(i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x>0 they know that 5 +-x 2 3 S(x) = x' +x² + 2x If the oil slick is assumed to be continuously distributed, how thick is expected to be at the source? 4x +7 1

Q: 2. Let V be the volume of a cylinder with height 5 feet and radius r feet. If the cylinder expands…

A:

Q: Given that fCx) = x"hc) h'(1)=6 Calculate f'(-1) =

A:

Q: Sand is pouring out of a container at a rate of 20 cm3/s and is forming a canonical pile on the…

A: The objective of this problem is to find the rate of change of the radius of the sand pile as it…

Q: A water tank in the shape of an inverted cone is being filled up with water at a uniform rate of…

A:

Q: 1. of the balloon is increasing when the diameter of the balloon is 20 cm. Air is being pumped into…

A:

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

Q: The work done 'W' by a gas on a piston is given by P2 W = CP dp Where 'P' is pressure and 'C' is…

A: Given : Work done W = ∫p1p2 CP-1ndp Where P is pressure and C is constant.   To find : Show that…

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find da/dt in…

A: Given that  Area of the circle =A  Radius of the circle =r  To find the rate of change of area

Q: The length x, width y and height z of a rectangular box are changing with time as x = 2+ sin 2t, y =…

A: length, x = 2 + sin2t width, y = 3 + cost height, z = 4 - sin3t   dVdt=? when t =π

Q: A draining reservoir has the shape of an inverted right circular cone with a base radius of 30 m and…

A:

Q: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

A: proof:

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A:

Q: Let f(x) = (cosh x)² be defined on (0, 0), find %3D d 1/2) . dy

A:

Q: 3. The area of a circle increases at a rate of 47 cm²/s. How fast is the radius changing when the…

A: We can find the required answer in the below steps using the given data.

Q: 14. A number of grade nine students were surveyed and asked the question "Do you Feel Safe at…

A: Total number of opinions in the survey=6+20+35+29=90 Category Number of opinions corresponding to…