the following equation in slope-intercept form. 14x − y = –15
y = 14x + 15 would be the slope-intercept form
help asap yall
What is the solution for x2 + 4x > 77?
x < –7 or x > 11
x < –11 or x > 7
–7 < x < 11
–11 < x < 7
Answer:
x <−11 or x >7
Step-by-step explanation:
Answer:
x < –11 or x > 7p
explanation:
I got it right on the test.
please answer this fast i got 5 minuets
ABC and XYZ are similar. Find the missing side length.
Hello there!
∆ABC and ∆XYZ are simular so:
[tex] \displaystyle \frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ} \\ \\ \frac{2}{10} = \frac{5}{25} = \frac{AC}{20} \\ \\ \frac{1}{5} = \frac{1}{5} = \frac{AC}{20} \\ \\ \frac{AC}{20} = \frac{1}{5} \\ \\ AC = \frac{20 \times 1}{5} = 4[/tex]
Answer: 4
Answer:
4
Step-by-step explanation:
We have to find length of AC in ΔABC
Since ΔABC is similar to ΔXYZ, the corresponding sides of ΔABC to the corresponding sides of ΔXYZ should be of similar ratio
Equivalently stated
[tex]\dfrac{AB}{XY} = \dfrac{BC}{YZ} = \dfrac{AC}{XZ}[/tex]
Plugging in known values we get
[tex]\dfrac{AB}{XY} = \dfrac{2}{10} = \dfrac{1}{5}\\\\\dfrac{BC}{YZ} = \dfrac{5}{25} = \dfrac{1}{5}\\[/tex]
Thus we see that the length of each side of ΔABC is one-fifth the length of each corresponding side of ΔXYZ.
So
[tex]AC =\dfrac{1}{5} XZ = \dfrac{1}{5} \cdot 20 = 4[/tex]
What is the area? 8 mi 6 mi
In the figure below, =m∠JKM 88°, =m∠NKM 26°, and KN bisects ∠LKM. Find m∠JKL.
The value of the missing angle m<JKL is; 46º
How to find the missing angles?Since we are told that the angle KN bisects ∠LKM then to get m<LKN, we just multiply 26° by 2 to get;
m<LKM = 26° * 2
= 52º
Now, since JKM is the total of all angle measurements, then we can say that;
88 - 52 = 36 degrees
Thus; m<JKL = 46º
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Consider the scatter plot shown. Which shows the line of best fit? Explain your reasoning.
The line of the best fit of the scatter plot is line 2
How to determine the line of best fitFrom the question, we have the following parameters that can be used in our computation:
The graph
A good line of best fit would have equal number of points on either sides
On the graph, we can see that the lines 1 and 3 divide the points on the line unevenly
Where as, the line 2 divides the scatter points approximately evenly
Hence, the line of the best fit is line 2
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Please help! Trig!!!!!!!l. Look at the image! And answer the question! Thank u!
Answer:
IF tan(theta) = -8/7 = opposite side/adjacent side, then that means that sin(theta) = -8/(sqr(64+49) = -8/sqr113 = about -0.7526
Step-by-step explanation:
the tangents are negative in the quadrant II or IV
and sines are negative in the quadrant III or IV
so i think that this angle is in quadrant IV to satisfy for the of the both requirements.
but angle 0 seems to try and mean something other than 0 degrees or 0 radians. so It probably just means theta, which is a 0 probably with a line through it
IF tan(theta) = -8/7 = opposite side/adjacent side, then sin(theta) = -8/(sqr(64+49) = -8/sqr113 = about -0.7526
I hope this helps
What is five point six as a fraction?
Answer: 28/5
Step-by-step explanation:
5.6/1x10/10= 56/10
56/10=28/5
which of the representations define a function? SELECT TWO THAT APPLY. Explain why you chose those answers, I will mark you brainliest.
Mark bought a new car. The total amount he needs to borrow is $28,716. He plans on taking out a 4-year loan at an APR of 3.12%. What is the monthly payment?
The monthly payment with given simple interest will be $673.
What is simple interest?
Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.
Simple interest formula is given as:
SI=P*R*T/100
Where SI = simple interest
P = principal
R = interest rate (in percentage)
T = time duration (in years)
In order to calculate the total amount, the following formula is used:
Amount (A) = Principal (P) + Simple Interest (SI)
Now,
Amount to Borrow=$28716
Rate=3.12%
Time=4 years
SI=28716*3.12*4/100
=$3584
Total amount to pay=28716+3584
=$32300
Hence,
monthly payment for 4 years =32300/48
monthly payment=$673
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Is 904 divisible by 9?
No , 904 is not divisible by 3 because sum of 9+0+4 =13 which is not divisible by 3 so number 904 is not divisible by 3
There are 301 numbers less than 904 divisible by 3, as per arithmetic progression.
What is an arithmetic progression?
"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."
Let, there are 'n' terms less than 904 divisible by 3.
Now, the first term divisible by 3 is(a) = 3.
The second term divisible by 3 is = 6.
Therefore, the common difference between terms divisible by 3 is(d)
The last term that is less than 904 and divisible by 3 is() 903.
Now, if we compare it with arithmetic progression, then:
The required number is 301.
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Please help I need the answers ASAP!
Answer:
Refer to the step-by-step
Step-by-step explanation:
Since ∠1 and ∠2 are alternate exterior angles, m∠2=108°
How do you tell if a graph is exponential growth or decay?
To tell if a log graph is a growth or decaying, look at the slope of the line. If the slope is positive, then it is growth; if the slope is negative, then it is decay.
A positive slope indicates that the value is increasing over time, while a negative slope indicates that the value is decreasing over time. To find the slope, take two points on the line and calculate the change in the y-value divided by the change in the x-value.
If the answer is positive, the graph is growth; if the answer is negative, the graph is decay. Additionally, you can look at the y-intercept of the graph, which is the value where the line meets the y-axis. If the y-intercept is positive, the graph is growth; if the y-intercept is negative, the graph is decay.
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Malik uses an app on his phone to track how far he rides his bike. Yesterday, he biked a new trail in a total of 57.5 minutes, including a 2.5-minute water break. The app notified Malik that he rode 10 miles. What was Malik's average pace while biking?
The average pace of Malik is 0.182 mile per minute.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Distance Malik rode on a trail = 10 miles
Malik biked a new trail in a total of 57.5 minutes.
But he took 2.5 minutes as water break.
Total time Malik took to cover the distance = 57.5 minutes - 2.5 minutes
= 55 minutes
We have to calculate the average pace of Malik which is actually the speed.
Speed = Distance / Time
= 10 miles / 55 minutes
= 0.182 mile per minute
Hence Malik rides in an average pace of 0.182 mile per minute.
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Question 3
Suppose you take a trip that covers 147.4 km and takes 8.6 hours.
What is your average speed (km/h)?
Question 4
1 pts
1 pts
Answer:
17.13953 mph
I just did it these ways with a speed calculator
Step-by-step explanation:
diagnosis codes are required to explain the ________ for the services provided.
Answer:
medical necessity
Garrett went to Good Buys where all prices are discounted 15%. He buys a vintage Waring blender, after the 15% discount, for $42. What is the original price of the blender before the discount. Round your answer to the nearest hundredths.
The original price of the blender before the discount is $49.41.
How to calculate the original price of the blenderWe shall represent the original price of the blender with the letter x so that we use $x to evaluate for the original price before the discount price as follows:
x - 15x/100 = $42 {simply the left hand expression to a single fraction}
(100x - 15x)/100 = $42 {simply the terms in the bracket}
$85x/100 = $42
$85x = $4200 {cross multiplication}
$85x/$85 = $4200/$85 {divide through by $85}
x = $49.41
Therefore, the original price of the blender before the discount is $49.41
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Can you explain this too me please?
The situation regarding the experimental probability is described as follows:
The probability that she makes a shot is of 62.5% = 5/8. Use whole numbers from 1 to 8, with 1-5 representing shots that she makes, and 6-8 representing the shots that she misses. For each trial, generate 10 random numbers. Count the number of trials in which the numbers 1 - 5 appears 3 or more times. Divide the number of trials in which she made at least 3 shots by the total number of trials.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The theoretical probability of making a shot in this problem is given as follows:
62.5%.
The equivalent fraction is given as follows:
5/8.
Hence, to obtain the experimental probability, we need to design an experiment for which there are eight possibilites, with five of them composing a success and three of them composing a failure.
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On a necklace of 150 beads 75 beads are glass and 78 are ceramic what percent of beads are glass
Answer:
Doesn't make sense but with the information given. To find the percentage of glass beads on the necklace, you need to divide the number of glass beads by the total number of beads and multiply by 100.
You can use the formula:
percent = (number of glass beads / total number of beads) x 100
In this case:
percent = (75 / 150) x 100 = 0.5 x 100 = 50
So, 50% of the beads on the necklace are glass.
when f(x) = 6x² - 2x - 5, evaluate f(-2)
Answer:
23
Step-by-step explanation:
Given Information:
f(x) = 6x² - 2x - 5If we have to evaluate f(-2), we can consider that f(x) = f(-2) = 6x²- 2x - 5.
So, if f(x) = f(-2), then we have the following solution: x = -2.Now, we can substitute the solution into the quadratic equation and simplify it to its simplest possible form using the solution (x = -2).
⇒ f(-2) = 6x² - 2x - 5 ⇒ f(-2) = 6(-2)² - 2(-2) - 5 ⇒ f(-2) = 6(-2)(-2) - 2(-2) - 5 ⇒ f(-2) = 6(4) + 2(2) - 5 ⇒ f(-2) = 24 + 4 - 5 ⇒ f(-2) = 24 - 1 = 23Therefore, the evaluated form for f(-2) is 23.
Jake has a shipping box with the following dimensions.
length: 12 inches
width: 4 inches
height: 8 inches
Havana has a shipping box similar to Jake's box, but each dimension is half as long.
How many times greater is the volume of Jake's box than Havana's box?
Jake's box is 8 times greater than Havana's box.
What is the volume of the cuboid?The volume of a cuboid is found by multiplying the length by the breadth by the height.
Given here: Two boxes Jake's and Havana's with Havana's box with dimensions half of Jake's
Therefore the ratio of the volume is = 12× 4 ×8 /6× 2× 4
=8
Hence, ake's box is 8 times greater than Havana's box.
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Find the area of the floor of a quare room in quare meter whoe each ide i 800 cm
The area of the floor of a square room in square meter whose each side is 800 cm is 640000 cm ^ 2.
The area of a square or square shaped figures is:
area = side x side or (side) ^2
The length of the side of the floor of the given square room is:
800 cm
Therefore, area of the floor of the given square room is:
800 cm x 800 cm = 640000 cm ^ 2.
Thus, the area of the floor of the given square room in square meter whose each side is 800 cm is 640000 cm ^ 2.
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Help
Directions: Identify the binomial factors of the following trinomials.
1. x2 + 9x + 20
2. x2 + 7x + 12
3. x2 + 8x + 15
4. x2 + 7x + 12
5. x2 + 11x + 10
6. x2 + 7x + 6
7. x2 + 5x + 4
8. x2 + 10x + 21
9. x2 + 10x + 16
10. x2 + 10x + 9
11. x2 + 12x + 20
12. x2 + 15x + 14
13. x2 + 13x + 42
14. x2 + 9x + 18
15. x2 + 16x + 60
Answer:
1. x= -1 & x= -13
2. x= -3 & x= -4
3. x= -3 & x= -5
4. x= -6 & x= -2
5. x= -5 & x= -2
8. x= -7 & x= -3
9. x= -8 & x= -2
10. x= -3 & x= -3
11. x= -5 & x= -4
12. x= -2 & x= -2
13. x= -6 & x= -7
14. x= -6 & x= -3
15. x= -10 & x= -7
Step-by-step explanation:
hope this help :)
Under a dilation centered at the origin, the point (-4,3) has image at (8, -6).
What is the scale factor of the dilation?
Answer:
The scale factor is 3. Step-by-step
Step-by-step explanation:
is 333 is in the sequence 2,5,8,11,14...why
i need some help. please help me
Answer:
HK and GJ is the diameter of circle L.
Step-by-step explanation:
Answer:
Either GJ or HK
Step-by-step explanation:
Im not sure if im reading ot correctly bit ye diameter is the full line in the moddle and they both are so it's probably those 2
Jesse bought 24 gallons of gas for $45.58. What was the price per gallon?
Answer:
$1.899
Step-by-step explanation:
Divide $45.58 by 24 for the unit price of each gallon
Answer: Approx. $1.899
Step-by-step explanation:
let the price per gallons be G
24G = 45.58
G = 45.58/24 = 1.899