4 [It is given that a sphere of radius r has volume 3 cm r cm Handle Cover Disc cm Body h cm 1 cm r cm 1 cm 1 cm Front view of container Cross-section of body A container is made up of 2 parts. A cylindrical body, opened at one end, of external radius r cm (where r> 1), external height h cm and thickness 1 cm throughout. A cover consisting of a solid cylindrical disc with radius r cm and height 1 cm and a hemispherical handle with radius one-third of the radius of the disc. The internal volume of the cylindrical body is 30 cm³ when full. The material used to make the body and the cover of the container costs $0.50 per cm'. (i) Find an expression for h in terms of r. (ii) Show that the cost, $ C , to make the container is given by C =Tr'+ 81 15r? +ar² -15. (r-1) (iii) Given that r =r, is the value of r which gives the stationary value of C, show tnat n satisfies the equation 27 30r +2ar 0. Hence find the values of r and A (r-1) which give the minimum value of C. [(i) h =- 30 +1, (iii) r = 2.66, h = 4.48] T (r-1)

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When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

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The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.