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3 years ago

How should this problem be solved? (a^3)^2

Mathematics

1 answer:

fiasKO [112]3 years ago

7 0

(a^3)^2
= a^(3*2)
= a^6
or
a^3 * a^3
= a^(3+3)
= a^6

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Step-by-step explanation:

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A school is selling tickets to a drama performance. On the first day of ticket sales the school sold 3 adult tickets and 1 child

baherus [9]

Answer:

System of linear equations

$\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.$

a: adult ticket price and c: child ticket price

Step-by-step explanation:

This system of equations can be used to find the price of the adult and child tickets.

We have two equations (one for each day) and two unknowns (adult ticket price and child ticket price).

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we have for the first day that 3 adult tickets and 1 child ticket adds $38:

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and for the second day we have that 2 adult tickets and 2 child tickets adds $52:

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If we write this as a system of equations, we have:

$\left\{\begin{matrix} 3a+c=38 \\\\ 3a+2c=52 \end{matrix}\right.$

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2 years ago

Find the derivative.

krek1111 [17]

Answer:

$\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Expanding/Factoring

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \frac{\sqrt{x}}{e^x}$

Step 2: Differentiate

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Basic Power Rule: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}$
Exponential Differentiation: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}$
Simplify: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}$
Rewrite: $\displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}$
Factor: $\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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The answer to this is C.

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