Solution :
Given :
The rate of change of y is proportional to y.
Therefore, [tex]$\frac{dy}{dt} \propto y$[/tex]
[tex]$\frac{dy}{dt} = k y$[/tex] , where k is the proportionality constant
[tex]$\frac{dy}{y}=k \ dt$[/tex]
Taking integration on both the sides,
[tex]$\int \frac{dy}{y}=\int kdt$[/tex]
[tex]$\int \frac{dy}{y}=k\int dt$[/tex]
[tex]$\ln |y| = kt+C$[/tex], where C is the integration constant
[tex]$y=e^{kt+C}$[/tex]
[tex]$y=e^{kT}e^C$[/tex]
[tex]$y(t)=C_1e^{kt}$[/tex] ....................(1)
When t = 0, y = 2, so
[tex]$2=c_1e^{k\times 0}$[/tex]
[tex]$2=c_1e^{ 0}$[/tex]
[tex]$2=C_1$[/tex]
From equation (1),
[tex]$y=2e^{kt}$[/tex] ........................(2)
when t = 2, y = 4
[tex]$4=2e^{k\times 2}$[/tex]
[tex]$e^{2k}=\frac{4}{2}$[/tex]
[tex]$e^{2k}=2$[/tex]
[tex]$2k= \ln(2)$[/tex]
[tex]$k=\frac{1}{2} \ln(2)$[/tex]
From (2),
[tex]$y=2e^{\frac{1}{2}\ln(2)t}$[/tex]
[tex]$y=2e^{\frac{t}{2}\ln(2)}$[/tex]
[tex]$y=2e^{\ln(2)^{t/2}}$[/tex]
[tex]$y=2.2^{t/2}$[/tex]
When t = 3,
[tex]$y = 2 . 2 ^{3/2}$[/tex]
[tex]$y=2[(\sqrt2)^2]^{3/2}$[/tex]
[tex]$y= 2. 2\sqrt2$[/tex]
[tex]$y=4 \sqrt2$[/tex]
Arrange the numbers in descending order 374430,802343,980377 and 230392,650863,364321
Please help!!!!!!!!!!! Will give brainlist
Answer:
0.2
Step-by-step explanation:
When you have a decimal problem you add a 0 before the number. But if its a fraction ike 4 5/8 the decimal would be 4.58.
PLS HELP ME WITH THIS PLS
Answer: $0.50 per pound of bananas
Step-by-step explanation:
Take the total price of five pounds of bananas ($2.50) and divide them
2.50/5
You will get
$0.50
Arianna and Tiana go for a mani/pedi. When they get their check, they see that their total bill with tax is $50.25. Arianna and Tiana had good service and decided to leave the staff a 20% tip on the total cost of their mani/pedi. What was the total amount of money that Arianna and Tiana spent at the salon?
Answer:
20/100 × 50.25/1
=10.05
$50.25 + $10.05
=$60.3
Round 15.92453786 to the nearest thousandths
Answer:
15.925
Step-by-step explanation:
PLEASE HELP QUICKLY!! The sum of two numbers is 12. Their product is 2. What are the two numbers?
Answer:
the answer is six and two
find the volume of rectangular prism of 2,3,6
Answer:
36 un³
Step-by-step explanation:
2 un *3 un *6 un = 6*6 = 36 un³
A pet store has a special offer this weekend. For every 120 dollors that customers spend, the store will donate 3 dollors to a pet rescue program. How much do customers have to spead in order to raise 1000 for the pet rescue program
Answer:
40,000
Step-by-step explanation:
The computation of the amount spend by the customers is shown below:
For every 120 dollars will donate $3 dollars
Now for 1,000 it would spend
= 1000 × 120 ÷ 3
= 40,000
Which city had the highest temperature?
Which city had the lowest temperature?
Which city had a temperature greater than Oakland?
What was the difference in temperature between Detroit and Oakland?
degrees Celsius.
What is the values of a and b on the line?
[tex] \sf \red \: a = 6 \\ \sf \: b = 4[/tex]
#BeBrainly :)
Answer: a = 6 b = 6
Step-by-step explanation:
Catherine put $5500 into a savings account that earns 4% compound
interest monthly. After six months, how much money will she have total?
The cargo area of a truck is ink 1/2 feet long 6 ft wide and 10 1/2 ft High the volume of the cargo area is what cubic feet
Answer:
31 1/2 ft^3
Step-by-step explanation:
volume = length x breadth x height
1/2 x 6 x 10 1/2
1/2 x 6 x 21/2 = 63/2 = 31 1/2 feet³
1, Find the value of a in the following equation 3a=24.
If f(x)=4x^2 and g(x)=x+1, find (f-g)(x)
Answer:
I need help
Step-by-step explanation:
-5(3v-2)+8v=5(v+5)
PLS HELP FAST
Answer:
v = -1 1/4
Step-by-step explanation:
1. -5 x -1 1/4 = 3 3/4
2. -5 x -2 = +10
3. 8 x 1 1/4 = 10
4. 5 x 1 1/4 = 6 1/4
5. 5 x 5 = 25
Now just substitute the values.
Hope that helps!
Find the distance between these two points (5,9) and (-7,-7)
Answer:
20
Step-by-step explanation:
Use the distance formula:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}\\d = \sqrt{(-7 - 5)^2 + (-7 - 9)^2}\\d = \sqrt{(-12)^2 + (-16)^2}\\d = \sqrt{144 + 256}\\d = \sqrt{400} = 20[/tex]
The distance between the points (5,9) and (-7,-7) will be 20 units.
What is the distance between two points?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D² = (x - p)² + (y - q)²
The points are given below.
(5,9) and (-7,-7)
Then the distance between the points will be
D² = (5 + 7)² + (9 + 7)²
D² = 12² + 16²
D² = 144 + 256
D² = 400
D = 20 units
Learn more about the distance between two points here:
brainly.com/question/16410393
#SPJ2
It’s due tonight help please
Answer:
:)
Step-by-step explanation:
A) 4,4
B) 2,2
C) 4,3
Hope this helps
HEEEEEELP MEEEEEEEEEEEE
How to add/subtract like radical expressions?
[tex] \sf{in \: your \: own \: words \: please}[/tex]
9514 1404 393
Explanation:
"Like" radicals can be added and subtracted in the same way any like terms can be combined. It can be helpful to simplify the radical as much as possible so that it can be seen whether the radicals are "like" or not.
Examples:
√2 +√3 . . . . cannot be combined
√2 +√8 = √2 +2√2 = 3√2 . . . . the simplified radicals can be combined
Area of shape please help
Answer:
i think its 230cm but i could be wrong let me know
Step-by-step explanation:
What's a linear function that has a slope of -3 and a y intercept of -2?
Answer:
y = -3x - 2
Step-by-step explanation:
Y = Mx + b
[slope = m, y-intercept = b]
plug in values:
y = -3x - 2
(P.S. - I saw your last question, sorry people aren't answering. I'll try my best to answer your questions if you have any others :) )
Without the y provided alongside the slope and y intercept, this problem can not be solved.
Step-by-step explanation:
PLEASE HELP ME WITH THIS I FINSIH MY QUARTER TONIGHT FOR SCHOOL AND I NEED TO GET THIS DONE!! Austin and his children went to the grocerie store and bought 14$ worth of apples and peaches. Each Apple costs 1$ and each peach cost 2$ he bought a total of 9 apples and peaches all together. Graphically solve a system of equations to determine the number of x, apples and y, peaches
Answer:
[tex]1a+2p=14\\a+p=9\\\\a=4\\p=5[/tex]
Step-by-step explanation:
[tex]1a+2p=14\\a+p=9\\\\a+p=9\\a=9-p\\\\1(9-p)+2p=14\\9-p+2p=14\\9+p=14\\p=5\\\\a=9-(5)\\a=4[/tex]
Graphing:
Slope intercept form y=mx+b
a is y, p is x
y=-2x+14
y=-x+9
Intercept at (5,4)
Helppp. Please give workings too.
Answer:
The numerical value is 7.
Step-by-step explanation:
If 4 x is 3 y, then 8 x must be 3 x 2, which is obviously 6.
6y + y = 7y
--
7y/y
=7
1. A rectangular picture 6cm by 8cm is enclosed by a frame 1/2cm wide. Calculate the area of the frame. A.15sq cm B. 20 sq cm C. 13 sq cm D. 16 sq cm E. 17
Answer:
The area of 1/2 cm wide frame = 48 - 35 = 13 cm²
Step-by-step explanation:
Length of rectangular picture frame = 6 cm
Width of rectangular picture frame = 8 cm
Area of rectangular picture frame = 6×8 cm² = 48 cm²
Length, excluding 1/2 cm wide frame of rectangular picture = (6–1/2-1/2) = 5 cm
Width, excluding 1/2 cm wide frame of rectangular picture = (8–1/2-1/2) = 7 cm
Area, excluding 1/2 cm wide frame of rectangular picture = 5×7 cm² = 35 cm²
Area of 1/2 cm wide frame = 48 - 35 = 13 cm²
Therefore, the area of 1/2 cm wide frame = 48 - 35 = 13 cm²
please send the solution
Please use photomath haha
Can someone please check my answer???
Answer:
your answer will be option B
Step-by-step explanation:
hope it helps ^_^
The length of one side of APTV is given. Use the relationship between the sides of a 30°-60°-90° triangle to find the lengths of the other two sides.
Answer:
your answers will be 3 and 6
Step-by-step explanation:
have a nice day !!^_^
i need help please i really don’t get it
Answer: no se ve bien
Step-by-step explanation:
mucha ilumnacion
What is the area of this figure?
Answer:
104
Step-by-step explanation:
Answer:
537 cm²
Step-by-step explanation:
21 × 31 = 651 cm²
4 × 12 = 48 cm²
6 × 11 = 66 cm²
651 - 48 - 66 = 537 cm²
how to factor a polynomial in the form p^2-m^2
HELP!!
Answer: if you are going to put it like p^2-m^2 no one going to have that answer so I need the p and the m like for example the p=5 and the m=4
Step-by-step explanation: so it going to be like
Evaluate for m=4,p=5
5^2−4^2
=9
So I can’t answer how you put it