After solving the given differential equation, the resultant answer is: y = C(t^2+1)^{1/2} (t-3)/(2t)
To solve the differential equation (t2+1)dydt=yt−y(2+1), we need to first separate the variables y and t. We do this by dividing both sides of the equation by (yt-y(2+1))/(t^2+1) to get:
dy/(y - (2+1)/t) = dt/(t^2+1)
Now, we use the method of partial fractions to simplify the left-hand side of the equation. Let's write:
y/(y - (2+1)/t) = A + Bt/(t^2+1)
where A and B are constants that we need to find. Multiplying both sides by the denominator (y - (2+1)/t)(t^2+1), we get:
y = A(y^2+1) + Bt(y-(2+1)/t)
Expanding and collecting like terms, we get:
y^2(A-B/t) + Bt^2y - B(t+2) = 0
Since this equation must hold for all y and t, we can equate coefficients of y^2, y, and the constant term to get three equations:
A - B/t = 0
Bt^2 = 1
-B(t+2) = 0
From the second equation, we get B = 1/t^2. Substituting this into the first equation, we get A = 1/t. Finally, the third equation tells us that B = 0 if t = -2. Thus, the partial fraction decomposition is:
y/(y - (2+1)/) = 1/t + t/(t^2+1)
Substituting this into the separated differential equation, we get:
(1/t + t/(t^2+1)) dy = dt/(t^2+1)
Integrating both sides, we get:
ln|y - (2+1)/t| + 1/2 ln(t^2+1) = ln|C| + arctan(t)
where C is the constant of integration. Solving for y, we get:
y = C(t^2+1)^{1/2} (t-3)/(2t)
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As a fundraiser, the music boosters wrapped gifts at the mall one weekend. out of the 100 gifts they wrapped, 310 3 10 were for weddings, and 37100 37 100 were for baby showers. the rest of the gifts were for birthdays. what fraction of the gifts was for birthdays? enter your answer in the boxes.
For birthday events 33/100 gifts were packed by the music boosters at the mall.
Calculation of the fractionTotal number of gift items = 100
For the wedding purpose,out of 100 gifts, 3/10 number of gifts were boxed = 3/10*100 = 30
For the baby shower, out of 100 gifts, 37/100 gifts were packed = 37
The rest amount of the gift = 100-( wedding + baby shower)
= 100-(30+37) = 33
So, according to the question, these 33 numbers gift was for a birthday.
When it is expressed as a fraction,
The fraction should be = 33/100
Therefore, it is concluded that 33/100 gifts were packed for birthday occasions.
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THIS IS VERY HARD PLSSS
Answer:
[tex]y=3\sqrt{x-1}-7[/tex]
Step-by-step explanation:
We are given the function [tex]y=\sqrt{x}[/tex]. Let's apply each transformation separately and see what we get. First, let's apply the vertical shift. We are told that the graph shifts downwards by 7 units. In other words, when x is 0, y should be -7 instead of 0. We can accomplish that by changing the y-intercept of the graph and subtracting our function by 7: [tex]y=\sqrt{x} -7[/tex]. Notice that the -7 is outside the square root.
Next, we can apply the horizontal transformation. We are told that the graph shifts to the right 1 unit. This means that, for [tex]y=\sqrt{x}[/tex], if y is 0, x should be 1. We can accomplish this by doing [tex]y=\sqrt{x-1}[/tex] (if x = 1, y will be 0). Now, we can combine the two transformations we have done so far: [tex]y=\sqrt{x-1}-7[/tex].
Lastly, we need to vertically stretch the function by a factor of 3. All we have to do here is multiply sqrt(x) by 3 (this way, if x is equal to 1, y should be 3 instead of 1 (3 times x)). So, we get something like this: [tex]y=3\sqrt{x}[/tex]. Now, we can combine all of the transformations we did to get our final answer:
[tex]y=3\sqrt{x-1}-7[/tex]
Factor the greatest common factor: −6m2 18m − 36. −6(m2 − 3m 6) −1(6m2 − 18m 36) −6m(m2 − 3m 6) −6(m2 3m − 6)
Answer:
Step-by-step explanation:
−6m2 18m − 36
= -6(m2 - 3m + 6)
rewrite the exponential expression to have the indi cated base.
(1/8)2*, base 2
Answer:
2^-6
Step-by-step explanation:
(1/8)^2 = (2^-3)^2 = 2^-6
Use the grouping method to factor this polynomial completely. 3x^3+12x^2x+8
Answer:171x+8
Step-by-step explanation:
3x^3+12x^2x+8
=27x+144x+8
=171x+8
1.) Write a word problem that can be described by the division expression 3 divided by 1/4.
2.) Solve your word problem using a model. Use complete sentences to describe your model, and interpret the quotient in the context of your word problem. If you wish, you may upload a copy of your model.
3.) Use multiplication to check your answer in question #2. Show or explain all of your work.
The word problem can be:
"let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?"
And the solution is N = 12.
How to write the word problem?We want a problem that can be described by 3 divided by 1/4.
So, let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?
The solution to that question is given by:
[tex]N = \frac{3}{1/4}[/tex]
2) To solve this, we can use a really simple model.
In one unit, we have 4 fourts.
Then in 3 units, we have 3*4 = 12 fourts.
Then the answer is 12.
3) How to use multiplication?
Remember that dividing by a fraction is equivalent to multiplying by the inverse of said fraction, then:
[tex]N = \frac{3}{1/4} = 3*(4/1) = 12[/tex]
We got the same thing as above.
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Helpppppp Asap!!!!!! The question is in the picture
The approximate length of side AB is 14.0. The correct option is B. 14.0 units
Law of sinesFrom the question, we are to determine the measure of side AB
First, we will determine the measure of angle A
A + B + C = 180° (Sum of angles in a triangle)
A + 65° + 35° = 180°
A = 180° - 65° - 35°
A = 80°
Now, using the law of sines
c/sinC = a/sinA
c = AB
a = BC = 24
Thus,
c/sin35° = 24/sin80°
c = (24×sin35°)/sin80°
c = 13.978
c ≈ 14.0
∴ AB = 14.0
Hence, the approximate length of side AB is 14.0. The correct option is B. 14.0 units
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Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
14.7 (Because you asked for no units)
Step-by-step explanation:
The volume of this triangular prism is 1/2 BHL
0.5 * 3.5 * 2 * 4.2 = 14.7 ft^3
Please help ASAP!! I need to turn this is right now!!!!
Paolo used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer and saved $3,314.85 to live on during the next two semesters of school. Paolo will receive a scholarship each semester for $926.65. If he plans to use up all of his savings while at school, how much money can Paolo spend each month, on average, for things like groceries, entertainment, and miscellaneous items?
Assume two semesters equals 8 months total. Also assume Paolo has no other expenses than what he has listed here.
Scholarship for each Semester: $926.65
Tuition & Books Cost per Semester: $1,800
Housing Cost for a two-semester Contract: $1,075
If he has money left, what is the average monthly amount Paolo can afford to spend each month?
If he has overspent, what is the average monthly amount Paolo would be in debt each month?
(Indicate this amount with a negative sign)
The computation shows that the average monthly amount is 61.64.
How to calculate the value?The amount that's left will be:
= 3314.85 + (2 × 926.65) - (1800 × 2) - 1075
= 3314.85 + 1853.3 - 3600 - 1075
= 493.15
The average monthly amount will be:
= 493.15/8
= $61.64
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how meny yards are in 100 meters?
Answer:
109.36 yards to nearest hundredth
Step-by-step explanation:
1 meter = 1.09361 yards
So 100 m = 109.361 yards
Brendan is 30. Anna is 5 years older than Cassie and 10 years younger than Brendan. How old is Cassie
Answer:
20 because Brendan is 30
HELPPP DOES ANYONE KNOW THE ANSWER???
Answer:
B
Step-by-step explanation:
solve equation.
The 24 retail stores located in the Mall of America numbered 00 through 23 are: A systematic sampling procedure will be used. The first store will be selected and then every third store. Which stores will be in the sample
The stores that will be in the sample are - 00, 02, 05, 08, 11, 14, 17, 20, 23.
What comprises the sample?
An analytical subset of a larger population is referred to as a sample in statistics. A sample are used in research so that it can be done quickly and with more manageable data. However, obtaining such a sample may be costly and time-consuming. Randomly generated samples do not have significant bias if they are large enough.
Stores in the Sample
Since it is given that the sample is made up of every third store, starting from the first retail store. The stores have been numbered systematically from 00 to 23. Since a systematic sampling is done, after picking the first store, the third store will be picked, that is, 02, and then 05, and so on till 23.
Thus, the following retail stores will be present in the sample,
00, 02, 05, 08, 11, 14, 17, 20, 23
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Suppose that f'(4) = 3 , g'(4) = 7 , g(4) = 4 and g(x) not= to 4 for xnot= to 4 . then cmpute lim xgose to 4 f(g(x))/x-4-f(4)/x-4
It looks like the limit you want to compute is
[tex]\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}[/tex]
Since [tex]g(4)=4[/tex], this limit corresponds exactly to the derivative of [tex](f\circ g)(x) = f(g(x))[/tex] at [tex]x=4[/tex]. Recall that
[tex]f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}[/tex]
By the chain rule,
[tex](f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}[/tex]
Since [tex]g'(4)[/tex] exists, [tex]g[/tex] is differentiable at [tex]x=4[/tex] so it must be continuous.
SOMEONE PLEASE HELP!!! Instructions: Find the length of the arc. Round your answers to the nearest tenth.
The length of the arc is 15.70 km
Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).
The formula is given by
s = ϴ × r,
where
s is the arc length
r is the radius of the circle
θ is the central angle of the arc in radians
Given :- Radius = 10km
Angle = 90 ° = [tex]\pi[/tex]/2 radians (1 radian = 180°/[tex]\pi[/tex])
By using formula we get
Length of arc = 10 x[tex]\pi[/tex]/2 = 5[tex]\pi[/tex] km ([tex]\pi[/tex] = 3.14)
= 15.70 km
Thus the length of the arc is 15.70 km
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seven twelfths plus two twelfths equals one half 1 one and one half 2
Answer:
the answer is 3/4 because 7/12 + 2/12 is 9/12 which simplified is 3/4
Step-by-step explanation:
Use the quadratic formula to solve the equation below.
x (x + 16) = − 64
Mateo teaches a continuing education class at the library on tuesday nights. he estimates that 75% of his students are satisfied or very satisfied with the class. last week, he asked a random sample of students to take a survey on their experience in the class. however, the results showed that only 70% indicated that they are satisfied or very satisfied with the class. he decides to randomly survey more of his students. how will mateo know whether his model is valid or not?
The computed value must closely match the real value for a model to be considered valid. If the percentage of pleased or very satisfied students remains close to 75% after Mateo surveys additional students, Mateo's model is still viable. The model is faulty if the opposite is true.
How will mateo know whether his model is valid or not?In general, a valid model is one whose estimated value is close to the real value. This kind of model is considered to be accurate. It must be somewhat near to the real value if it doesn't resemble the real value.
If the findings of the survey are sufficiently similar to one another, then the model may be considered valid.
P1 equals 75%, which is the real assessment of the number of happy pupils
P2 is 70 percent; this represents the second assessment of happy pupils
In conclusion, The estimated value of a model has to be somewhat close to the real value for the model to be considered valid. If the number of students who are either pleased or extremely satisfied remains close to 75 percent following Mateo's survey of more students, then Mateo's model is likely accurate. In any other scenario, the model cannot be trusted.
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3, -3/2, -6, -21/2… what is the explicit function that defines the sequence
The explicit function that defines the sequence is 15/2 - 9n/2
How to determine the explicit rule?The sequence is given as:
3, -3/2, -6, -21/2
The above sequence is an arithmetic sequence, with the following parameters
First term, a = 3Common difference, d = -9/2 i.e. -3/2 - 3The explicit formula is then calculated as:
T(n) = a + (n -1) * d
This gives
T(n) = 3 +(n -1) * -9/2
Expand
T(n) = 3 + 9/2 - 9n/2
Evaluate
T(n) = 15/2 - 9n/2
Hence, the explicit function that defines the sequence is 15/2 - 9n/2
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Find the area of this circle
Answer:
[tex] {75ft}^{2} [/tex]
Step-by-step explanation:
[tex]a = \pi{r}^{2} = 3 {r}^{2} \\ a =3 ({ \frac{10}{2} })^{2} = 3 \times {5}^{2} \\ a = 3 \times 25 = 75[/tex]
First, we replace π with 3, since we were told to.We know 10 is the diameter and the radius is half of the diameter, so we divide 10 by 2.We get 5. 5 squared is the same as (5×5). Finally, we multiply 3 by 25.To start solving this exercise, we obtain as data:
π = 3r = 10 ft²a = ?To find the area of the circle. We apply the following formula: A =π r², where
a = areaπ = pir = radiusWe substitute our data in the formula and solve:
Substituting values into the equation:
[tex]\boldsymbol{\sf{A=3*(10 \ ft)^{2} }}[/tex]Taking the square root:
[tex]\boldsymbol{\sf{A=3*100 \ ft^{2} }}[/tex]Multiplying
[tex]\boxed{\boldsymbol{\sf{A=300 \ ft^{2} }}}[/tex]Therefore, the area of the circle is 300 ft².
How to simplify equations
Simplifying equation is done by either reducing the complexity or the components parts of an equation for better understanding.
SimplifyThis means to make simpler, either by reducing in complexity, reducing to component parts, or making easier to understand.
Simplification is an act of simplifying an equation or expression.
For instance,
Simplify 4(3x + 2) - 4(2x)
open parenthesis= 12x + 8 - 8x
= 12x - 8x + 8
= 4x + 8
Simplify 1/2 + 2/3
= (3+4) / 6
= 7/6
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What must be added to x² + 6x²-x+ 5 to make it exact divisible by (x + 3)
Let f(x) = x² + 6x²-x+ 5 then ,
number to be added be P
then,
f(x) = x² + 6x²-x+ 5 +P
According to the qn,
(x+3) is exactly divisible by zero then,
R=0
comparing .. we get a= -3
now by remainder theorm
R=f(a)
0=f(-3)
0=(-3)² + 6(-3)²-(-3)+ 5 + P
0= 9 + 54 + 3 + 5 + P
-71=P
therefore, -71 should be added.
Hope you understand
halp pls ok
x =x=x, equals
^\circ
∘
Answer:
60
Step-by-step explanation:
The yellow and green angles form a right angle, so the measures of those combined will be 90 degrees.
90 - 30 = 60
11. Find the slope of the line that passes through the pair of points. (1, 7), (10, 1)
Answer:
m = [tex]-\frac{2}{3}[/tex]
Step-by-step explanation:
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{1-7}{10-1}[/tex]
m = [tex]\frac{-6}{9}[/tex]
m = [tex]-\frac{2}{3}[/tex]
Answer:
-2/3
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (1 - 7)/(10 - 1)
slope = -6/9
slope = -2/3
If you flip the graph of the absolute value parent function, f(x)=|x|, over the x-axis, what is the equation of the new function?
The equation of the new function is f'(x) = -|x|
How to determine the equation of the new function?The function is given as:
f(x) = |x|
The rule of flipping the graph over the x-axis
(x, y) = (x, -y)
So, we have:
f'(x) = -f(x)
Substitute f(x) = |x|
f'(x) = -|x|
Hence, the equation of the new function is f'(x) = -|x|
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Can someone help me please?
The surface area of the cone is: A. 184π units².
What is the Surface Area of a Cone?Surface area of a cone = πr(l + r), where r is the radius and l is the slant height.
Given the following:
Slant height (l) = 15 unitsRadius = (r) = 8 unitsSurface area of a cone = π8(15 + 8)
Surface area of a cone = 184π units²
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Instructions: Find the missing side. Round your answer to the nearest tenth.
Using the sine ratio, the length of the missing side is: 11.8.
How to Find Missing Side Using the Sine Ratio?The sine ratio is, sin ∅ = opposite/hypotenuse.
Given the following:
∅ = 24°
Opposite = x
Hypotenuse = 29
sin 24 = x/29
x = (sin 24)(29)
x = 11.8
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If the polynomials p(x) = ax³+4x²+3x-4 and q(x) = x² - 4x + a, leave the same remainder when divided by (x-3), find value of a.
Steps pls
Answer:
a = -22/13.
Step-by-step explanation:
By the Remainder Theorem
p(3) = remainder when p(x) is divided by x-3.
q(3) is equal to the same remainder.
So we have:
p(3) = q(3) , so
a(3)^3 + 4(3)^2 + 3(3) - 4 = 3^2 - 4(3) + a
27a + 36 + 9 - 4 = 9 - 12 + a
27a - a = 9 - 12 - 36 - 9 + 4
26a = -12 - 36 + 4
26a = -44
a = -44/26
a = -22/13.
How many three-digit numbers use only the digits 0,1 and 5
Answer:
18
Step-by-step explanation:
3*3*3 = 27, assuming all 3 digits can occupy each space
However, 0 cannot start a number, so it becomes:
3*3*2, which is 18.
Which statement defines a translation?
OA A translation proportionally stretches or compresses an object based on a given scale factor.
OB. A translation moves points a specified distance along a line parallel to a specified line.
OC. In a translation, each point in the preimage and its corresponding point in the image are at equal distances from a given line.
Also, the line segment joining two such points is perpendicular to the given line.
OD. A translation is when an object moves in a circular arc around a point
the statement which defines a translation is option A that is "A translation proportionally stretches or compresses an object based on a given scale factor".
What is Translation ?
"Translation" moves points the same distance along lines that are parallel to each other.
Translation involves the initial object called the pre-image and the final object called the image. As you can see in the picture above, the rust-colored item represents the pre-image, and the blue item represents the image. Because of the arrow, we can tell the direction in which the image was moved. For other images, you may receive instructions on which image is the pre-image, or you may be asked to find the pre-image from the image.
Reflection, on the other hand, moves points along a specified line in such a way that the line bisects each line segment connecting corresponding pre-image points and image points.
There, the statement which defines a translation is option A that is "A translation proportionally stretches or compresses an object based on a given scale factor".
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Answer:
The correct answer is: A translation moves points a specified distance along a line parallel to a specified line
Step-by-step explanation: I got it right on plato.