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4 years ago

8

There were 149 angelfish and goldfish in an aquarium. There were twice as many guppies as angelfish. After selling 35 goldfish

there are half as many goldfish as angelfish. How many fish are left in the aquarium?

2 answers:

jeka57 [31]4 years ago

5 0

$x- \ angelfish\\
y-\ goldfish\\
z-\ guppies\\\\
\left\{\begin{array}{l} x+y=149\\2x=z\\2(y-35)=x \end{array} \\\\

2y-70+y=149\\
3y-70=149\ \ |Add\ 70\\
3y=219\ \ |:3\\y=73\\\\
x=149-73\\
x=76\\
z=2x\\
z=2*76=152\\\\
All\ fishes:\\
x+y+z=76+152+73=301\\
After\ selling\ 35\ goldfishes\ there\ are\ 266\ fishes\ in\ aquarium.
$

aleksklad [387]4 years ago

4 0

149goldfish and 149angilfish Guppies Twice as many angilfish So 149angilfish × 2 ------------- 298guppies 298 +148 -------- 447total fish 447 - 35 --------- 414 left over

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2.29 ft of side length and 1.14 height

Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

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3 years ago

A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u

OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

$\displaystyle\frac{8000\pi\sqrt{2}}{3}$

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

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$\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx$

That can be solved by substitution:

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The limits of integration also change:

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$\displaystyle -\int_{200}^{0}\pi \sqrt{u}du$

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

$\displaystyle \int_{0}^{200}\pi u^{1/2}du$

Then applying the basic rule we get:

$\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}$

Since that is just half of the solid, we multiply by 2 to get the complete volume:

$\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}$

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3 years ago

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natta225 [31]

Answer:

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Step-by-step explanation:

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We complete the square to obtain;

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Multiply through by 4; to get

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Write in general form;

$4(x')^2+4(y')^2-10x'-10\sqrt{3}y'-12 =0$

Divide through by 2.

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4 years ago