Hi! can someone answer these calculus questions for me. The topic is derivatives and relative rates, etc.... Thanks

Question 1:

A farmer is tilling a rectangular garden. If the perimeter of the garden is to be 153 find the largest side length that maximizes the area. O a. 12.37 O b. 153 O c. 76.50 O d. 38.25Consider the function y = I In r. Determine the y-intercept for the tangent line passing through the point r = 28. O a. y=93.30 O b. y=-28 O cy=0 O d. y=-23.67Electricity faces resistance as it travels through biological tissue. If we assume that a certain cell has two resistors in parallel such that the total resistance R is 1 1 1 R RI R2 If R, and R2 are increasing at rates of 0.27 ohms/s and 0.14 ohms/ respectively, how fast R changing when R, = 98 ohms and R2 = 112 ohms? O a. 0.0358 ohms/s O b. 0.0536 ohms/s O c. 0.215 ohms/s O d. 0.107 ohms/sFind the largest of two positive numbers whose product is 52 and whose sum is a minimum. O a. 26.00 O b. 52 O c. 7.21 O d. 3.61\fA cylindrical tank with radius 26 m is being filled with water at a rate of 6 m/min. How fast is the height of the water increasing? O a. 0.69 m/min O b. 0.037 m/min O c. 0.23 m/min O d. 0.0028 m/minThe value of a stock relative to its initial purchase value is given by V(t) - 13-912 + 8t. Determine the latest time the value of the stock is zero using one iteration of Newton's method starting at t = 9. O a. t=8.1910 O b. t=8.0028 O c. t= 1.0071 O d. t=8The height on a roller coaster for t > 0 is given by h(t) = -3t* + 36+3 - 48t- + 20. Find the time 7 such that the height only decreases for t > T. O a. T=9 O b. T=0 O c T=1 O d. T=8Determine the rate at which the volume of a spherical ball is changing when its radius is 6 m and its surface area is shrinking at 5.3 m per day. O a. -15.90 m^3/day O b. -599.42 m^3/day O c. -10.60 m^3/day O d. -2397.66 m^ 3/dayThe rate at which photosynthesis takes place in a certain plant species is given by 41 P(I) = 72 + 1+ 81 where I is the light intensity. Determine the light intensity that leads to the largest photosynthetic rate. O a. I=18.00 O b. 1=36 O c1=9 O d. 1=0\fApproximate the value r where the function y = e * = 0.38 using two iterations of Newton's method starting at = = 0. O a. x=0.62000000 O b. x=0.96758403 O c x=0.91360734 O d. x=0.96705291Consider the function y = 9 + 3r? - 4r + 63. Find the largest point where the tangent slope is 6. O a. x=0.25 O b. x=0.76 O c. x=0.51 O d. x=-0.73