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Mathematics

1 answer:

lora16 [44]3 years ago

5 0

The answer is: the light rays refract toward a central axis.

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Given the expression 12 over 12 to the third power.

4vir4ik [10]

Part 1:
Before we begin, you need to remember the following rule:
$\frac{x^a}{x^b} = x^{a-b}$

The given expression is:
$\frac{12}{12^3}$

Since the base is the same in both numerator and denominator, we can apply the above rule. This means that:
$\frac{12}{12^3}$ = 12¹⁻³ = 12⁻²

Part 2:
Before we begin, you need to remember the following rule:
x⁻ᵃ = $\frac{1}{x^a}$

Now, from part 1, we simplified the expression into 12⁻²
Since the power is negative, we can apply the above rule.
This means that:
12⁻² = $\frac{1}{(12)^2} = \frac{1}{12*12} = \frac{1}{144}$

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Verify the identity. Show your work. (1 + tan^2u)(1 - sin^2u) = 1

yuradex [85]

$\bf \textit{Pythagorean Identities}
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sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)
\\\\ 1+tan^2(\theta)=sec^2(\theta)\\\\
-------------------------------\\\\\
[1+tan^2(u)][1-sin^2(u)]=1
\\\\\\\
[sec^2(u)][cos^2(u)]\implies \cfrac{1}{cos^2(u)}\cdot cos^2(u)\implies \cfrac{cos^2(u)}{cos^2(u)}\implies 1$

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