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3 years ago

Is 1/40 grater than or less then 4%?

1 answer:

3 0

Greater. Four percent is 4 out of 100. So if you made them an equal denominator, 4% would be 160/4000 while 1/40 would be 100/4000

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A chemical substance has a decay rate of 6.9% per day. The rate of change of an amount N of the chemical is given by the equatio

GaryK [48]

Answer:

a) $N=N_0e^{-0.069t}$

b) $N=696.9$ grams

c) $t=10$ days

Step-by-step explanation:

We are going to use separation of variables to solve.

Get all your t's to one side and your N's to opposing side.

$\frac{dN}{dt}=-0.069N$

Multiply both sides by $dt$ :

$dN=-0.069N dt$

Divided both sides by $N$ :

$\frac{dN}{N}=-0.069 dt$

Integrate both sides:

$\ln|N|=-0.069t+C$

The equivalent exponential form is:

$e^{-0.069t+C}=N$

Using law of exponents you can write this as:

$e^{-0.069t}e^C=N$

$e^C$ is just a positive constant that I'm going to replace with K:

$e^{-0.069t}K=N$

Applying the symmetric property of equality:

$N=e^{-0.069t}K$

Applying the commutative property of multiplication:

$N=Ke^{-0.069t}$

K actually represents the initial amount of chemical substance since when plugging in 0 for t you get K for N, like so:

$N=Ke^{-0.069 \cdot 0}$

$N=Ke^{0}$

$N=K(1)$

$N=K$

We are given at time 0 the amount of chemical substance,N, is K. They want us to represent this value with $N_0$ instead. So the exponential equation is:

$N=N_0e^{-0.069t}$

We are given $N_0=800$ at $t=0$ .

We are asked to find how much of the chemical substance, N, remains after 2 days. So we replace t with 2 in $N=800e^{-0.069t}$ :

$N=800e^{-0.069 \cdot 2}$

Put into calculator:

$N=696.9$ (this was rounded to the nearest tenths)

The last part is asking for how many days will it take a initial 800 grams to go down to half of 800 grams.

We need to see the following equation:

$\frac{1}{2}(800)=800e^{-0.069t}$

$400=800e^{-0.069t}$

Divide both sides by 800:

$\frac{400}{800}=e^{-0.069t}$

Reduce the fraction:

$\frac{1}{2}=e^{-0.069t}$

Convert to logarithmic form:

$\ln(\frac{1}{2})=-0.069t$

Divide both sides by -0.069:

$\frac{\ln(\frac{1}{2})}{-0.069}=t$

Input into calculator:

$10.0=t$

$t=10.0$

$t=10$

6 0

3 years ago

F n and m are integers and n2 m2 is even, which of the following is impossible?

iren2701 [21]

So, I think that you mean that

n²+m² is even? (the "plus" sign is missing, but I think this is correct).

this can only happen if either:

both n and m are even
or
both n and m are odd

That's because a sum of two expressions is even if either both or none of the expressions summed is even, and a power of a number is even only if the number is even too.

are those some of the options?

yes!
n and m are even,- possible!
n and m are odd, -possible!
n+m is even, - possible; it would be the case if either both n and m are even or both n and m are odd n+m is odd,

so the option we'll choose is:

none of these are impossible

6 0

4 years ago

5/8 divided by 13/3 integer or simplified fraction

sveta [45]

Answer:

a simplified fraction

Step-by-step explanation:

4 0

3 years ago

Solve this proportion x/14 6/21

Gemiola [76]

Answer:

X=4

Step-by-step explanation:

Solution: x equals 4

x/14-(6/21)=0

1. Simplify 2/7

x/14- 2/7 is 0

It’s too much steps

5 0

3 years ago

To the nearest cent what is $47.40 decreased by 58%

Rashid [163]

4700 is the answer hope it helps

3 0

4 years ago

Read 2 more answers