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2 years ago

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The number of fish in a pond triples every 7 years. By what percent does the population change each year? 0 17% decay O 117% gro

wth O 17% growth O 85.5% growth

1 answer:

Ira Lisetskai [31]2 years ago

7 0

Answer: O 17% growth it was a little bit confusing but this is the answer I came up with

Step-by-step explanation: hope it helps

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7th out of 10 questions

Viktor [21]

Hello!

Let's make each of these ratios have a common denominator of 36.

5/36, 8/36, 6/36, 12/36

As you can see, our largest ratio is 12/36.

Therefore, our answer is D) 1:3.

I hope this helps!

3 0

2 years ago

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Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

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2 years ago

Does the point (4, 8) satisfy the equation y = x + 6

Oksanka [162]

It can, it just depends upon the slope

Do you know what the slope is?

7 0

2 years ago

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Grayson baked 24 sugar cookies. His family ate 1/3 of the cookies. How many cookies did they eat? How many cookies are left?

horrorfan [7]

Answer:

His family ate 8 sugar cookies.

16 sugar cookies are left.

Step-by-step explanation:

His family ate 1/3 <em>of </em>the 24 sugar cookies: 1/3 x 24= 8

How many are left: 24-8=16

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3 years ago

a six sided number cube has faces with the numbers 1 through 6 marked on them. what is the probability that a number less than 3

Charra [1.4K]

1/3 would be the answer

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2 years ago