CPhill

If it's "rectangular," then we would need to know the length of the prism, as well.

Just do this [(26 + 1/3) - (10 + 1/4) ] / 2 =

[79/3 - 41/4 ] / 2  =

[79*4 - 3*41] / [12 * 2] =

[316 - 123] / 24 =

193/ 24 =

8 + 1/24  inches from the edge

270  factors as 27 x10  = 3^3 x 5 X 2

675 factors as   135 x 5 = 27 x 5^2  =  3^3 x 5^2

So...the gcf is  3^3 x 5  = 135

I assume you want to find the area between y= x and y =x^3/9

We have

3                                                           

∫ x - x^3/9 dx   =  

0

[x^2/2  - (1/36)x^4] from 0 to 3  = [3^2/2 - (1/36)3^4 ]= 9/2 - 81/36 = [162 - 81] / 36 = 81/36 = 9/4 =  2.25 sq units

5x^2-23=57   add 23 to both sides

5x^2=  80      divide both sides by 5

x^2  = 16       take the positive and negative square root of both sides 

x = ±√16 = ± 4

If you passed the person in second place, you would now be in second place....!!!

4x - 3= 18    add 3 to both sides

4x = 21     divide both sides by 4

x = 21/4

I assume we have

[ x+ 6 ] / 2 = 9   multiply both sides by 2

x + 6 = 18       subtract 6 from both sides

x = 12

Triangle BAC is 95 degree, with BA 6.8CM and BC 8.1. Find angle BCA

We have a SSA situation here, so there's a possibility of more than one triangle

We have

sin95/ 8.1 = sin BCA / 6.8

And, using the sine inverse, we have

sin-1 (6.8 * sin95 / 8.1) = about 56.75°

So....angle ABC = (180 - 95- 56.75) = 28.25°

Now, ABC might also be supplementary to 28.25° = 151.75°

But, since BAC is 95°, this is impossible, because BAC + ABC would be greater than 180°

So....only one triangle exists.....

There is no answer to this......here's why....

The surface area is given by

Sa  = 480 =  2(lw + wh + lh)

240 = w( l + h) + lh

w = [240 - lh] / (l + h)

And the volume is given by

V = 2208 = lwh

2208/ [lh] = w

And setting the "w's"  equal, we have

2208/[lh] = [240- lh] / (l + h)    ..... cross-multiply

2208(l + h) = [240 - lh] lh

2208(l + h) = 240lh - (lh)^2     set to 0

(lh)^2 + 2208(l + h) - 240lh = 0

Now.....letting x = l and h = y.....look at the graph of

(xy)^2 + 2208(x + y) - 240xy = 0