Physics Properties Of Matter Level: Misc Level
The patient is to receive an intravenous injection of medication . In order to work properly, the pressure of fluid containg the medication must be 104 kPa at the injection point.
(a) If the fliud has a density of 1017 kg/m3, find the height at which the bag of fluid must be suspended above the patient. Assume that the pressure inside the bag is one atmosphere.
*answer in m*
Physics Properties Of Matter Level: Misc Level
In the hydraulic system shown in Figure 15-28 the piston on the left has a diameter of 5.3 cm and a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 3.9 kg.If the density of the fluid is 750 kg/m3, what is the height difference h between the two pistons?
*answer in m*
Mathematics Integration Level: Misc Level
An open box with a square base is to be made of given iron sheet of area 27 square meters. Show that the maximum volume of the box is 13.5 cubic meter.
Mathematics Integration Level: Misc Level
Show that the surface area of a closed cuboid with square base and given volume is minimum when it is a cube
Mathematics Integration Level: Misc Level
Find the point on the parabola y2 = 4x which is nearest to the point (2,-8)
Mathematics Integration Level: Misc Level
A window is in the form of a rectangle above which there is a semicircle. If the perimeter of the window is p cm, show that the window will admit maximum possible light only when the radius of semicircle is cm
Mathematics Integration Level: Misc Level
A wire 10 meters long is cut into two parts. One part is bent into the shape of a circle and the other into the shape of an equilateral triangle. How should the wire be cut so that the combined area of the two figures is as small as possible?
Mathematics Integration Level: Misc Level
Two sides of at triangle have lengths a and b, and the angle between them is . What value of
will maximize the area of triangle? Also find the maximum area of the triangle
Mathematics Integration Level: Misc Level
Prove that of all rectangles with given perimeter, the square has the largest area
Mathematics Integration Level: Misc Level
Prove that the perimeter of a right-angled triangle of given hypotenuse is maximum when the triangle is isosceles
Mathematics Integration Level: Misc Level
Three numbers are given whose sum is 180 and the ratio of first two of them is 1:2 if the product of the numbers is greatest, find the numbers
Mathematics Integration Level: Misc Level
Find two positive numbers x and y such that their sum is 35 and the product x2y5 is maximum
Mathematics Integration Level: Misc Level
The sum of two positive numbers is 20. Find the numbers if the product of the squares of one and the cube of the other is maixmum
Mathematics Integration Level: Misc Level
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is minimum
Mathematics Integration Level: Misc Level
Find the points of local maxima and minima (if any) of the following function. Also find the local maxima and minima values
f(x) = Sin x + Cos x, 0<x<
