Question 23 of 70intermediate🔧 ApplyShort Answer4 marks

The length LL (in centimetre) of a copper rod is a linear function of its Celsius temperature CC. In an experiment, if L=124.942L = 124.942 when C=20C = 20 and L=125.134L = 125.134 when C=110C = 110, express LL in terms of CC.

Correct Answer

L = 41875\frac{4}{1875}C + 1873491500\frac{187349}{1500} or equivalently L = 16C+9367457500\frac{16C + 936745}{7500}

Exercise: EXERCISE 9.2 | Q: 15 | (Chapter: 14)
For More Understanding

Explanation

This question tests the concept of linear function and slope-intercept form from the chapter. Since L is a linear function of C, we can write L = mC + c, where m is the slope and c is the L-intercept. The slope is calculated using the two given points (20, 124.942) and (110, 125.134). Using the slope formula m = (L₂ - L₁)/(C₂ - C₁), we get m = 0.192/90 = 4/1875. The intercept c is found by substituting one point into the equation.

Solution Steps

  1. Step 1: Since L is a linear function of C, write L = mC + c (slope-intercept form).

  2. Step 2: Calculate the slope using given points (20, 124.942) and (110, 125.134): m = (125.134 - 124.942)/(110 - 20) = 0.192/90 = 4/1875

  3. Step 3: Find the intercept c using point (20, 124.942): c = L - mC = 124.942 - (4/1875)(20) = 124.942 - 80/1875 = 124.942 - 16/375

  4. Step 4: Convert to fractions: 124.942 = 62471/500 = 187413/1500 and 16/375 = 64/1500

  5. Step 5: Calculate c = (187413 - 64)/1500 = 187349/1500

  6. Step 6: Write the final equation: L = (4/1875)C + 187349/1500 or L = (16C + 936745)/7500

PreviousNext