the cost of plastering the wall of a room which is 4m high and breadth is one third of its length is Rs 640 at the rate of Rs 5/ meter square. What will be the cost of carpeting its floor at rate of rs 250/ meter square.

Step-by-step explanation:

Please refer to the attachement. I defined the height (H), width (W), and length (L) and set:

H = 4m and W = (1/3)L. The total cost of 640 Rs/m^2 is divided by the rate cost of Rs 5/m^2 to give 128 m^2 that was plastered. The total area of the walls must be 128 m^2, so then calculate the total wall area: The walls for the length are 2*LH and for the width are 2*WH. Substituting, we have a total of 8*L + (4/3)L = 128 m^2. Solve for L to obtain L = 12m. W is 1/3L, or 4m. The room is (W,L,H) 4, 12, and 4 meters. The floor is W*L, or 48m^2. At Rs 250/m^2, the rug will cost Rs 12000. Ouch.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.