Determine if the mean value theorem for integrals applies to the function f(x) = 3 - x2 on the interval the closed interval from 0 to the square root of 3 . if so, find the x-coordinates of the point(s) guaranteed by the theorem

Ben wants to play a carnival game that costs $2. in his pocket he has 5 red tickets worth 35 cents each, and 15 blue tickets worth 10 cents each. which of the following systems of inequalities correctly represents the constraints on the variables in this problem? let represent the red tickets and b represent the blue tickets.

Find the volume of the described solid.the solid lies between planes perpendicular to the x-axis at x = 0 and x=7. the cross sectionsperpendicular to the x-axis between these planes are squares whose bases run from the parabolay=-31x to the parabola y = 30/x.a) 441b) 147c) 864d) 882

Askyscraper is 396 meters tall. at a certain time of day, it casts a shadow that is 332 meters long.at what angle is the sun above the horizon at that time?