Given that a stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of 3.4 ft/sec. Complete parts a through c. a) Find a function for the radius in terms of t. r(t)=___ (Use integers or decimals for any numbers in the expression.)

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SabadisO · Accepted Answer

Step 1   Given that a stone is thrown into a pond, creating a circular ripple that spreads over the pond in such a way that the radius is increasing at a rate of 3.4 ft/sec.   Step 2  Since, in one second the increment in radius is 3.4 ft. So, after t second the increment in radius is given by  r(t)=3.4t  Step 3   Answer: The radius function is given by r(t)=3.4t.

Nick Camelot · Accepted Answer

Answer:3.4 ft/secExplanation:The rate of change of the radius with respect to time is given as 3.4 ft/sec. This means that the derivative of the radius function with respect to time is 3.4:drdt=3.4To find the function for the radius, we need to integrate this expression with respect to time. Integrating both sides gives:∫drdtdt=∫3.4dtr=3.4t+CHere, C represents the constant of integration. Since we are given that the radius starts from zero when t=0, we can determine the value of C.When t=0, r=0, so we substitute these values into the equation:0=3.4(0)+C0=CTherefore, the function for the radius in terms of time is:r(t)=3.4tThe radius increases linearly with time at a rate of 3.4 ft/sec.

Eliza Beth13 · Accepted Answer

Let&#039;s denote the radius of the ripple at time t as r(t). We know that the radius is increasing at a rate of 3.4 ft/sec. This means that the derivative of r(t) with respect to t is equal to 3.4 ft/sec.Using calculus, we can set up the differential equation:drdt=3.4To solve this differential equation, we can integrate both sides with respect to t:∫drdtdt=∫3.4dtThe integral of drdt with respect to t is simply r(t), and the integral of 3.4 with respect to t is 3.4t:r(t)=3.4t+CHere, C is the constant of integration. To determine the value of C, we need additional information. If we have an initial condition, such as the initial radius of the ripple, we can substitute the values of r and t into the equation and solve for C.

Given that a stone is thrown into a pond, creating a circular ripple that spread

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