CPhill

3/4 min  =   45 seconds......so

1/45 of this  = 1 second ....so....  

1/45   * 5.85   =  0.13 cm per second

Images not displaying for me....(sometimes).....

Sometimes the image shows....sometimes I get "Waiting for Moderation".......huh????

Note, Rebirth....adding the angles  4n + 7  and 4n + 5....we want to combine like terms.....so

4n + 4n    + 5 + 7  =

8n  + 12

Volume  = side^3

Surface area  = 6*side^2

So......take the cube root of the volume.....this will equal the side

Then......square that value and multiply by 6.......this will be the surface area......

Note that the two angles designated as 4n + 7  and 4n + 5  are straight angles.....they sum to 180

So...let's solve for n....and we have

4n + 7  + 4n + 5  = 180   simplify

8n  + 12  = 180   subtract 12 from both sides

8n  = 168   divide by 8 on both sides

n  = 21

Now....by the Exterior Angle Theorem....m equals the sum of [ 4n + 5]  + [26]

And  n  = 21......so....m  =  4(21) + 5 + 26  =  84 + 5 + 26  =  89 + 26  =  115

Call A the original amount in the portfolio......when $20000 is added to the high-risk component [ without adding anything to the safe component ], the new value of the portfolio   = A + 20000

So, with reference to the safe component.....20% of the new amount  =  30% of the original amount

.20(A + 20000)  = .30A

.20A  + 4000 = .30A

.10A  = 4000

A   = 40000   .....this is the original value of the portfolio

A + 20000   =  40000 + 20000  =  $60000 = new value of the portfolio

[ Melody is correct....this is a good "thinking"  problem ]  

X - 12    .........where X is the number

Each dimension was enlarged 4 times....so....since a cylinder is a three dimensional object, the original volume was  (1/4)^3 of the enlarged volume = (1/64)*2240  = 35 cubic units

f(x) = - x^2  -6x  + 3

The x coordinate of the vertexx =  6 / (2 * -1)   =  -3 To find the y coordinate...put this back into the function   =

 - (-3)^2 - 6 (-3)  + 3  =  -9 + 18 + 3  = 12

So the vertex  = ( -3, 12 )

The axis of symmetry  →   x = -3

This parbola turns "upside" down, so the vertex is a max

Graph : https://www.desmos.com/calculator/rzmxqd4pqh

( -2.5, 3) across the y axis  =   ( 2.5, 3)

Then.....

(2.5, 3) across the x axis  =  ( 2.5, -3)

It would be the same result had we chosen to reflect across x   and then y......