Which of the following lists the three named stars in order of increasing mass (lowest mass first)?
a.) barnard’s star, altair, spica

b.) altair, barnard's star, spica

c.) spica, altair, barnard’s star

d.) barnard’s star, spica, altair

Option (A)

Step-by-step explanation:

The Barnard's Star is usually considered to be a red dwarf, that is approximately six light-years away from the location of earth. It is present in the Ophiuchus constellation and forms the 4th proximate star to the sun.

Altair refers to the bright shining star present in the Aquila constellation. It forms the 12th brightest star that occurs in the night sky.

Spica is one of the proximate stars to the earth and that is extremely large having a mass of almost ten times the mass of the sun.

The mass of Barnard's star is= 2.864 × 10^29 kg

The mass of the Altair is= 3.56 × 10^30 kg

The mass of the Spica= 19.89 × 10^30 kg

The arrangement of these given stars in the increasing order are as follows-

Barnard's star (minimum) < Altair star < Spica star (maximum)

Hence, the correct answer is option (A).

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.