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Paha777 [63]
3 years ago
8

Can someone help me for this question?​

Mathematics
1 answer:
xeze [42]3 years ago
8 0

Answer:

Step-by-step explanation:

To find the equation of the tangent to the given function, you must differentiate the function with respect to 'x'. The derivative (y prime) will give the tangent line at any point along the function. After we find the tangent equation, we let x equal zero which will alow us to find the slope at that point.

Begin by bringing the entire denominator to the top. If not, you'll have to do the quotient rule which is very annoying 99% of the time. You will get:

y=5(e^{2x} +3)^{-1}

With this now, you can use the chain rule twice. Begin by differentiating:

\frac{dy}{dx} =5\frac{d}{dx} [e^{2x} +3)^{-1}]

Use the chain rule:

\frac{dy}{dx} =-5(e^{2x} +3)^{-2}\frac{d}{dx} [e^{2x} +3]

Use the chain rule again:

\frac{dy}{dx} =-5(e^{2x} +3)^{-2}[2e^{2x} ]

Simplify:

y'=-\frac{10e^{2x} }{(e^{2x}+3)^{2}}

Let x = 0 to get:

y'=-\frac{10}{4^{2}} =-10/16=-5/8=-0.625

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Steve put 1/8 of the box of baking soda in each one of the five bottles to make them bubble up like volcanoes.

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Hi

As "Steve performed the chemistry experiment in which divided 5/8 of a box of baking soda evenly among the five bottles...", So we only have to make a simple division, therefore \frac{5}{8}Box \div 5 Bottles=\frac{5}{8 \times 5}Box/Bottle=\frac{1}{8} Box/Bottle, so Steve put 1/8 of the box of baking soda in each one of the five bottles.

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