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3 years ago

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Can somebody pls help me I appreciate it

1 answer:

LuckyWell [14K]3 years ago

7 0

y=3-2x

please mark brainliest and have a nice day!

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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

A plot of land is in the shape of a triangle. If one side is x meters, a second side is

Rudiy27

First side is = x
Second side is = 3x-3
Third side is = 44x - 66

Perimeter = Sum of sides
P = x + 3x + 44x -66 -3
P = 48x - 69

8 0

3 years ago

The top question. How do I find the equation of the graph?

Setler79 [48]

This document has the answer

5 0

3 years ago

Set up the equation to find the AREA of the SMALL rectangle with a length of (x) and width (x+7)

Igoryamba

<u>Answer:</u>

<h3>( $x$ ) x ( $x + 7$ ) </h3>

<u>Step-by-step explanation:</u>

To find the area of a rectangle, we have to multiply the length with the width.

In the question, the given length is 'x' and the width given is 'x +7'

So, the area would be

( $x$ ) x ( $x + 7$ )

The area = $x^{2} + 7x$

So, the equation to find the area of such a rectangle would be:-

( $x$ ) x ( $x + 7$ )

7 0

2 years ago

Solve the equation. 9+2 14x – 31 = 19<br> Please answer it step by step

siniylev [52]

Answer:

$x = \frac{41}{28} = 1 \frac{13}{28}$

Step-by-step explanation:

$9 + 2(14x - 3) = 19$

$9 + 28x - 31 = 19$

$- 22 + 28x = 19$

$28x = 19 + 22$

$28x = 41$

$\boxed{\green{x = \frac{41}{28} = 1 \frac{13}{28}}}$

4 0

3 years ago