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XA = ZA =XZ = 10

So right triangle LAZ has two sides given:  10 (hypotenuse)     and   1/2(10) = 5   (one leg)

  use pythag theorem to compute the second leg (AL) ....then add all three sides together .....

We can draw a right triangle where the hypotenuse is the slant height and the legs are the radius and the height of the cone. Then if we can find the slant height and the radius of the base of the cone, we can use the Pythagorean theorem to find the height.

The slant height of the cone is the same as the radius of the sector, which is 18

Now we need to find the radius of the base of the cone.

The circumference of the base is the same as the length of the sector, which we can find like this:

\(\frac{\text{arc length of sector}}{\text{circumference of circle}}=\frac{288^\circ}{360^\circ} \\~\\ \frac{\text{arc length of sector}}{2\pi(\text{radius of circle})}=\frac{288^\circ}{360^\circ} \\~\\ \frac{\text{arc length of sector}}{2\pi(18)}=\frac{288^\circ}{360^\circ} \\~\\ \text{arc length of sector}=\frac{288^\circ}{360^\circ} \cdot 2\pi(18)\\~\\ \text{arc length of sector}=28.8\pi\)   (The circle here is the circle from which the sector is taken)

And so

circumference of base   =   28.8 pi

radius of base   =   circumference of base  /  (2 pi)   =   28.8 pi / (2 pi)   =   14.4

Now that we know the radius of the base of the cone and we know the slant height of the cone, we can use the Pythagorean theorem to find the height of the cone.

(radius of base)² + (height)²   =   (slant height)²

                                                                               Plug in what we know...

14.4²  +  ( height )²   =   18²

                                                        Subtract  14.4²  from both sides

( height )²   =   18² - 14.4²

                                                        Simplify the right side

( height )²   =   116.64

                                                        Take the positive square root of both sides

height   =   10.8

Here is the pattern....you can compute the 8th term

1        x 7    -2

5        x 7    -2

33      x 7    -2

229    x 7    -2

1601  x 7    -2

...

p q + 2 p + q = 348,
q r + 4 q + 3 r = 208,
r s + 8 r + 6 s = 722, solve for p, q, r, s

r = 16 and s = 27 and p = 34 and q = 8

Let  a  and  b  be the roots. Then we can make these two equations:

ab  =  18     and     a  =  2b

Substituting  2b  in for  a  into the first equation, we get:

(2b)b  =  18

2b²  =  18

b²   =   9

b   =   ± 3

Which means.....

a   =   2 * (± 3)

a   =   ± 6

So  3  and  6  is one possible solution,  and the other possible solution is  -3  and  -6  

Guest is probably correct......I don't know if we  can  consider single digits as  having a sum !!!

Thank you

Mmmm...let's see  ( I'm not sure myself  !!!)

The first 9 positive integers are all divisible  by their sum

Then   10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50

I get  23    !!!

We want to find the value of  t  when the height is  22.  So let's plug in  22  for  h  and solve for  t .

22  =  -t² + 9t + 2

                                   Subtract  22  from both sides of the equation

0  =  -t² +9t - 20

                                   Multiply both sides of the equation by  -1

0  =  t² - 9t + 20

                                   Now we want to factor the right side. What two numbers add to  -9  and multiply to  20 ?  -4  and  -5

0  =  (t - 4)(t - 5)

                                   Set each factor equal to zero and solve for  t

t - 4 = 0      or      t - 5 = 0

 t  =  4                   t = 5

The rock first reaches  22  meters at time 4 seconds.

Then it goes above 22 meters and comes back down to 22 meters at time 5 seconds.

So it stays above 22 meters for  5 seconds - 4 seconds  =  1 second

10 , 12 , 18 , 20 , 21 , 24 , 27 , 30 , 36 , 40 , 42 , 45 , 48 , 50>> Total =  14 such numbers

a)  We have that

60  = k (2 -1)^3  (2 +3)     simplify

60  = k ( 1) ^3 * 5         divide both sides  by  5 and simplify

60 =  5 k      divide  both sides  by 5

k  =12

b )   x intercepts  =  -3  and  1

y intercepts....let x =  0     and we  have that  12 ( -1)^3 (3)  =   -36

c)  Here's the graph  : https://www.desmos.com/calculator/aucqv32fyl

plz help for the first one i need help quick i got the other 2 right just the first one pl plz

help needed quick

Thanks, Melody....and yeah, Cal....I DO exist   (but just barely....LOL!!!!  )

Call Sarah's score, S

The Greg's score = S - 40

So....we have  that    [ Sarah's score + Gref's score ]  /  2  =  102

[ S +  S - 40  ]  /2  = 102      multiply both sides by 2

2S - 40 = 204      add 40 ro  both sides

2S  = 244         divide  both sides by 2

S =  122  = Sarah's score

I need help fast!

The answer is 7.

Here is the diagram.

The total surface area is ( 2* pi *  r ) ( r  + h)

The lateral surface area is (2 * pi * r ) * h  =  .80  ( 2 * pi * r) ( r + h)     

Divide out 2* pi * r  from both sides and we have that

h  = .80 ( r + h)   simplify    

h = .80r + .80h        

h - .80 h =  .80r

.20 h  = .80 r     divide both sides by .80

(1/4) h =  r       divide  both sides by h

(1/4)  = r / h        [ the base radius is 1/4 the height ]

159 , 168 , 177 , 186 , 195 , 249 , 258 , 267 , 276 , 285 , 294 , 339 , 348 , 357 , 366 , 375 , 384 , 393 , 429 , 438 , 447 , 456 , 465 , 474 , 483 , 492 , 519 , 528 , 537 , 546 , 555 , 564 , 573 , 582 , 591 , 609 , 618 , 627 , 636 , 645 , 654 , 663 , 672 , 681 , 690 , 708 , 717 , 726 , 735 , 744 , 753 , 762 , 771 , 780 , 807 , 816 , 825 , 834 , 843 , 852 , 861 , 870 , 906 , 915 , 924 , 933 , 942 , 951 , 960 , Total =  69 such numbers

The polynomial is x^4 - 5x^3 + x^2 - 3x - 2.

Angle A'B'C' is 45 degrees.

There are 288 ways.

Good job, Guest!