The rate at which a planet receives heat from a hot sphere such as sun varies directly with the fourth power of the sun’s absolute tempature, directly with the surface area of the Sun, and inversely with the square of the distance from the Sun to the planet. a) Write a general equation for the rare at which a planet receives heat (h) in terms of absolute temperature (T), surface area (A), and distance (d)

To find the extreme values of a function f(x. y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x, y)=xy

Look at the figure below: triangle abc is a right triangle with angle abc equal to 90 degrees. the length of ac is 5 units and the length of ab is 4 units. d is a point above c. triangle adc is a right triangle with angle dac equal to 90 degrees and dc parallel to ab. what is the length, in units, of segment cd?

What is the location of point g, which partitions the directed line segment from d to f into a 5: 4 ratio? –1 0 2 3