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3 years ago

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The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled

by: m(x)=-x^2+14x How many centimeters of rain will produce the maximum number of mosquitoes?

1 answer:

GarryVolchara [31]3 years ago

4 0

Answer:

7 centimeters of rain will produce the maximum number of mosquitoes (49 millions of mosquitoes)

Step-by-step explanation:

we have the function

$m(x)=-x^2+14x$

where

m(x) is the number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes)

x is the rainfall (in centimeters)

This is a vertical parabola open downward

The vertex represent a maximum

The x-coordinate of the vertex represent the centimeters of rain that will produce the maximum number of mosquitoes

so

Convert the quadratic equation into vertex form

$m(x)=-x^2+14x$

Factor -1

$m(x)=-(x^2-14x)$

Complete the square

$m(x)=-(x^2-14x+7^2)+7^2$

$m(x)=-(x^2-14x+49)+49$

Rewrite as perfect squares

$m(x)=-(x-7)^2+49$

The vertex is the point (7,49)

therefore

7 centimeters of rain will produce the maximum number of mosquitoes (49 millions of mosquitoes)

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Need help quick, please?

My name is Ann [436]

Remember that the general formula for a circle is <span>
(x – h)</span>² + (y – k)² = r²<span>, where (h,k) is the coordinate of the center.
We already know that (h,k) = (5,-4), since we know the center's coordinates. We need to find r, the radius, using the distance between the center and the point (-3,2).
To do this, we can either use the distance formula, or plug in the points in our circle equation and solve for r.
Let's do the second one, plugging in and solving for r.
We can use the point (-3,2) for (x,y):
</span>(x – h)² + (y – k)² = r²
(-3 - 5)² + (2 - -4)² = r²
(-8)² +(6)² = r²
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The equation of the circle is:
(x – 5)² + (y + 4)² = 100

8 0

3 years ago

Exercise 7.3.5 The following is a Markov (migration) matrix for three locations        1 5 1 5 2 5 2 5 2 5 1 5 2 5 2 5 2

fredd [130]

Answer:

Both get the same results that is,

$\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

Step-by-step explanation:

Given :

$\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

and initial population,

$\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]$

a) - After two times, we will find in each position.

$P_2=[P].[M]^2=[P].[M].[M]$

$M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]$

$=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

b) - With in migration process, 500 people are numbered. There will be after a long time,

$After\;inifinite\;period=[M]^n.[P]$

$Then,\;we\;get\;the\;same\;result\;if\;we\;measure [M]^n=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]$

$=\left[\begin{array}{ccc}140\\160\\200\end{array}\right]$

4 0

3 years ago

Please explain to me how to find y. I’m so confused.

koban [17]

Every triangle angles add up to 180.

So because one angle is 90 degrees you would subtract it from 180 to get 90 and then divide it by two which is 45 degrees.

Hope this helps, have a nice day! :)

7 0

3 years ago

What is the multiplicative rate of change of the function

mario62 [17]

Answer: B $\frac{2}{3}$

Step-by-step explanation:

From the given table

When x changes from 1 to 2 , value of y changes from 6 to 4

The multiplicative rate of change= $\frac{4}{6}=\frac{2}{3}$

Similarly we can check

When x changes from 2 to 3 , value of y changes from 4 to $\frac{8}{3}$

The multiplicative rate of change= $\frac{\frac{8}{3}}{4}=\frac{2}{3}$

When x changes from 3 to 4 , value of y changes from $\frac{8}{3}$ to $\frac{16}{9}$

The multiplicative rate of change= $\frac{\frac{16}{9}}{\frac{8}{3}}=\frac{2}{3}$

Therefore, the multiplicative rate of exponential function = $\frac{2}{3}$

5 0

3 years ago

Read 2 more answers

Find the maximum value or minimum value for the function f(x) = 0.15(x + 1)² - 3.

il63 [147K]

Answer:

The minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

Step-by-step explanation:

Given function is $f(x) = 0.15(x + 1)^2 - 3$

We need to find the maximum value or the minimum value for the function.

Now, differentiate $f(x) = 0.15(x + 1)^2 - 3$ w.r.t $x$ .

$f'(x) =\frac{d}{dx}(0.15(x + 1)^2 - 3)\\f'(x)=\frac{d}{dx}(0.15(x+1)^2-\frac{d}{dx}(3)\\$

$f'(x)=2\times 0.15(x+1)\frac{d}{dx}(x+1)-0\\f'(x)=0.3(x+1)(1)\\f'(x)=0.3(x+1)$

Now, we will equate $f'(x)=0$ to find critical point.

$0.3(x+1)=0\\x=-1$

Plug this critical point in to the function $f(x) = 0.15(x + 1)^2 - 3$ we get,

$f(-1) = 0.15(-1 + 1)^2 - 3\\f(-1)=-3$

Also, $f''(x)=0.3$ which is positive, We have minimum value.

So, the minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

7 0

3 years ago