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I assume S8 is a molecule of 8 Sulfur atoms    Sulfur 32.06    8*32.06 = 256.48 gm    per mole

                C60 is a molecule of 60 Carbon atoms   Carbon 12.011   12.011 * 60 = 720.66 gm  per mole

DCO....since CO = DO.....the angles opposite those sides are equal

So DCO = x

CBO....angle OBQ = 90°  [tangent meeting a radius forms a right angle ]

So CBO = 90 - 2x

OCB   .......since OB = OC, the angles opposite those sides are equal

So OCB = CBO =  90 - 2x

BCD = DCO + OCB =  (x) + ( 90 - 2x) =  ( 90 - x)   [angle addition postulate ]

DOB is a central angle that is twice the measure of BCD = 2(90 - x) = 180 - 2x  = measure of minor arc   DB   [ a central angle measures twice  an inscribed angle intercepting the same arc ]

Note that arc DCB = 360° - minor arc DB  =  360 - (180 - 2x) = 180 + 2x

[ the sum of arcs in acircle = 360° ]

Angle  y  =  (1/2) [ difference of  arc DCB - arc DOB] 

[ The angle formed by the intersection of 2 tangents, 2 secants or 1 tangent and 1 secant outside the circle equals half the difference of the intercepted arcs ]

Read more: https://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php#ixzz5YI50pVkl

(1/2) [ (180 + 2x) - (180 - 2x) ]  =

(1/2) [  2x + 2x ]  =

(1/2) [ 4x]  =   

2x

1a. What would be the greatest height the telescope could reach above the ground?

The greatest height will be when a = 0  =  7 meters

1b. What is the diameter of the telescope?

We can find the a value where the hight of the telescope = 7 m on the right side 

7 = a^2 -  a + 7     subtract 7 from both sides

0 = a^2 - a

a^2 - a  =  0     factor

a ( a - 1)  =  0

Setting both factors to 0 and solving for a  gives that

a =  0     (we know this)     or  a =1

So.....the diameter of the telescope is 1 meter

1c. What is the depth of the telescope?

The low point of the telescope will be where   a = (1/2) 

So....to find the height at that point, we have

(1/2)^2 - (1/2) + 7  =  1/4 - 1/2 + 7  =  7 - 1/4  =  6.75 m

So.....the depth of the telescope is    7 -  6.75  =  .25m  

We can break this up into: \((130+3)(130+3)\) . Now, by distributing, we have \(16900+390+390+9=\boxed{17689}\) .

Since BC bisects angle ABQ then angle ABC = angle CBQ = x

[Definition of an angle bisector ]

Since angle CBQ = x, then minor arc  BC = 2x

[ A tangent meeting a chord forms an angle that is 1/2 the measure of the arc intercepted by the chord ]

Angle A =  (1/2 ) minor arc BC  =  (1/2)(2x)  = x

[ A is an inscribed angle....ts measure = 1/2 of its intercepted arc ]

Since angle A = angle ABC, the sides opposite these angles are also equal

So AC = BC

[ In a triangle.....sides opposite equal angles are also equal ]

Minor Arc  AB  = (2) 72  = 144°

[  A tangent  meeting a chord forms an angle half that  of the arc intercepted by the chord ]

Angle C  =  (1/2) measure of minor arc AB = (1/2) 144 = 72°

[ C is an inscribed angle.....its measure is 1/2 the measure of its intercepted arc

Angle A =  180 - 72 - 54  =  54°

[ The sum of the interior angles of a triangle = 180° ]

So.....triangle ABC is isosceles because angles A and B are equal

Is Alcumus okay? I've been seeing a few Alcumus questions posted here.

Yeah thanks!

Example .....to find a side length.....use the distance formula

Are you familiar with this???

Distance from A to B   =

sqrt  [ ( 1 - 2)^2 + (3 - 0)^2 ]  = sqrt [ (-1)^2 + 3^2] = sqrt [ 1 + 9 ] =  sqrt (10)

Then find the distances between B,C     C,D      and      D,A

They should all be =  sqrt (10)

Let me know if you have trouble

2 outcomes for flipping the coin and 6 outcomes for rolling the die

So....the number of total  outcomes =  

No. of Outcomes of first thing  x  No. of Outcomes of second thing

Based on this.....what is the answer, NSS???

And how do I do that...

Not B

Note that we will have either   "H" or "T"  paired with  a number

Knowing this....what do you think ????

Here's the way I might do it, RP

1. Find the side lengths

2. Show that the diagonals have the same length

3. Show that the length  of any side = 

     diagonal length / √2

3. This will mean that we have a  square because the sides are congruent,  the diagonals are congruent and because of the proof of  (3),   they will meet at right angles

I think it would B

Uhh is it 

AC=1/3

BD=3/-1=-3/1

1/3*-3/1=-3/3=-1

Which do you think it might be, NSS ??

Since AB = BC......the angles opposite those sides are equal   = x

So....angle B    =  180 - 2x

But....the sum of angles B and D =  (180 -2x) + 2x  =  180°

And when opposite sides of a  quadrilateral are supplementary [ sum to 180° ], the quadrilateral is a cyclic quadrilateral

We have 15 choices * 3 choices    =  45 choices

Thanks, heureka......!!!

[ I think we tried to make it more complicated than need be...!!!]

press sin^-1 on the calc

\(C = 2\pi r\\ 8\pi = 2 \pi r\\ 4 = r\\ r=4~cm\)

\(f(x) = x^2\\ g(x) = x-3\\ f(g(x)) = f((x-3)) = (x-3)^2\)

\(2x+4y=6\\ y = -\dfrac 1 2 x + \dfrac 3 2\\ m=-\dfrac 1 2 \\ m_\perp=-\dfrac{1}{m} = 2\\ \text{so using point slope form the equation defining the perpendicular line is}\\ (y-4)=2(x-6) \\ -2x+y = -8\)