Consider the differential equation dy/dx = 1/3x(y-2)^2.
(a) A slope field for the given differential equation is shown below. Sketch the solution curve that passes through the point (0, 2), and sketch the solution curve that passes through the point (1, 0).
(b) Let y = f(x) be the particular solution to the given differential equation with initial condition f(1) = 0. Write an equation for the line tangent to the graph of y = f(x) at x = 1. Use your equation to approximate f(0.7).
(c) Find the particular solution y = f(x) to the given differential equation with initial condition f(1) = 0.
Answers
The graph is given below and the value of the function is -0.4 at x = 0.7.
What is a differential equation?Any equation with a variable difference in it is a difference equation. The following variables affect how different equations are categorized. • The equation's order. The highest order of difference in the equation is represented by the order.
y = Mt (x - 1) + 0
Where Mt = 1/3* 1(0-2)²
Mt = 1/3*4
Mt = 4/3
From equation 1
y = (4/3)(x - 1)
Function at x = 0.7
f(0.7) = 4/3(0.7 -1 )
= 4/3(-0.3)
F(0.7) = -2/5
Let, u = y - 2
du = dy
[tex]\int\limits {1/(y-2)^2} \, dy = \int\limits {x/3} \, dx \\\int\limits{du/ u^2} \, du = 1/3 \int\limits{x} \, dx[/tex]
-1/u = 1/3( x²/2) + c
-1/(y+2) = x²/6 + c
At point(1 , 0 )
c = 2/6
Thus
-1/(y-2) = x²/ 6 - 1/3
y = -6/(x² + 2) + 2
Therefore, value of the function is -0.4 at x = 0.7.and function at x = 1 is
y = -6/(x² + 2) + 2
Learn more about differential equations here:
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Related Questions
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Answers
9514 1404 393
Answer:
k = 45 . . . miles per hourk = 1/45 . . . hours per mileStep-by-step explanation:
One way we can relate distance and time is ...
time = k × distance
Then the value of k (the constant of proportionality) is ...
k = time/distance = 4 hours/(180 miles)
k = (1/45) hours/mile
__
Another way we can relate the variables is ...
distance = k × time
Then the value of k (the constant of proportionality) is ...
k = distance/time = (180 miles)/(4 hours)
k = 45 miles/hour
5. A company intends to collect a random sample of size n from a population
with population proportion of interest p. Which of the following situations would
result in the smallest standard deviation of the sampling distribution of p?
Answers
Answer:D
Step-by-step explanation:
The situations that would result in the smallest standard deviation of p is; The population proportion p ≠ 0.5, and the sample size is n.
What is the standard deviation?The formula for the standard deviation here is;
SD = √(n(p(1 - p))
Now, for the standard deviation to be maximum, it means that p = 0.5 and as such 1 - p will also be 0.5.
However, for Standard deviation to be smallest, then it means that p ≠ 0.5.
Secondly, for the sample size, it will have to remain as n and not 2n because when we say 2n, we are increasing the sample size which will in turn increase the standard deviation.
Read more about standard deviation at;
Find the surface area of the rectangular prism (above) using its net (below).
Correct answer will receive a cookie and branilist
Answers
Answer:
62
Step-by-step explanation:
15+15+10+10+6+6= 62
5, 4, 16/5 find the 7th term
Answers
Answer:
a₇ = [tex] \frac{4096}{3125} [/tex]
The quadratic equation y = –6x2 + 100x – 180 models the store’s daily profit, y, for selling soccer balls at x dollars.
The quadratic equation y = –4x2 + 80x – 150 models the store’s daily profit, y, for selling footballs at x dollars. Use a graphing calculator to find the intersection point(s) of the graphs, and explain what they mean in the context of the problem.
Answers
Answer:
The quadratic equation y = -4x2 + 80x - 150 models the store's daily profit, y, for selling footballs at x dollars. you can subtract 150 from both sides and use the quadratic formula to find x=4. It can make at most 120 units in one day. 3 1. Backward Bending Supply Curve.
I need some help with my grade 10 math work
A music store had a sale on tapes and CDs. Tapes were on sale for $5 each and CDs were on sale for $7. During the sale, 32 tapes and CDs were sold. The cash receipts from the sale of the tapes and CDs, before taxes, were $200. Let x represent the number of tapes and let y represent the number of CDs sold during the sale.
Answers
Answer:
12 tapes and 20 CDs were sold.
Step-by-step explanation:
Since a music store had a sale on tapes and CDs, and tapes were on sale for $ 5 each and CDs were on sale for $ 7, and during the sale, 32 tapes and CDs were sold, and the cash receipts from the sale of the tapes and CDs, before taxes, were $ 200, to determine the number of CDs and tapes sold during the sale, the following calculation must be performed:
7 - 5 = 2
32 x 5 = 160
200 - 160 = 40
40/2 = 20
32 - 20 = 12
12 x 5 + 20 x 7 = X
60 + 140 = X
200 = X
Therefore, 12 tapes and 20 CDs were sold.
Find the dot product of vectors u = -4i + 7j and v = 2i + j
Answers
Answer:
The desired dot product is -1
Step-by-step explanation:
To find the dot product of the given vectors, multiply the magnitudes of the 'i' and 'j' terms together, separately, and then add the results:
dot product of u and v = (-4)(2) + (7)(1) = -8 + 7 = -1
The desired dot product is -1
please help me
A book is marked 21% off. If the original price is $23.42, what will the sale price be?
Round your answer to the nearest cent. Do not include units with your answer.
Answers
Answer:
$18.51
Step-by-step explanation:
23.42×.21= 4.91 then 23.42-4.91= your sale price which is $18.51
Need the answer for x and y
Answers
Answer:
x = 7°
y = 10°
Step-by-step explanation:
7x = 49
x = 7°
180 = 13y + 1 + 49
combine like terms:
13y = 130
y = 10°
Answer:
X equals to 7 & y equals to 10 'cause ;
7X=49
X=7
50 + 13 y + 1 = 180
13y = 130
y=10
Step-by-step explanation:
Good luck.
hope it was helpful for u .
What is the measurement of Angle E? A) 45° B) 600 ( 75° D) 90°
Answers
Not sure if you accidentally typed 600 instead of 60, but the answer should be 60º
explanation:
angles in a triangle sum to 180º, as shown by the triangle on the right (45+75+60=180)
so the missing angle E would be 60º
What is the value of C in the matrix equation below?
|-18 3 51-c-[-22 1 12
o -40
217]
01-40 27]
10142-7)
0 14 2 17]
Answers
Given:
The matrix equation is:
[tex]\begin{bmatrix}-18&3&5\end{bmatrix}-C=\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]
To find:
The value of matrix C.
Solution:
Let [tex]A=\begin{bmatrix}-18&3&5\end{bmatrix},B=\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]. Then the given equation can be rewritten as
[tex]A-C=B[/tex]
[tex]-C=B-A[/tex]
[tex]C=-(B-A)[/tex]
[tex]C=A-B[/tex]
On substituting the values of the matrices, we get
[tex]C=\begin{bmatrix}-18&3&5\end{bmatrix}-\begin{bmatrix}-22&1&12\end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}-18-(-22)&3-1&5-12\end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}-18+22&2&-7\end{bmatrix}[/tex]
[tex]C=\begin{bmatrix}-4&2&-7\end{bmatrix}[/tex]
Therefore, the correct option is C.
Answer: C
Step-by-step explanation: [ 4 2 -7 ]
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answers
Answer:
It is 47.5 or 47 1/2
Step-by-step explanation:
The formula for volume of a prism is base x height.
The base is the area of the rectangle at the bottom. The area of a rectangle is, of course, length times width, so 2.5 x 4=10.
So, the base is 10.
Now, the second part of the formula is height.
The height is 4.75.
Now, do the formula: Base x height : 10 x4.75
The answer is 47.5.
Don't report me lol. I promise it is correct.
Answer:
I need 5 Brainliest before I can become Ace
Step-by-step explanation:
Plz help NO LINKS this is due today
Answers
It is C, the metric system
Using the order of operations, what are the steps for solving this expression? 40/8+3^2+(15-7)*2 Arrange the steps in the order in which they are performed.
Answers
9514 1404 393
Answer:
simplify parenthesesevaluate the exponential termdivide 40/8multiply 8*2add 5+9add 14+16Step-by-step explanation:
40/8+3^2+(15-7)*2 . . . . given
The order of operations tells you to start by evaluating expressions in parentheses. Here, that is the subtraction of 7 from 15.
40/8 +3^2 +8*2 . . . . (15-7) = 8
Then you evaluate exponential terms.
40/8 +9 +8*2 . . . . . 3^2 = 9
Then perform multiplication and division, left to right. Here, division is first, then multiplication.
5 +9 +8*2 . . . . . divide 40/8 = 5
5 +9 +16 . . . . . . multiply 8*2 = 16
Finally, perform addition and subtraction, left to right.
14 +16 . . . . add 5+9
30 . . . . . . . add 14+16
Answer:
it is 8
Step-by-step explanation:
The area of the triangle below is 44.59 square centimeters. What is the length of the
base?
9.1 cm
Answers
Answer:
6 cm.
Explanation: 6
cm.
Explanation:
Since they've given use the area of the triangle, we can use the area formula to find the base of the triangle.
The formula to find the area of a triangle is:
a = 1 2 h b
→ ( h = height , b= base )
We know:
a = 24 h = 8
So we can substitute them in and find
Multiply by sides by 2 and then divide:
The base of the triangle is
6 cm. -step explanation:
-6x+8y=12 and -3x+4y=6
Answers
Answer:
3441
Step-by-step explanation:
PLS HOPE THIS HELP
Round 12,628 to nearest 1,000
Answers
Answer:
13000
Step-by-step explanation:
it's closer to 13000 than to 12000
Answer:
13000Step-by-step explanation:
12628 >>>13000
Me:
This is easy like what grade are you in?
A duck swims at a speed of 1 meter per second. How long does it take for it to cross a 50 meter wide pond?
Answers
Answer:
50 seconds.
Step-by-step explanation:
Hope this helps!
Answer:
50 seconds.
Step-by-step explanation:
If it takes 1 meter per second.
50 meter = 1 × 50 seconds
= 50 seconds.
PLEASE HELP!!!!!!!!!! BRAINLIEST
Add the following fractions. Simplify and reduce to the lowest terms.
9/16 + 3/16
Answers
Answer:
3/4
Step-by-step explanation:
12/16
divided by 4
3/4
Answer: /34
Step-by-step explanation:
9/16 + 3/16
=(9+3)/16 ⇔ Fractions with the same denominator can subtract or add
=12/16 ⇔ Simplify
=(3×4)/(4×4) ⇔ Factor each number
=3/4 ⇔ Divide 4 on both numerator and denominator
Hope this helps!! :)
Please let me know if you have any questions
What does MIJ equal ?
Answers
Please help will give brainliest
Answers
Answer:
A+B=180°(linear pair)
a+ 52°=180°
a=180°-52°
a=128° is your answer
The graph of f (x) = (x - 2)² + 1 is shown below. What would the new equation of the function be if it is shifted up 2 units?
Answers
Answer:
f (x) = (x - 2)² + 3
Step-by-step explanation:
Adding 2 to the constant k would shift the entire equation upwards by 2.
6(5 - 8n) + 12 = -54
please step my step
Answers
Answer:
Look Below
Step-by-step explanation:
6(5 - 8N) + 12 = -54
-48N + 30 + 12 = -54
-48N + 42 = -54
(-48N + 42) + (-42) = -54 + (-42)
-48N = -96
-48N / 48 = N
-96 / 48 = 2
N = 2
Hope This Helps! If you find any fault in my answer please let me know. Thanks! Have a good day!
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answers
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
Hakima and Joshua both opened savings accounts. Both started with a balance of zero dollars. For every $3 that Hakima saves in her account, Joshua saves $5. If they have saved a total of $336, how much did Hakima save?
Answers
Approximately how long will it take a jet to travel 400 miles at a rate of 120
miles per hour?
A.) 3 1/3
B.)3 1/2
C.)4 1/2
D.)4 1/3
Answers
Answer:
3 1/3
Step-by-step explanation:
Apr 08, 12:51:17 AM
Brittney wants to buy grapes and apples to bring to a party. Grapes cost $1.60
per pound and apples cost $1.75 per pound. If she only has $10 to spend on
grapes and apples, which inequality represents the situation where she buys x
pounds of grapes and y pounds of apples?
1.60x + 1.75y < 10
1.60x + 1.75y > 10
Submit Answer
1.75x + 1.60y < 10
1.75% + 1.60y > 10
Type here to search
O
12:5
4/8/
Answers
Answer: did you get a answer yet?
Step-by-step explanation:
PLS HELP!!!!
72 REWARD BC ITS URGENT :(
Which of the following equations is not balanced?
A. N2 + 3H2 --> 2NH3
B. Mgl2 + Br2 --> MgBr2 + I2
C. KCIO3 --> KCI +O2
D. HCI + NaOH --> NaCI +H2O
Answers
A minute- hand of a clock is 16 in long. Find the distance traveled by the tip of the minute - hand in one hour.
Answers
8 * 8 = 64
64* 3.14 = 200.96
200.96 * 60 = 12057.6
Hope this helps (:
90:(3+6)-20.(60-55) propiedad
Answers
Answer:
https://www.commoncoresheets.com/Math/Properties/Applying%20Properties%20of%20Operations/Spanish/2.pdf
Step-by-step explanation:
This will help you:) not a spam link its a pdf that brings you straight to the worksheet <3