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3 years ago

The fact that sin(150°) = .5 and sin(-150°) = -.5 implies that the sine function is which type of function?

1 answer:

7 0

Answer: Choice A) Odd

The function sin(x) is odd because sin(-x) = -sin(x) for all values of x

As the example shows, sin(150) = 0.5 and sin(-150) = -0.5, so this shows sin(-150) = -sin(150).

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In 1859, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponen

Mashcka [7]

Answer:

a) P' = P

$P(t) = 24e^{0.693t}$ where t is step of 6 months

b) 7.7 years

c)1064.67 rabbits/year

Step-by-step explanation:

The differential equation describing the population growth is

$\frac{dP}{dt} = P$

Where t is the range of 6 months, or half of a year.

P(t) would have the form of

$P(t) = P_0e^{kt}$

where $P_0 = 24$ is the initial population

After 6 month (t = 1), the population is doubled to 48

$P(1) = 24e^k = 48$

$e^k = 2$

$k = ln(2) = 0.693$

Therefore $P(t) = 24e^{0.693t}$

where t is step of 6 months

b. We can solve for t to get how long it takes to get to a population of 1,000,000:

$24e^{0.693t} = 1000000$

$e^{0.693t} = 1000000 / 24 = 41667$

$0.693t = ln(41667) = 10.64$

$t = 10.64 / 0.693 = 15.35$

So it would take 15.35 * 0.5 = 7.7 years to reach 1000000

c. $P' = P_0ke^{kt}$

We need to resolve for k if t is in the range of 1 year. In half of a year (t = 0.5), the population is 48

$24e^{0.5k) = 48$

$0.5k = ln2 = 0.693$

$k = 1.386$

Therefore, $P' = 1.386*24e^{1.386t}$

At the mid of the 3rd year, where t = 2.5, we can calculate P'

$P' = 1.386*24e^{1.386*2.5} = 1064.67$ rabbits/year

4 0

3 years ago

F(x) = -2x + 5<br> f ( ) = 13

scZoUnD [109]

Answer:

Okay, I haven't done this a long time however I believe with this you have to solve the equation by doing substitution.

Step-by-step explanation:

so, if f (x) equals 13, you replace the x in the equation to 13.

f(x)=-2x+5

f(x)=-2(13)+5

f(x)=26+5

f(x)=31

I believe 41 would be your answer. Hope this is right and it helped!

4 0

3 years ago

What is a point-slope equation of the line with slope -10 that goes through the point (1,4)

KatRina [158]

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad \qquad \qquad 
% slope = m
slope = m\implies -10
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-4=-10(x-1)$

8 0

3 years ago

Read 2 more answers

(25 POINTS) Write the inequality of the following graph?

Ainat [17]

Answer:

f(x) > -x + 2

Step-by-step explanation:

First I found the equation of the line.

The y intercept is at 2 so I know to add 2 at the end

The slope is -1 since it is going downwards

Since the top side is shaded, that represents greater than, if it was shaded downwards, it would be less than

Putting all that together, the equation is f(x) > -x + 2

5 0

3 years ago

Please Helppppppppppp

sineoko [7]

Answer:

The width of the actual pool is 12 meters

Step-by-step explanation:

You can put Kiara's scale into a ratio or fraction to help visualize it better: 13/6. Now, let's put what we do know for the other ratio into a fraction. we know that the pool is 26 centimeters wide, and since the 26 matches with the 13, that goes in the numerater. since we don't know the denominator, we can just put 26/x (you can use whatever letter you like but I'll use x here)

So in order to get 13/6 to 26/x, we need to find how to figure out what we are doing to the original fraction. Since 13 x 2= 26, it looks like we are multiplying the ratios by 2. Now that we know that, we can multiply the denominator (6) by 2 to equal 12, our answer.

Hope this helps :)

8 0

2 years ago