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My answer is the same as EP's

EP you might like to look at my Latex here too :)

-5+2+9+16+...+261+268

This is the sum of an AP

a=-5, d=7,   

\(T_n=a+(n-1)d\\ T_n=-5+(n-1)*7\\ T_n=-5+7n-7\\ T_n=7n-12\\ Find\;n\;when\;T_n=268\\ 268=7n-12\\ 280=7n\\ n=40 \)

\(\displaystyle\sum_{n=1}^{40}\;7n-12 \\\)

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LATEX COMMAND

\displaystyle\sum_{n=1}^{40}\;7n-12 

f(-1) = 1.14

y intercept is at x = 0 ie y intercept is 3

I Think I answered a question similar to this some days ago. Not sure who for though. Anyway there are a number of standard pencil, straightedge(ruler) and compass (for circles) constructions. These include bisecting an interval, bisecting an angle and constructing perpendicular lines.

Triangles are amazing shapes as they have numerous characteristics and properties. For example did you know that the triangle is the strongest plane shape? Sorry I digressed a bit.

Back to your question : The circumcircle of a triangle which is what you require is found by first constructing the perpendicular bisectors of each side. Actually you only require 2 of the 3 as they all intersect at the same point. This point is the centre of your circle and the radius is the distance from this point to the vertex of the triangle. I am a techno dinasaur so I can't show you a picture but I am sure you can find out how to do the simple construction of bisecting an interval(line). Note : be very accurate and precise as any small error will result in a final result which is not quite right and press lightly with your pencil. hope this helps!

Area of pavillion =   x * 3x

Area of  pavillion + walkway = (x+6) * (3x+6)

Area of walkway =    (area of pavillion + walkway) - area of pavillion    =  396 ft^2

                                     (x+6)(3x+6)   - (x*3x) = 396

                                      3x^2 +24x +36  - 3x^2 = 396

                                          24x = 360

                                              x= 15

Pavillion = x * 3x = 15 x 45 ft     dimensions

Area of walkway = 396 ft^2   (given)   

If BA = AD   then by the law of sin s     AngleABC = Angle ADB   

If  AD = DC                 then   Angle DAC = Angle DCA  = 22.5

A triangle has 180 degrees in it   so  angle ADC = 180 - 2(22.5) = 135 degrees

Angle ADC + ADB = 180 degrees (a straight line)  

   ADB = 180 - ADC = 180 - 135 = 45 degrees

Now see the red above?   ADB = ABC = 45 degrees

Just put '8' in for 'x' :

1/2 *8^2 - ( 1/4 *8 +3) =

   32  - ( 5) = 27

pi/3 is the reference angle on the unit circle for sin = sqrt3/2    

Thanks so much!

Down the drain .........

https://www.reddit.com/user/CrimsonSlayyer/comments/7zt9pe/im_trying_to_find_out_what_language_this_book_is/

Down the drain .........

In this case  5 - 4  =  1  so the denominator just equals 1 

The product of the roots = c / a  =  c

So this implies that.......

[ -5 + √c] / 2  *  [ -5 - √c ] / 2    =  c

[25  - c] / 4  = c

25 -  c  =  4c

25  =   5c

5  =  c

V_avg  =  change in displacement

             ____________________

              change in time

Based on the following, I believe "c"  is correct :

(ii.) Every rational function is continuous everywhere it is defined, i.e., at every point in its domain. Its only discontinuities occur at the zeros of its denominator.