Solve the given differential equation by using an appropriate substitution. the de is a bernoulli equation. xdy/dx-(1 x)y=xy^2
-ln ( 1 - x/y - x) = c is a bernoulli equation. xdy/dx-(1 x)y=xy^2.
What is a differential equations explain?
Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)
[tex]\frac{-1}{y} = u[/tex]
[tex]\frac{y'}{y^{2} } = u'[/tex]
[tex]xy' - ( 1 + x )y = xy^{2}[/tex]
[tex]x\frac{y'}{y^{2} } - ( 1 + x ) \frac{1}{y} = x[/tex]
xu' + ( 1 + x )u = x
xu' + u + ux = x
xu = s
u + xu' = s'
s' + s = x
s - x =t
s' - 1 = t'
t' + 1 + t = 0
dt/dx = - ( 1 + t)
-∫ [tex]\frac{dt}{1 + t} =[/tex] ∫dx
-ln ( 1+ t ) = x + c
-in ( 1 + s - x ) = x + c
-ln ( 1 + xu - x ) = x + c
-ln ( 1 - x/y - x) = c
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Enclose the error in solving the polynomial multiplication. Then correct it.
Correction:
Answer:
Hello,
Step-by-step explanation:
[tex](t^3+4)(t^3-4)\\\\= (t^3)^2-(4)^2\\\\=t^6-16[/tex]
a) x³y²if x = 2 and y = 4
Answer:
128
Step-by-step explanation:
x³y²if x = 2 and y = 4
x³*y²
[tex](2)^{3} * (4)^{2}[/tex]
(2*2*2)*(4*4)
(8)*(16)
128
Explain why it’s a bad or good sample. Every other household in a neighborhood of 20 homes is surveyed to determine the country’s favorite presidential candidate?
Answer:
The sample is not random because every other household is surveyed. This means that the sample is not representative of the entire population.
Step-by-step explanation:
This is the answer because, the entire population is not being surveyed, only every other household.
What is the area of the semicircle? Use 3.14 for pi.
150.72 mm^2
138.16 mm^2
69.08 mm^2
189.97 mm^2
The area of the semicircle with the given diameter is 189.97 mm^2
How to determine the area of the semicircle?The given parameters are
Diameter, d = 22 mm
The area of the semicircle is calculated as
A = 1/2 * pi * (d/2)^2
So, we have
A = 1/2 * 3.14 * (22/2)^2
Evaluate the expression
A = 189.97 mm^2
Hence, the area of the semicircle with the given diameter is 189.97 mm^2
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Express the mass of 49,000 molecules of oxygen in scientific notation.
grams
The scientific notation for the mass of 49,000 molecules of oxygen is 4.9 × 10⁴ grams.
How do you define the scientific notation?To transform numbers into scientific notation, use the following rule: In scientific notation, the exponent equals the number of times the decimal point must always be shifted to produce a number between 1 and 10.
The proper scientific notation format is an x 10∧b, where an is a number or decimal number with an absolute value greater or equal to one and less than ten, or 1 |a| 10.Scientific notation is a method of writing extremely large or extremely small numbers in a way that makes them easier to read as well as work with. A number formed by multiplying a number greater or equal to one but less than ten by an integral power of ten.For the given value;
= 49,000 grams
write the number such that only one digit is left to the left of decimal of the number and the remaining digits to the write are written to the power of 10
= 4.9000 × 10⁴
This could be written as;
= 4.9 × 10⁴.
Therefore, the value of the mass of 49,000 oxygen molecules in the form of scientific notation is 4.9 × 10⁴ grams.
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Find the equation of the line shown.
Answer: y=0.5x+0.5
Step-by-step explanation:
[tex]\displaystyle\\(1,1)\ \ \ \ (-3,-1)\\\\\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }\\\\x_1=1\ \ \ \ x_2=-3\ \ \ \ y_1=1\ \ \ \ y_2=-1\\\\\frac{x-1}{-3-1}=\frac{y-1}{-1-1} \\\\\frac{x-1}{-4}=\frac{y-1}{-2} \\[/tex]
Multiply both parts of the equation by -2:
[tex]\displaystyle\\\frac{x-1}{2} =y-1\\\\\frac{x}{2}-\frac{1}{2} =y-1\\\\\frac{x}{2}-\frac{1}{2}+1 =y-1+1\\\\\frac{x}{2}+\frac{1}{2} =y \\[/tex]
Thus,
y=0.5x+0.5
The midpoint of a line segment ab is (1, 2). point a coordinates are (3,-3)
and point b coordinates are (x, 7). find the value of x.
The value of x in (x,7) is -1
Mid Point of a line segment is defined as the point which divides the line segment in equal ratio that means divides in two equal parts.
Let one end point of line segment be A(a,b) and other end be B(c,d)
then its mid point X(x,y) will be given by [tex]x=\frac{a+c}{2} , y=\frac{b+d}{2}[/tex]...….(1)
Given the points A(3,-3) and B(x,7) and the midpoint X(1,2)
The mid point [tex](1,2)=(\frac{3+x}{2} ,\frac{-3+7}{2} )[/tex]...............using (1)
On comparing the x coordinate we get
[tex]1=\frac{3+x}{2}[/tex]
On cross multiplying we get
[tex]2=3+x[/tex]
On solving further
[tex]x=-1[/tex]
Therefore , the value of x in (x,7) is -1.
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I need help with this asap
The function rules for each of the given tables are;
11) f(x) = 4x
12) f(x) = x - 3
13) f(x) = x + 12
14) f(x) = x/10
15) This doesn't have a function rule.
16) Function rule here is non existent
How to state the required function rule?
11) In this table, we can observe that the output values are all four times the input value. Thus, the function rule here is;
f(x) = 4x
12) In this table, we can observe that the output values are all 3 units less than the input value. Thus, the function rule here is;
f(x) = x - 3
13) In this table, we can observe that the output values are all 12 units more than the input value. Thus, the function rule here is;
f(x) = x + 12
14) In this table, we can observe that the output values are equal to the input value divided by 10. Thus, the function rule here is;
f(x) = x/10
15) This doesn't have a function rule as the values don't match a pattern
16) Function rule here is non existent
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Suppose that for a function g (x), g (4) = 7. Select all of the statements that are true.
A.
B.
C.
D.
E.
4 is in the range of g.
For a value a, it is possible that g (a) = 4.
For a value y, it is possible that g (4) = y.
The point (4,7) is on the graph of y = g(x).
The point (7,4) is on the graph of y = g(x).
If I spend $35 every 2 weeks, how much do I spend in a year?
One of the radioactive isotopes used in chemical and medical research is iodine-125, which has a half-life of 61 days. how long would it take for 0.25 g to remain of a 1.00 g sample of iodine-125?
Answer:122 days
Step-by-step explanation:
A magnetic levitation train travels between the city center of shanghai china and pudong international airport. the trip covers 30 kilometers i'm just 8 minutes. what is the average speed of the train in miles per hour
Average speed of the train as it covered 30 kilometers in 8 minutes is equal to 139.8 miles per hour.
As given,
Total distance= 30 kilometers
Total time taken = 8 minutes
1 kilometer = 0.62137 miles
30 kilometers = 30 × 0.62137
= 18.641 miles
8 minutes = ( 8 / 60) hour
Average speed= total distance / total time taken
= 18.641 / (8/60)
= 139.8 miles/ hour
Therefore, average speed of the train as it covered 30 kilometers in 8 minutes is equal to 139.8 miles per hour.
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I went to a toy shop and bought a toy car which costs $16.80, but there was a 20% discount. how much did I pay?
Step-by-step explanation:
16.80 - 20% of 16.80 = 13.44
you paid 13.44$
Answer:
=13.44
Step-by-step explanation:
0.20×16.80=3.36
16.80-3.36=13.44
the points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM : MN : NO is equal to 3 : 5 : 3. if LO = 11, find NO
Answer:
5
Step-by-step explanation:
Answer:
LM:MN:
NO =3:
3N
Step-by-step explanation:
Tyra launches a rocket in the air, and her physics teacher told her if h is height and t is time, she can find the height of the rocket at any given time using: h(t)= -16t^2+50t
Interpret the meaning of the point (3.125,0) in terms of the problem situation
The points ( 3. 125, 0) represents the time intervals for which the rocket reaches a height of - 312. 5 feet
How to determine the value
Given the function;
h(t)= -16t^2+50t
Where;
h is the height of the rocket t is the time taken to reach the heightThe time interval to reach the height of the rocket is ( 3. 125 , 0)
Time interval, t = 0 - 3. 125
Time interval, t = -3. 125
Substitute the value into the formula
h(t) = - 16(-3. 125)² + 50(-3. 125)
h(t) = -16(9. 765) - 156. 25
h(t) = - 156. 25 - 156. 25
h(t) = -312. 5 feet
Thus, the points ( 3. 125, 0) represents the time intervals for which the rocket reaches a height of - 312. 5 feet
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5 x=10
if u have 5 apple and 10 cakes how many do u come up with
Answer:
x = 2
Step-by-step explanation:
Equation: 5x = 10
--- Divide 5 on both sides
x = 2
This means that each apple can make 2 cakes.
Answer: 2
Step-by-step explanation: because if u divide both sides by 5
1.00 *10³ + 4.235 *10*
either 1042.35 or 1.04235*10^3
Aliya hikes up a mountain for 2 hours. During this time, she hikes a
distance of 1 miles. Which expression shows Aliya's rate in miles per
1
hour?
The expression shows Aliya's rate in miles per hour will be 1/2.
How to compute the expression?From the information, Aliya hikes up a mountain for 2 hours and during this time, she hikes a distance of 1 miles.
Therefore, the rate will be:
= Distance / Time
= 1 / 2
Therefore, the expression shows Aliya's rate in miles per hour will be 1/2.
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Given the points a(- 1, 2) and b(7, 10), find the coordinates of the point p on the directed line segment that partitions in the ratio 1:3. plot p along with segment ab
The coordinate of point p such that it is dividing line ab into 1:3 is (1,4).
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
Coordinate a point with intercept m: n and bounded by coordinate (x₁, y₁) and (x₂, y₂).
x = [m(x₂) + n(x₁)]/(m + n)
And,
y = [m(y₂) + n(y₁)]/(m + n)
So,
x = [1(7) + 3(-1)]/(1+3) ⇒ x = 1
y = [1(10) + 3(2)]/(1+3) ⇒ y = 4
Hence "The coordinate of point p such that it is dividing line ab into 1:3 is (1,4)".
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Please helppppp me !,!!!!
Answer:
The last option
y = ⅓x-3
Step-by-step explanation:
Slope-intercept form :
y=mx+c
[tex]x - 3y = 9 \\ - 3y = - x + 9 \\ \frac{ - 3y}{ - 3} = \frac{ - x}{ - 3} + \frac{9}{ - 3} [/tex]
[tex]y = \frac{1}{3} x - 3[/tex]
If Kevin has a total of 81 hours of service, how many weeks has he volunteered?
If Kevin has a total of 81 hours of service, then he volunteered for 0.48 weeks.
As per the question statement, Kevin served as a volunteer for 81 hours.
We are required to find out the number of weeks, he volunteered his service.
To solve this question, we just need to know that a week consists of how many hours ?
We can proceed with the facts that a week consists of 7 days and each day consists of 24 hours. Therefore, a week consists of [tex](24*7)=168[/tex] hours, of which, Kevin volunteered for 81 hours.
Therefore, as per the unitary method, we get that,
168 hours make 1 week, then
1 hour makes [tex](\frac{1}{168})[/tex] weeks, and
81 hours make [tex](\frac{81}{168})=0.48[/tex] weeks approximately.
Unitary Method: This is a technique for solving a problem where first, we find the value of a single unit, and then find the necessary value by multiplying the single-unit value.To learn more about Unitary Method, click on the link below.
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Martin wants to clean his swimming pool.
He hired a cleaning machine to do this job.
The cost of hiring the cleaning machine was
£35.54 for the first day,
then £18.25 for each extra day.
Estimate how much it would cost to rent the machine for 4 days.
Help plssss
Answer:
90.29
Step-by-step explanation:
I did math
The total number of data items with a value less than the upper limit for the class is given by the _____ distribution.
The cumulative frequency distribution indicates the total number of data items with values below the class's upper limit.
By cumulative frequency, what do you mean?Cumulative frequency analysis examines how frequently values of a phenomena occur that are less frequent than a reference value. The phenomenon could depend on time or place. Another name for cumulative frequency is frequency of non-exceedance. Each frequency from a frequency distribution table is added to the total of its predecessors to determine the cumulative frequency. Since all frequencies will have previously been added to the prior total, the final result will always be equal to the sum of all observations. The quantity of an element in a set is referred to as the element's frequency. The accumulation of all earlier frequencies up to the present time is another definition for cumulative frequency.
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Consider the set of ordered pairs (q, T), where T is the total value of q quarters in dollars, up to $1.50 in quarters (inclusive).
In the situation above, the domain is [Select] and the range is [Select].
The domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).
The range is going to be a set of real numbers from 0 to 6.
What is the range and domain?The domain of a function is the set of input values that we are allowed to plug into our function. This set is the x-values in a function.
The range of a function is the set of output values that the function assumes.
Now, we are told that there is a set of ordered pairs (q, T), where T is the total value of q quarters in dollars, up to $1.50 in quarters
Now, from conversions, we know that 1 quarters is equal to 0.25 dollar.
Thus, the domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).
The maximum output value will be; 1.5/0.25 = 6
Meanwhile, the range is going to be a set of real numbers from 0 to 6.
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How do answer this question?
Answer:(0,4)
Step-by-step explanation:
Answer:
(-5, -1)
Step-by-step explanation:
If 25,197,624 hot dogs are packaged in sets of 4, how many will be left over?
Answer:6,299,406
Step-by-step explanation:
Ms. Wells has 16 Pokemon cards, she left 12 of her cards at home. What is the fraction of Pokemon cards she left at home? Answers should be in simplest form.
Group of answer choices
6/18
12/16
3/4
1/12
Answer: 3/4
Step-by-step explanation: because 12/16 simplified is 3/4
of her loan?
10. Britta has been accepted into a 2-year medical assistant program at a career school. She has
been awarded a $6,000 unsubsidized 10-year federal loan at 4.29%. She knows she has the
option of beginning repayment of the loan in 2.5 years. She also knows that during this
nonpayment time, interest will accrue at 4.29%.
Britta made her last monthly interest-only payment on May 5. Her next payment is due on
June 5. What will be the amount of that interest-only payment?
Answer: $21.86 i just found this on the web buts its right
how much do we pay for the mesh around the garden, which has a shape of a square measuring 25m and one ordinary meter of mesh costs 23 euros.
The cost of the mesh measuring 25 m is 2300 euros .
The perimeter of a square is that the distance lined by its four sides. Perimeter surrounds or outlines the form in a very two-dimensional plane.Since all the edges of a sq. square measure equal, therefore, the perimeter of sq. are four times its aspect, i.e. 4 × Side.The perimeter of the sq. is outlined because the total length of the boundary of a sq.. we want to feature all the edges of sq. to seek out its perimeter. By the formula of perimeter of polygonal shape, we know;
Perimeter = add of all sides
Perimeter of sq. = add of the lengths of four sides
= aspect + aspect + aspect + aspect
= 4 × side
First , we will calculate the the perimeter of the square
Perimeter of square = 25 × 4.
= 100 m
Total cost = perimeter required × cost per meter .
Cost of mesh = 100 × 23
= 2300 euros
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