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____ [38]
2 years ago
13

Emily practices piano for 2/3 of an hour on Monday and 1/2 hour on Wednesdays. How many hours does Emily spend practicing piano

in one week?​
Mathematics
1 answer:
Sergeu [11.5K]2 years ago
4 0

Answer:

50 minutes

Step-by-step explanation:

Given:

\bullet \ \ \text{Monday:} \ \dfrac{2}{3} \times \text{Hour}\\\\\bullet \ \text{Wednesday:} \ \dfrac{1}{2} \times \text{Hour}

Since Emily only practiced on Monday and Wednesday, the sum of time on both days is the time Emily practiced on the piano for a week.

\implies \text{Monday + Wednesday = Total time practiced on piano for a week}

<u>Substitute the times in the equation</u>

\implies (\dfrac{2}{3}  \times \text{Hour}) + (\dfrac{1}{2}  \times \text{Hour}) = \text{Total time practiced on piano for a week}

<u>Simplify the equation</u>

\implies (\dfrac{2}{3}  \times 60 \ \text{minutes}) + (\dfrac{1}{2}  \times 60 \ \text{minutes}) = \text{Total time practiced on piano for a week}

\implies (20 \ \text{minutes}) + (30 \ \text{minutes}) = \text{Total time practiced on piano for a week}

\implies \boxed{50 \ \text{minutes} = \text{Total time practiced on piano for a week}}

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Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

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The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

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3 years ago
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