Answers
Hello!
This is a problem about the general solution of a differential equation.
What we can first do here is separate the variables so that we have the same variable for each side (ex. [tex]dy[/tex] with the [tex]y[/tex] term and [tex]dx[/tex] with the [tex]x[/tex] term).
[tex]\frac{dy}{dx}=\frac{x-1}{3y^2}[/tex]
[tex]3y^2dy=x-1dx[/tex]
Then, we can integrate using the power rule to get rid of the differentiating terms, remember to add the constant of integration, C, to at least one side of the resulting equation.
[tex]y^3=\frac{1}{2}x^2-x+C[/tex]
Then here, we just solve for [tex]y[/tex] and we have our general solution.
[tex]y=\sqrt[3]{\frac{1}{2}x^2-x+C}[/tex]
We can see that answer choice D has an equivalent equation, so answer choice D is the correct answer.
Hope this helps!
Related Questions
since the great drought left the soil completely useless, the people of that country were forced to______ food from other countries
A. export
B. import
C. report on
D. sell
What is the answer?
Answers
Answer:
B import food from other countries
HELP PLS DUE NOW BRAINLIEST AND A THANKS
Answers
Answer:
D
Step-by-step explanation:
The researcher did no prediction or any (possible)
Hope this helps :)
Helpppsppspspspspsp plssss
Answers
Answer: About 804.25
Step-by-step explanation:
Do the inverse of the circumference formula and then take the radius and put it into the formula for the area of a circle
ASAP PLEASE HELP
WILL MARK BRAINLIEST
Answers
Answer:
A, B, and C All have four sides, and they all have opposite sides that are equal. B and C have right angels. A has angels on opposite side that are the same
Step-by-step explanation:
Evaluate the math problem
Answers
Answer:
b. 25
Step-by-step explanation:
The square root cancels out
and you divide only 100 and 4
Answer:
5 or 25
Step-by-step explanation:
I first got the 25 but when I tried a different formula to make sure it's correct I got 5.
Height of 10th grade boys is normally distributed with a mean of 63.5 in. and a standard
deviation of 2.9 in.
The area greater than the Z-score is the probability that a randomly selected 14-year
old boy exceeds 70 in.
What is the probability that a randomly selected 10th grade boy exceeds 70 in.?
Answers
Answer:
P(Z>2.24) = P(70<X<1e99) = 1.25%
Step-by-step explanation:
Calculate Z-score:
Z=(x-μ)/σ
Z=(70-63.5)/2.9
Z=6.5/2.9
Z=2.24
Find area greater than Z-score:
P(Z>2.24) = P(70<X<1e99) = normalcdf(70,1e99,63.5,2.9) = 0.0125
So the probability that a randomly selected 10th-grade boy exceeds 70 inches is a 1.25% chance.
Answer this I’ll give brainalist + points, please help!
Answers
Answer:
B
Step-by-step explanation:
the mean of A
= (84 + 84 + 85 + 86) ÷ 4
= 339 ÷ 4
= 84.75
the median of A
= (84 + 85) ÷2
= 169 ÷ 2
= 84.5
84.75 > 84.5
the mean of B
= (74 + 79 + 82 + 87) ÷ 4
= 332 ÷ 4
= 80.5
the median of B
= (79 + 82) ÷2
= 161 ÷ 2
= 80.5
80.5 = 80.5
the mean = the median
the mean of C
= (63 + 66 + 67 + 68) ÷ 4
= 264 ÷ 4
= 66
the median of C
= (66 + 67) ÷2
= 133 ÷ 2
= 66.5
66 < 66.5
the mean of D
= (14 + 16 + 18 + 19) ÷ 4
= 67 ÷ 4
= 16.75
the median of D
= (16 + 18) ÷2
= 34 ÷ 2
= 17
16.75 > 17
Find each missing measure
PLS HURRY WILL GIVE BRANLIEST. DON'T RESPOND WITH LINKS
Answers
Answer: 1 = 90 2=58 3=90 6=58 7=8
Step-by-step explanation:
I don’t know what 4 and 5 are
PLEASE SOMEONE HELP ME WITH THE MATH!!! It's on the picture!!!
Answers
N is to the left of the zero which means it is a negative number.
P is the the right of zero which means it is a positive number.
A negative number is less than a positive number, so the answer would be:
The number with the least value is N
The number with the greatest value is P
Which statement best explains the importance of examining multiple perspectives about an event?
It reinforces a specific opinion about the event.
It determines which accounts are biased about the event.
It provides different and sometimes opposing viewpoints about an event.
It requires the use of both primary and secondary sources to learn about the event.
Answers
Answer:
It provides different and sometimes opposing viewpoints about an event.
What is the area of the triangle?
Answers
Answer:
45
Step-by-step explanation:
9x10/2=45
Find the surface area of the square pyramid
Answers
What is the estimated volume of a figure with a length of 3cm, a height of 4cm, and a width that is approximately 2 times the height?
Answers
Step-by-step explanation:
Given
length(l)=3cm
height(h)=4cm
breath or width (b)=2×h=2×4=8cm
now it is a cuboid
volume of cuboid=l×b×h=3×8×4=96cm³
Answer:32,cm3
Step-by-step explanation:
How many degrees and in what direction was the figure rotated?
90 degrees counterclockwise
180 degrees
90 degrees clockwise
Answers
Answer: 90 degrees clockwise
Step-by-step explanation:
What is the value of x in the figure qor =65 and dot =70 ? Not at is a straight line
Answers
Answer:
its 65
Step-by-step explanation:
if you add it up u would see
f(x) = 5x^2 + 9x – 4
g(x) = – 8x^2 – 3x – 4
Find (f + g)(x).
Answers
Answer:
(f + g)(x) = – 3x^2 + 5x - 8
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
= 5x^2 + 9x – 4 + (– 8x^2 – 3x – 4)
= 5x^2 + 9x – 4 – 8x^2 – 3x – 4
Combine
= – 3x^2 + 5x - 8
The sum of the given functions is defined as the expression (f + g)(x) which is equal to -3x² + 6x – 8.
Use the concept of quadratic function defined as:
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:
ax² + bx + c = 0
The given functions are:
f(x) = 5x² + 9x – 4
g(x) = – 8x² – 3x – 4
Since (f + g)(x) = f(x) + g(x)
Then put the functions,
(f + g)(x) = (5x² + 9x – 4) + ( – 8x² – 3x – 4)
Rearranging like terms,
(f + g)(x) = 5x²– 8x² + 9x – 3x – 4 – 4
Simplifying it,
(f + g)(x) = -3x² + 6x – 8
Hence,
The expression for (f + g)(x) is -3x² + 6x – 8.
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How come the tutors don't work??
Answers
Answer:
What do you mean? If you are talking about the Community not always answering Questions well that means your they don't know the right Answer
the Mods are Annoying and very skeptic of the Guidelines of Brainly.
What is a equivalent expression to 4(x+12)-3y
Answers
you can just distribute the 4 to x+12
There are 6 balls in a bucket and 3 of them
are white. If you choose a ball at random,
what is the probability that it will not be
white?
Answers
Answer:
[tex] \frac{3}{6} [/tex]
What is the constant rate of change shown in the table?
2
4
6
8
Answers
(The y intercept is 20 so subtract 20 from the y and divide by 2 to get your x)
Answer:
2
Step-by-step explanation:
Since with every 10 seconds, the distance increase by 20 meters
hence, 20/10 = 2
A book has been discounted by 30%. It is on sale for $22.40. Find the original price.
Answers
EXPLANATION:
Do 22.40 • 0.30 to get 6.72
Then take 6.72 and add it to 22.40
This gives you the original price, $29.12
The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the annual income of a typical family with college-age children (Money, April 2012). At private colleges, the average annual cost is equal to about 60% of the typical family's income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges
52.8 30.6 43.2 45.8 33.3
33.3 50.5 44.0 42.0 37.8
Public Colleges
20.3 22.8 28.2 18.5 15.6 25.6
24.1 14.4 28.5 21.8 22.0 25.8
Required:
a. Compute the sample mean and sample standard deviation for private and public colleges.
b. What is the point estimate of the difference between the two population means?
c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.
Answers
Answer:
(a)
[tex]\bar x_1 =41.33[/tex] [tex]\sigma_1 = 7.48[/tex]
[tex]\bar x_2 =22.3[/tex] [tex]\sigma_2 = 4.53[/tex]
(b)
[tex]d = 19.03[/tex]
(c)
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
Step-by-step explanation:
Given
[tex]n_1 = 10\\ n_2 = 12[/tex]
And the accompanying data for private (1) and public (2) colleges
Solving (a): The sample mean and sample standard deviations
Private College
Calculating sample mean
This is calculated as:
[tex]\bar x_i = \frac{\sum x_i}{n_i}[/tex]
[tex]\bar x_1 =\frac{52.8+30.6+43.2 +45.8 +33.3+33.3 +50.5 +44.0 +42.0 +37.8}{10}[/tex]
[tex]\bar x_1 =\frac{413.3}{10}[/tex]
[tex]\bar x_1 =41.33[/tex]
Calculating sample standard deviation
This is calculated as:
[tex]\sigma_i = \sqrt\frac{\sum(x_i - \bar x_i)}{n_i-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{(52.8-41.33)^2+(30.6-41.33)^2+.........+(37.8-41.33)^2}{10-1}[/tex]
[tex]\sigma_1 = \sqrt\frac{503.261}{9}[/tex]
[tex]\sigma_1 = \sqrt{55.9178888889[/tex]
[tex]\sigma_1 = 7.4778264816[/tex]
[tex]\sigma_1 = 7.48[/tex] -- approximated
Public College
Calculating sample mean
[tex]\bar x_2 =\frac{20.3 +22.8 +28.2 +18.5 +15.6 +25.6+ 24.1 +14.4 +28.5 +21.8 +22.0 +25.8}{12}[/tex]
[tex]\bar x_2 =\frac{267.6}{12}[/tex]
[tex]\bar x_2 =22.3[/tex]
Calculating sample standard deviation
[tex]\sigma_2 = \sqrt\frac{(20.3 -22.3)^2+(22.8 -22.3)^2+(28.2 -22.3)^2+(18.5 -22.3)^2+(15.6 -22.3)^2+................+(25.8-22.3)^2}{12-1}[/tex][tex]\sigma_2 = \sqrt\frac{225.96}{11}[/tex]
[tex]\sigma_2 = \sqrt{20.5418181818[/tex]
[tex]\sigma_2 = 4.532308262[/tex]
[tex]\sigma_2 = 4.53[/tex] -- approximated
Solving (b): Point estimate of the difference between the two population means
This is calculated as:
[tex]d = \bar x_1 - \bar x_2[/tex]
[tex]d = 41.33 - 22.3[/tex]
[tex]d = 19.03[/tex]
Solving (c): 95% confidence interval
First, calculate the degrees of freedom:
[tex]df = \frac{(\sigma_1^2/n_1 + \sigma_2^2/n_2)^2}{\frac{(\sigma_1^2/n_1)^2}{n_1 - 1} + \frac{(\sigma_2^2/n_2)^2}{n_2 - 1}}[/tex]
[tex]df = \frac{(7.48^2/10 + 4.53^2/12)^2}{\frac{(7.48^2/10)^2}{10 - 1} + \frac{(4.53^2/12)^2}{12 - 1}}[/tex]
[tex]df = \frac{53.3647}{31.3045/9 + 2.9244/11}[/tex]
[tex]df = \frac{53.3647}{3.7441}[/tex]
[tex]df = 14.2530[/tex]
[tex]df = 14[/tex]
Calculate the critical value (t)
At 95% confidence interval and df = 14;
[tex]df = 14[/tex]
The confidence interval is then calculated as:
[tex]CI = (\bar x_1 - \bar x_2) \± \sqrt{\sigma_1^2/n_1 + \sigma_2^2/n_2}[/tex]
[tex]CI = (41.33 - 22.3) \± \sqrt{7.48^2/10 + 4.53^2/12}[/tex]
[tex]CI = 19.03 \± \sqrt{7.305115[/tex]
[tex]CI = 19.03 \± 2.70[/tex]
Split
[tex]CI = 19.03 - 2.70[/tex] to [tex]19.03 + 2.70[/tex]
[tex]CI = 16.33[/tex] to [tex]21.73[/tex]
This implies that:
Private colleges have population mean annual cost of $16.33 to $21.73 more expensive than public colleges
What is m∠G to the nearest tenth? A right angle triangle EFG. The length of EF is 28.2 and GF is 45.8. Angle GFE is given as 90 degrees.
Answers
Answer:
31.6°
Step-by-step explanation:
The triangle given us a right angled Triangle
We solve the above question using the trigonometric function of Tangent
The formula is given as:
tan θ = opp/adj
θ = m∠G = ?
Opposite = EF is 28.2
Adjacent = GF is 45.8
tan θ = 28.2/45.8
θ = arc tan (28.2/45.8)
θ = 31.621459805°
Approximately
m∠G = 31.6°
in what number base is the addition 456+24+225=1050
Answers
This additition is false
the true answer is 705
Its base on my understanding:)
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Just please, idols ,if we are going to answer questions here on brainly, don't do the ones from the internet, then just copy and paste You can search on the internet but make your own sentence okay? Thank you
in how man ways can you arrange 12 books in a shelf
A:479,001,160
B:479,000,600
C:479,100,600
D:479,001,600
Answers
Aaron works at a furniture store. He sells a table that normally costs $670 but is on sale
for 15% off. If he makes 8% commission on
the sale price, how much will he make in
commission?
Answers
Answer :$45.56
Self explanation:
3. A box containing 90 oz. of cereal cost $4.50. What is the price per ounce
Answers
Answer: 0.05$ per ounce
Step-by-step explanation:
Answer:0.05 per oz.
Step-by-step explanation: divide 4.50 by the oz
Thao says she can find the answer to 8 x 90 by halving the 8 and doubling the 90 again and again until she gets down to 1 x 720. Is she correct?
Prove your answer.
Answers
Answer:
Yes
Step-by-step explanation:
4*180
2*360
1*720
8*90 = 720
Yes, halving the denominator and doubling the numerator gives the same results so she is correct.
What is numerator and denominator?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It shows how many parts have been taken out of the whole. The numerical number that comes before the sum of all the factors is the denominator of a fraction.
Let's consider a multiplication a × b
If we do half of a and double of b
Then,
a/2 × 2b = a × b
Again,
(a/2)/2 × 2(2b) = a × b
So it will remain the same.
So similarly 8 x 90 will also remain the same.
Hence "Yes, halving the denominator and doubling the numerator gives the same results so she is correct".
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please help i don't understand this question
A the cost of buying the tablet
B the cost per month of internet service
C the number of months after wich the total cost is 0 dollars
D none of the above
Answers
Answer:
Pretty sure it would be b because it keeps scaling as the x axis continues with time
A ladder leans against the side of a house. The angle of elevation of the ladder is 68 , and the top of the ladder is 15 above the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.
Answers
Answer:
6.06
Step-by-step explanation:
first draw a diagram, that'll make life easier,
then;
tan68 = opposite/adjacent
tan68 = 15/x
x = 15/tan68
x = 6.06