Question

cal asymptotes of rational functions
visible light | wavelength (m) | frequency (thz) | k
blue | 450 | a | 301,500
green | 520 | 580 | b
yellow | c | 540 | 302,400
red | 635 | 480 | 304,800
a = 670
b = 301, 600
c =

Explanation:

Step1: Identify the relationship

We can observe that for each visible light, the product of wavelength (\( \lambda \)) and frequency (\( f \)) might be related to \( k \), or maybe \( k = \lambda \times f \)? Wait, let's check with Red: \( 635 \times 480 = 304,800 \), which matches \( k = 304,800 \). For Yellow: \( c \times 540 = 302,400 \).

Step2: Solve for \( c \)

We have the equation \( c \times 540 = 302,400 \). To find \( c \), we divide both sides by 540: \( c = \frac{302400}{540} \).

Step3: Calculate the division

\( \frac{302400}{540} = \frac{30240}{54} = \frac{5040}{9} = 560 \)? Wait, no, wait: 540 × 560 = 540×500 + 540×60 = 270000 + 32400 = 302400. Wait, but let's check again. Wait, 302400 ÷ 540: divide numerator and denominator by 10: 30240 ÷ 54. Divide by 6: 5040 ÷ 9 = 560. Wait, but let's check with other rows. Wait Blue: 450 × a = 301500? Wait 450 × 670 = 450×600 + 450×70 = 270000 + 31500 = 301500, which matches \( k = 301,500 \). Green: 520 × 580 = 301,600? Wait 520×580: 500×580 + 20×580 = 290000 + 11600 = 301600, which matches \( b = 301,600 \). So the relationship is \( k = \lambda \times f \). So for Yellow: \( c \times 540 = 302,400 \), so \( c = 302400 / 540 = 560 \). Wait, but let's compute 302400 ÷ 540: 540 × 560 = 302400, yes. So \( c = 560 \).

Answer:

\( c = 560 \)