Consider points A(2,3) and B(6,9). Find point C on the x-axis so AC + BC is a minimum. The point that minimizes AC + BC is C ( , ).

the point C(x,0) = C(3,0) is the point where AC + BC is minimum.

Step-by-step explanation:

Solution:

This question is very simple to solve.

We need to find the x and y elements of point C, which is on the x-axis such that AC + BC = minimum.

So,

As, we have said that, point C is on the x-axis then, it means its y co ordinate will be equals to zero.

Now, we just need to find x co ordinate of the point C.

C (x, 0) as it is on the y -axis.

So, for that, we need to take the mirror image of point B. It means, its x co-ordinate will remain same but y co-ordinate will be negative.

So, our mirror image of B(6,9) = B'(6,-9)

Now, we have to join the points A and B'. Point C, which we are trying to find is the point where this line AB' intersects with x - axis.

So,

Slope of the line AB'

m =

m = =  

m = = -3

m = slope = -3

We also know that the equation of line:

y = mx + b

where b = y-intercept.

Now, we need to find the y - intercept of this line.

y = (-3) x + b

where y = -9 and x = 6

so,

-9 = (-3) (6) + b

b = -9 + 18

b = 9 = y - intercept.

SO,

y = mx + b

and For point C(x, 0) y = 0

0 = -3x + 9

Solve for x:

3x = 9

x = 3

Hence, the point C(x,0) = C(3,0) is the point where AC + BC is minimum.

the answer is: d) o, f, and kr.

atomic radius of bromine (br) is 114 pm.

atomic radius of oxygen (o) is 73 pm.

atomic radius of fluorine (f) is 72 pm.

atomic radius of krypron (kr) is 112 pm.

the atomic radius of a chemical element is a measure of the size of its atom.

the atomic radius varies with increasing atomic number, but usually increases because of increasing of number of electrons.

the atomic radius decreases across the periods because an increasing number of protons, because greater attraction between the protons and electrons.