the classroom has four desks in each row there are five rows how many decks five rows how many desks are in the classroom

A solution initially contains 200 bacteria. 1. Assuming the number y increases at a rate proportional to the number present, wri

GuDViN [60]

Answer:

1. $\frac{dy}{dt}=ky$

2.543.6

Step-by-step explanation:

We are given that

y(0)=200

Let y be the number of bacteria at any time

$\frac{dy}{dt}$ =Number of bacteria per unit time

$\frac{dy}{dt}\proportional y$

$\frac{dy}{dt}=ky$

Where k=Proportionality constant

2. $\frac{dy}{y}=kdt$ ,y'(0)=100

Integrating on both sides then, we get

$lny=kt+C$

We have y(0)=200

Substitute the values then , we get

$ln 200=k(0)+C$

$C=ln 200$

Substitute the value of C then we get

$ln y=kt+ln 200$

$ln y-ln200=kt$

$ln\frac{y}{200}=kt$

$\frac{y}{200}=e^{kt}$

$y=200e^{kt}$

Differentiate w.r.t

$y'=200ke^{kt}$

Substitute the given condition then, we get

$100=200ke^{0}=200 \;because \;e^0=1$

$k=\frac{100}{200}=\frac{1}{2}$

$y=200e^{\frac{t}{2}}$

Substitute t=2

Then, we get $y=200e^{\frac{2}{2}}=200e$

$y=200(2.718)=543.6=543.6$

e=2.718

Hence, the number of bacteria after 2 hours=543.6

4 0

3 years ago

Simplify √ 96/8 a.√2/4 b.1/2√3 c.4√3/√2 d. 2√3

VARVARA [1.3K]

The first one is: √ 96/8=2 √ 3

5 0

3 years ago

Solve the equation m²+4m=-2

UNO [17]

Step 1: Subtract -2 from both sides.
m2+4m−(−2)=−2−(−2)
m2+4m+2=0
Step 2: Use quadratic formula with a=1, b=4, c=2.
m=−b±√b2−4ac2a
m=−(4)±√(4)2−4(1)(2)2(1)
m=−4±√82
m=−2+√2 or m=−2−√2

4 0

3 years ago

Read 2 more answers

Guys im stuck on 7 + 3 please help and I have to explain how I got that answer please explain also thanks

blsea [12.9K]

Answer:10

Step-by-step explanation:If you add 3 to seven with your fingers you get 10.

4 0

3 years ago

Read 2 more answers

The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation y = −0.4x2 + 3x, where y is the he

V125BC [204]

We can find the answer by solving the two equations simultaneously.

equation 1: y = -0.4x^2 +3xequation 2: x + y = 10
We need to write equation to with y as the subject:equation 2: y = 10 - x

equation 1 = equation 2:
10 - x = -0.4x^2 + 3x0.4x^2 - 4x + 10 = 02x^2 - 20 + 50 = 0(2x - 10)(x - 5) = 0x = -10/2 or x = 5

But x >= 0 (the question says it's a height above the water), so x = 5

Substituting x = 5 into one of the equations:
y = 10 - x
y = 10 - 5
y = 5

So the answer is C

7 0

3 years ago

Read 2 more answers