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pantera1 [17]
3 years ago
6

Bane currently uses a ratio of Venom to water, 8:31. if Bane used 16 cups if Venom, how many cups water does he need?

Mathematics
1 answer:
san4es73 [151]3 years ago
3 0

Answer:

62 cups

Step-by-step explanation:

This ratio problem can easily be solved if we write 2 fractions and equate to each other.

The leftside fraction would be the "ratio", that is 8/31.

The right side fraction would be the actual amount, that is:

16 cups for venom

x cups for water

We need to find x. Remember to keep Venom on top (numerator) and water on bottom (denominator). Let's write the ratios (fractions) and equate and cross multiply and solve:

\frac{8}{31}=\frac{16}{x}\\8x=16*31\\8x=496\\x=\frac{496}{8}\\x=62

So,

Bane needs 62 cups of water

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Step-by-step explanation:

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation  

                y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

             \frac{dy}{dx} = -2( 2x) +5(1) =  -4x +5

Equating zero

            \frac{dy}{dx} = 0

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⇒      -4 x = -5

⇒          x = \frac{5}{4}

<em> The rocket hit the ground at     </em>x = \frac{5}{4}<em></em>

<u><em>Step(ii):</em></u>-

    \frac{dy}{dx}  =  -4x +5  ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

 \frac{d^{2} y}{dx^{2} }  = - 4(1)

The maximum height at x = \frac{-5}{4}

  y = -2 x² + 5 x + 7

 y = -2 (\frac{5}{4})^{2}  + 5 (\frac{5}{4} )  + 7

y = \frac{-2(25)+ 25 (16)+7(64)}{64}

y = \frac{798}{64} = 12.468 feet

<em>The maximum height of the rocket = 12.468 feet</em>

       

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3 years ago
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