Answer:
y = [tex]\frac{3}{2 + 3Ce^{-3t} }[/tex]
Step-by-step explanation:
As given , y' = 3y - 2y²
⇒y' - 3y = -2y²
Divide by y² in the above equation
⇒[tex]\frac{y'}{y^{2} } - \frac{3y}{y^{2} } = -\frac{2y^{2} }{y^{2} }[/tex]
⇒[tex]\frac{y'}{y^{2} } - \frac{3}{y } = -2[/tex] ........(1)
Now , let [tex]\frac{1}{y}[/tex] = u
⇒-[tex]\frac{1}{y^{2} } \frac{dy}{dt} = \frac{du}{dt}[/tex]
⇒-[tex]\frac{1}{y^{2} }y' = \frac{du}{dt}[/tex]
∴ equation (1) becomes
-[tex]\frac{du}{dt}[/tex] - 3u = -2
⇒[tex]\frac{du}{dt}[/tex] + 3u = 2
It is a linear differential equation
Now,
Integrating factor = I.F = [tex]e^{\int\limits {3} \, dt }[/tex] = [tex]e^{3t}[/tex]
∴ The solution becomes
u.(I.F) = [tex]\int\limits {2.(I.F)} \, dt[/tex] + C
⇒u.([tex]e^{3t}[/tex]) = [tex]\int\limits {2.(e^{3t} )} \, dt[/tex] + C
⇒u.([tex]e^{3t}[/tex]) = [tex]\frac{2e^{3t} }{3}[/tex] + C
⇒u = [tex]\frac{2}{3} + Ce^{-3t}[/tex]
As [tex]\frac{1}{y}[/tex] = u
⇒[tex]\frac{1}{y}[/tex] = [tex]\frac{2}{3} + Ce^{-3t}[/tex]
⇒ y = [tex]\frac{1}{\frac{2}{3} + Ce^{-3t} } = \frac{3}{2 + 3Ce^{-3t} }[/tex]
⇒ y = [tex]\frac{3}{2 + 3Ce^{-3t} }[/tex]
PLS HELP FAST!!! WORTH 20 POINTS!!!!
Enter the data to create a histogram. Then answer the question. A 1-column table with 10 rows. Column 1 is labeled books with entries 2, 3, 5, 6, 4, 5, 5, 2, 2, 5. Sinclair keeps track of the number of books he reads every month for 10 months. How many months did he read 4 or more books?
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
What is the percent change from 250 to 620
Answer:
A change from 250 to 620 represents a positive change (increase) of 148%
Use the formula found below on this webpage to find the percent change by replacing the given values:
Percent change = New - Old
|Old|
× 100%
Percent change = 620 - 250
|250|
× 100% =
370
250
× 100 = 148% (increase)
Where: 250 is the old value and 620 is the new value. In this case, we have a positive change (increase) of 148 percent because the new value is greater than the old value.
Step-by-step explanation:
Last year a poll of 1,000 voters conducted by the staff of Senator Chun found that 522 people approved of the job the senator was doing. This year, a new poll of 1,000 voters shows that 423 people approve of the senator's performance. Find the percent of change in the number of voters who approved of the senator's performance, and identify it as an increase or decrease.
A 19%, increase
B 23.4%; decrease
C 23.4%, increase
D 19%; decrease
Answer:
19% decrease
Step-by-step explanation:
First, find out how much it decreased by. 522 - 423 = 99. Then, since it decreased by 99/522 you find the percent this is equal to, which would be
18.96%. = about 19%
It is going down, so it's decreasing
find the value of x and y thanks
Answer:
y=5 and x= 35÷6 = 5,83
Step-by-step explanation:
we have an equilateral triangle
so it means that his three sides have the same length:
35 = 7y = 6x
- we have 35 = 7y <=> y = 35÷7 = 5
- we have 35 =6x <=> x = 35/6 = 5,83
x = 5,83y = 5Help pls and explain
How does the graph below change between point A and point B?
The line is an upside U shape from A to B
This means the graph increases, then decreases.
Help please this is due at 11:59
3(G-2) Please Answer fast With WORK
Answer:
3G-6
Step-by-step explanation:
3 with inside of the ()
Due to the drought in California, many communities now have tiered water rates. There are different rates for Conservation Usage, Normal Usage, and Excessive Usage. The usage is measured in the number of hundred cubic feet (hcf) that the property owner uses.
During the summer, a property owner will pay $24.72 plus $1.32 per hcf for Conservation Usage. The bill for Conservation Usage would be between or equal to $31.32 and $52.12. How many hcf can the owner use if she wants her usage to stay in the conservation range?
Enter truncated values for answers. Example: Enter 8.93 as 8 and 6.34 as 6.
Answer:
Step-by-step explanation:
31.32≤24.72+1.32x≤52.12
31.32−24.72≤24.72−24.72+1.32x≤52.12−24.72
6.6≤6.61.32≤1.32x≤27.41.32x1.32≤27.41.32
5≤x≤20.76
The property owner can use 5–20 hcf and still fall within the Conservation Usage billing range.
Someone please help and thank you
Answer:
A. 4 units
Step-by-step explanation:
factor by grouping:
vx+7v-3x-21
Answer:
Solving the expression [tex]vx+7v-3x-21[/tex] using factor by grouping we get [tex]\mathbf{(x+7)(x-3)}[/tex]
Step-by-step explanation:
We need to solve the expression [tex]vx+7v-3x-21[/tex] using factor by grouping
Factor by grouping requires to group first two terms together and last two terms together and try to find out the common numbers in the groups.
We can group:
[tex](vx+7v)(-3x-21)[/tex]
Taking v common from first group and -3 from second
[tex]v(x+7)-3(x+7)[/tex]
Taking x+7 common
[tex](x+7)(x-3)[/tex]
So, Solving the expression [tex]vx+7v-3x-21[/tex] using factor by grouping we get [tex]\mathbf{(x+7)(x-3)}[/tex]
how many times can 67 go into 148
Answer:
2 Times Remainder 14
Or 2.20895522388 times
Step-by-step explanation:
67 x 2 = 134
148 - 134 = 14
It will go in two times with a remainder of 14
35 points! Will mark Brainliest! Real answers only!
Answer:
Yay ty for the free points!
Step-by-step explanation:
2 1/4 divided by three what is the answer please explain
Answer:
0.75
Step-by-step explanation:
2 1/4 = 9/4
9/4 = 2.25
2.25 / 3
0.75
Find the centroid of AABC if
A = (0, 6), B = (2,0), and C = (10, 0).
([?], [ ]
Pls help! :)
Answer:
Centroid of ΔABC = (4,2)
Step-by-step explanation:
Explanation:-
Given points are A(0,6) , B(2,0) and C(10,0)
Centroid of ΔABC
= [tex](\frac{x_{1}+x_{2} +x_{3} }{3} ,\frac{y_{1}+y_{2} +y_{3} }{3})[/tex]
= [tex](\frac{0+2+10}{3} , \frac{6+0+0}{3} )[/tex]
= [tex](\frac{12}{3} , \frac{6}{3} )[/tex]
= (4 , 2)
Centroid of ΔABC = (4,2)
Which of the following expressions have a
simplified value of 3a + 2? Choose ALL that
apply.
A. - 6a + 9a + 4 - 2
B. - a + 4 + 5a - a - 6
C. - 8 + 3a + 10 - a
D. - 10 – 5a + 12 + 8a
Helpppp
Your friend Michelle just graduated and has two job offers that she is considering. Both job offers pay the same, but JobA
contributes $1,700 annually to Michelle's retirement plan while Job B does not offer a retirement plan at all. Assuming that Michelle
will be at her first job for 5 years and that she will earn 6.60% annually on her retirement savings plan, how much will Michelle have
in her retirement plan at Job A? (Round answer to nearest whole number)
Money offered to Michelle per annum in Job A = $1700
Number of years she will work in job A = 5
Percentage of earnings per annum for her retirement plan = 6.60%
Money she will earn will be the simple interest at the end of 5 years.
We know that :
[tex]\color{plum}{ \tt{Simple \: interest = \frac{Principle \ \: \times \: Rate \: \: \times \: \: Time}{100} }}[/tex]
Principal = $1700
Rate = 6.60%
Time = 5 years
Which means :
[tex] = \frac{1700 \times 6.60 \times 5}{100} [/tex]
[tex] = \frac{56100}{100} [/tex]
[tex] = \color{plum}\$561[/tex]
We also know that :
[tex]\color{plum}\tt \: Amount = Principal + Interest [/tex]
Amount Michelle will earn at the end of 5 years for her retirement plan :
[tex] = 1700 + 561[/tex]
[tex] =\color{plum}\bold{\$ 2261}[/tex]
2261 can be rounded off to 2260.
Therefore, Michelle will earn $2260 at the end of 5 years for her retirement plan.
PLEASE ANSWER THESE QUSTIONS I WILL GIVE BRANLYIEST TO YOU AND ALL MY POINTS PLZ
He works for 8 hours and 20 minutes, he charges 350 dollars and hour. How much does he make?
Answer:
2800
Step-by-step explanation:
multiply 350 by 8
Answer:2870
Step-by-step explanation: 350×8 and then 350×.2 and then add those both up and get 2870
will make brainliest what is 2,837 to the nearest 10????????????????????????
Answer:
2,840
Step-by-step explanation:
since the three is in the tens place and 7 in single if 5 and up round up fi 4 and below leave it alone you will then take the 3 and round up to give you 2,840
Which postulate proves these two
triangles are congruent?
A. HL
B. SSA
O. ASA
D. SAS
Answer:
HL
Step-by-step explanation:
It give you that the hypotenuse and one leg is congruent
A function is described by f(x) - 2x -3. The replacement set for the independent variable is
{-1, -2, 1,5). Which of the following would belong to the corresponding set of values of the
dependent set?
Answer:
The corresponding set of values of the dependent set is: {-5, -7, 0}
Step-by-step explanation:
Dependent variable and independent variable:
Suppose we have a function f(x).
The independent variable is the input value of the function, that is, x.
The dependent variable is the output value of the function, that is, f(x).
The replacement set for the independent variable is (-1, -2, 1,5).
The values of the dependent set are respectively, f(-1), f(-2) and f(1.5). So
We have that: [tex]f(x) = 2x - 3[/tex]. So
[tex]f(-1) = 2(-1) - 3 = -2 -3 = -5[/tex]
[tex]f(-2) = 2(-2) - 3 = -4 -3 = -7[/tex]
[tex]f(1.5) = 2(1.5) - 3 = 3 -3 = 0[/tex]
The corresponding set of values of the dependent set is: {-5, -7, 0}
A constant force acts on a 30-g object and produces an acceleration of 2 m/s2. Find the force in dynes.
Answer:
Force F = 60 ×10⁻⁵ N
Step-by-step explanation:
Given that mass of the given object (m) = 30 grams
Given that the acceleration
a = 2 m/s²
Force:-
The push or pull on an object with mass that causes it to change its velocity
Force can make a body that is rest to moveit can accelerate the speed of a moving bodyFormula for force
The formula for force F = m a
F = 30 × 2
F = 60 gm/s²
F = 60 ×10⁻⁵ N (∵ 1 d y n = 1gm² = 10⁻⁵N
Determine if the side lengths could form a triangle 29ft, 38ft, 9ft
Answer:
yes it would be an obtuse triangle i think
Step-by-step explanation:
what is the exspression for five less than n
Answer:
n-5
Step-by-step explanation:
Answer:
n - 5 is the expression
There are 60 marbles in a bin and 75% of the marbles are red. How many red marbles are the bin?
Answer:
45 marbles
Step-by-step explanation:
I need help with this
Diameter = 4 cm
Radius = Diameter/2 = 2 cm
Area of circle :
[tex] = \pi{r}^{2} [/tex]
[tex] = 3.14 \times 2 \times 2[/tex]
[tex] = 3.14 \times 4[/tex]
[tex] = 12.56 \: {cm}^{2} [/tex]
Circumference of circle :
[tex] = 2\pi r[/tex]
[tex] = 2 \times 3.14 \times 2[/tex]
[tex] = 12.56 \: \: {cm}^{2} [/tex]
Therefore, Diameter = 4 cmRadius = 2 cmArea = 12.56 cm²Circumference = 12.56 cm[tex]\bold{\color{plum}\tt \: Answer \: \: 2 :}[/tex]Circumference = 15 feet (given)
Radius :
[tex] = 2\pi r[/tex]
[tex] = 2 \times \frac{22}{7} \times r = 15[/tex]
[tex] = \frac{44}{7} \times r = 15[/tex]
[tex] = 44r = 15 \times 7[/tex]
[tex] = 44r = 105[/tex]
[tex] = r = \frac{105}{44} [/tex]
[tex] = r = 2.38 \: feet[/tex]
Diameter = r×2 = 2.38 × 2 = 4.76 feet
Area :
[tex] = \pi {r}^{2} [/tex]
[tex] = 3.14 \times 2.38 \times 2.38[/tex]
[tex] = 17.78 \: {ft}^{2} [/tex]
Therefore, Diameter = 4.76 feetRadius = 2.38 feetArea = 17.78 ft²Circumference = 15 feet[tex]\color{plum}\tt \: Answer \: \: 3 :[/tex]Diameter = 2 cm (given)
Radius = D/2 = 2/2 = 1 cm
Circumference :
[tex] = 2 \pi r[/tex]
[tex] = 2 \times 3.14 \times 1[/tex]
[tex] = 6.28 \: feet[/tex]
Area :
[tex] = \pi {r}^{2} [/tex]
[tex] = 3.14 \times 1 \times 1[/tex]
[tex] = 3.14 \: {ft}^{2} [/tex]
Therefore, Diameter = 2 cmRadius = 1 cm Area = 3.14 ft²Circumference = 6.28 feet[tex]\color{plum}\tt \: Answer \: \: 4 :[/tex]Radius = 4.3 mm
Diameter = r×2 = 4.3 × 2 = 8.6 mm
Circumference :
[tex] = 2\pi r[/tex]
[tex] = 2 \times 3.14 \times 4.3[/tex]
[tex] = 27 \: mm[/tex]
Area :
[tex] = \pi {r}^{2} [/tex]
[tex] = 3.14 \times 4.3 \times 4.3[/tex]
[tex] = 3.14 \times 18.49[/tex]
[tex] = 58.05 \: {mm}^{2} [/tex]
Therefore, Diameter = 8.6 mmRadius = 4.3 mmArea = 58.95 mm²Circumference = 27 mmHow did you solve the equation
convert the following percent to a fraction and decimal. (THIS IS NOT MULTIPLE CHOICE!!)
a. 90% b. 0.9% c 900% d 9/10%
Answer:
90%=9/10=0.9
0.9=90%=9/10
900%=900/1000=0.9
9/10%=0.9=90%
Step-by-step explanation:
Answer: A 9/10 or 0.9
B 0.9 = 9/10 or 90%
C 0.9 or 900/1000
D 0.9 or 90%
Step-by-step explanation:
Challenge A large university accepts 40% of the students who apply. Of the students the un
accepts, 30% actually enroll. If 30,000 students apply, how many actually enroll?
Answer:
100,000
Step-by-step explanation:
Answer:
The answer is: 3,600 students enroll.
Step-by-step explanation:
1) There's 30,000 applicants to start. 40% of them are accepted, and 40% of 30,000 is 12,000 students.
2. 30% of those 12,000 students enroll, so that's 3,600 students.
Hope this helps! Feel free to give me Brainliest if you feel this helped. Have a good day, and good luck on your assignment. :)
