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3 years ago

9

2.

1 answer:

9966 [12]3 years ago

8 0

Answer:

c. 2/3

Step-by-step explanation:

To find the slope, you subtract y^1 from y^2 and divide it by x^2 - x^1

Our y^2 is 7 and our y^1 is 1.

7-1 = 6

Our x^2 is 3 and our x^1 is -6.

3 - (-6) = 3+ 6 = 9

so our slope is 6/9, reduced is 2/3

I hope this helped, please mark Brainliest, thank you!!

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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:

a)

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:

$N=N_0e^{-0.069t}$

b)

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)

c)

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

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.

Delicious77 [7]

ANSWER

$y = 5\sin( \frac{\pi}{3} x - \frac{2\pi}{3} )$

EXPLANATION

Let the equation of the sine curve be of the form;

$y = a \sin(bx + c)$

where a=5 is the amplitude and period,

$\frac{2\pi}{b} = 6$

This implies that

$b = \frac{2\pi}{6}$

$b = \frac{\pi}{3}$

We substitute the values we got so far into our equation to obtain;

$y = 5\sin( \frac{\pi}{3} x + c)$

When we substitute (2,0) we obtain;

$0= 5\sin( \frac{2\pi}{3} + c)$

Solve for c.

$\sin( \frac{2\pi}{3} + c) = 0$

$\frac{2\pi}{3} + c = \sin^{ - 1} (0)$

$\frac{2\pi}{3} + c = 0$

$c = - \frac{2\pi}{3}$

Hence our equation becomes

$y = 5\sin( \frac{\pi}{3} x - \frac{2\pi}{3} )$

The correct choice is D.

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Ted is a single guy who’s living the good life. The spreadsheet below shows Ted’s cash flow for a month.

svet-max [94.6K]

Its not there, the picture.

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soldi70 [24.7K]

Answer:

A: predictions

Step-by-step explanation:

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Tallahassee, FL has a population of 483,493. New York, NY has 345,876 more people than Tallahassee. Phoenix, AZ has 279,426 less

Svetach [21]

Answer:

600,000

Step-by-step explanation:

Phoenix AZ has approximately 600,000 people

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