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Note that the question asks for real numbers - it doesn't restrict the solution to integers.

What does APR mean??

Can you explain more clearly?

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Welcome aboard, Atlas  !!!!!

Thanks!!

When the ball hits the ground the  height   = 0

Multiplying the original equation through by -1   and  setting this to 0  we have

16t^2  + 18t  - 405  = 0

Use the Q Formula

t  =  (  -18  ± sqrt  [ 18^2  + 4*16 *405 ] )  /  [ 2 * 16 ]  =    [  -18 ±  162 ] / 32

Take the positive root

t =  [ -18 + 162 ]  /32   =    144 / 32   =    4.5 sec

y =  k x / z^2

6 = k (32)  / (4)^2

6 = (32/16)k

6 = 2k

k = 3  = variation constant

So......

3 = 3 x / (10)^2

1 =  x / 10^2

x = 10^2   =  100

                  B

                          4

C 30°          10                  A

4^2  = 10^2 + BC^2  -  2 (10)(BC) ( sqrt 3)/2)

16 = 100 + BC^2  - (10sqrt 3)BC

BC^2 - (10sqrt 3)BC + 84   = 0

[ No real solutions for BC     since the discriminant is  negative ] 

100  [ 1 .06] ^ 180  ≈   $ 3,589,680.10

Note that cos AMC =   - cos (AMB)

Using the Law of Cosines twice

4^2  = (2a)^2 + a^2   - 2 ( 2a)(a)(cos AMC)  ⇒  16 = 5a^2 - 4a^2 ( -cos AMB) ⇒

16  = 5a^2 + 4a^2 (cos AMB)  ⇒   cos AMB  =  [16 - 5a^2 ] / [4a^2]        (1)

And

3^2 =  (2a)^2 + a^2  -  2 (2a)(a) ( cos AMB )   ⇒   9 = 5a^2 -4a^2 ( cos AMB ) ⇒

cos AMB  =   [9- 5a^2 ] / (-4a^2)     =   [5a^2 - 9 ] / [4a^2]    (2)

Equate (1)  and (2)

[16 - 5a^2 ] / [4a^2 ]  =  [5a^2 - 9 ] / [ 4a^2]

16 -5a^2  = 5a^2 - 9

25  = 10a^2

a^2  =  25/10  

a =    5  /sqrt 10

2a =  10 / sqrt 10  =  BC =   sqrt 10

Find the sum of alldistinct of BC.

Hello Guest!

\(c^2=a^2+b^2-2bc\ cos\ \gamma\\ 4^2=x^2+10^2-2\cdot 10\cdot x\cdot cos\frac{\pi}{6}\\ x^2-20\cdot cos\frac{\pi}{6}\cdot x+100-16\\ x=8.66\pm\sqrt{8.66^2-84}\\ x\in \{\} \)

\(BC\in\{\}\)

  !

What is a?

Hello Guest!

\(c^2=a^2+b^2-2bc\ cos \alpha\\ 12^2=a^2+10^2-2\cdot a\cdot 10\cdot cos\ 60°\\ a^2-10a-44=0\\ a=5\pm \sqrt{25+44}\\ \color{blue}a=13.31\)

  !

The formula for the volume of a cone is: \({r^2 \pi h } \over 3\)

Plugging in the values, we have: \({18^2 \pi 20 \over3} = \color{brown}\boxed{2160 \pi}\)

I think he used a site to calcuate every single of them

It's also undefined when a = 0,