A vessel without a lid has the shape of a cylinder. The height of the vessel is 1.5 m, and the diameter of the base represents 40% of the height. Determine if 1 kg of paint is enough to completely paint the vessel inside and out, if it is known that for 1 square meter of surface 150g of paint is consumed.​

Yes, 1 kg of paint is enough to completely paint the inside and outside surfaces of the vessel.

Step-by-step explanation:

For the given vessel without a lid,

diameter = 0.4 x 1.5

               = 0.6 m

radius = =

           = 0.3 m

Total external surface area of the vessel = 2rh +

                             = [2 x x 0.3 x 1.5] + [ x ]

                             = 2.8286 + 0.2829

                             = 3.1112

Total external surface area of the vessel is 3.1112 square meter.

Total internal and external surface area = 2 x 3.1112

                                                              = 6.2224

But for 1 square meter, 150 g of paint is consumed. Thus;

for 6.2224 = 6.2224 x 150 g

                       = 933.36 g

Thus, 6.2224 of area would require 933.36 g of paint.

So that,

= 0.93336 kg

Therefore, 1 kg of paint is enough to completely paint the inside and outside surfaces of the vessel.

solve by  completing the square.

x2+6x+13=0

move the constant to the right side by subtracting 13 from each side.

x2+6x=−13

divide the coefficient of the  x  term by  2.

x2+6x=−13

62=3

square the result and add it to both sides.

32=9

x2+6x+9=−13+9

factor the left side and simplify the right side.

(x+3)(x+3)=−4

rewrite as the square of the binomial. note that the  3  in the binomial is the same value  3  that resulted from dividing the coefficient of the  x  term by  2.

(x+3)2=−4

square root both sides and solve for  x.

√(x+3)2=√−4

x+3=±2i

x=−3±2i