If [k + 4 -1] [3 k - 6] = [a -1] [3 -4], then find the value of a. If determinant [k 8 4] = 4, then value of k will be -3, 3, -5, 5. If y = secx - 1 / secx + 1 then find the... If [k + 4 -1] [3 k - 6] = [a -1] [3 -4], then find the value of a. If determinant [k 8 4] = 4, then value of k will be -3, 3, -5, 5. If y = secx - 1 / secx + 1 then find the value of dy/dx. If r = 4.9 cm, the rate of increase of circumference is 1.47, 6π, 6.1π, none of these. Value of ∫(1/√(1-x^2))dx will be 2, -1, -2, 1. The degree of the differential equation dy/dx + y = e^x will be 1, 2, 0, 3. Find the angle between two vectors a and b. Read more

Steps to Solve

1. Finding the rate of increase of circumference

The circumference ( C ) of a circle is given by the formula:

$$ C = 2\pi r $$

To find the rate of increase of the circumference with respect to time, we differentiate both sides with respect to ( t ):

$$ \frac{dC}{dt} = 2\pi \frac{dr}{dt} $$

2. Substituting the values

Given that ( \frac{dr}{dt} = 0.7 ) cm/s and ( r = 4.9 ) cm, we substitute these values into the derivative:

$$ \frac{dC}{dt} = 2\pi (0.7) $$

3. Calculating the final answer

Now calculate:

$$ \frac{dC}{dt} = 2 \times 0.7 \times \pi = 1.4\pi $$

The numerical value will provide the required increase in circumference per second.

4. Comparing with the options

The options are:

• (a) ( 1.47 )
• (b) ( 6\pi )
• (c) ( 6.1\pi )
• (d) None of these

We know that ( 1.4\pi \approx 4.4 ) which does not match any provided options, suggesting to round to the given values or clarify the context.