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A bird enclosure at a zoo was initially housed with 350 birds. The total population of birds in the enclosure is expected to inc

Lelu [443]

ANSWER

Find out which function accurately describes the population of the birds in the enclosure, f(x), after x years.

To proof

As given

A bird enclosure at a zoo was initially housed with 350 birds.

The total population of birds in the enclosure is expected to increase every year by 5%.

Now the increase in the population of the bird is shown by

$f(x) = a ( 1 + \frac{r}{100})^{t}$

where a = initial value

r =rate percent

t = time

put the value in the above equation

initial population = 350 bird

rate = 5 %

time = x

than

$f (x) = 350 ( 1 + 0.05)^{x}$

this equation represented the population of the birds in the enclosure after x years .

Hence proved

7 0

4 years ago

Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Expr

Levart [38]

Ratio is :- Heads: number of coin flips

So now we plug in the numbers.

A ratio compares two values.

Ratio: 125:300

Now we simplify by dividing both values by the same number.

125:300 =

125/5= 25
300/5= 60

We aren't done yet, because we can still simplify more.

25:60=

25/5= 5
60/5= 12

Our final ratio: 5:12

5 0

3 years ago

Read 2 more answers

Find the volume of the ellipsoid x^2+y^2+9z^2=64

yuradex [85]

Parameterize the ellipsoid using the augmented spherical coordinates:

$\begin{cases}x=\frac18\rho\cos\theta\sin\varphi\\\\y=\frac18\rho\sin\theta\sin\varphi\\\\z=\frac38\rho\cos\varphi\end{cases}$

Then the Jacobian for the change of coordinates is

$\mathbf J=\dfrac{\partial(x,y,z)}{\partial(\rho,\theta,\varphi)}=\begin{bmatrix}\frac18\cos\theta\sin\varphi&-\frac18\rho\sin\theta\sin\varphi&\frac18\rho\cos\theta\cos\varphi\\\\\frac18\sin\theta\sin\varphi&\frac18\rho\cos\theta\sin\varphi&\frac18\rho\sin\theta\cos\varphi\\\frac38\cos\varphi&0&-\frac38\rho\sin\varphi\end{bmatrix}$

which has determinant

$\det\mathbf J=-\dfrac3{512}\rho^2\sin\varphi$

Then the volume of the ellipsoid is given by

$\displaystyle\iiint_E\mathrm dx\,\mathrm dy\,\mathrm dz=\iiint_E|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

where $E$ denotes the spaced contained by the ellipsoid. In particular, we have the definite integral and volume

$\displaystyle\frac3{512}\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\dfrac\pi{128}$