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Oops I meant 420 feet

x= 0   seconds at takeoff

h = - 3 (0-3)^2 + 108

    = -27 + 108 = 81 ft

69 feet

Drawing a sketch, placing Charles at point C, the base of the building immediately below Charlie at point Z, the car at point Y, and the truck at point X. 

Call the distance from Y to Z 'c', the distance from  to Z 'c + 800', and the height of the building 'h'.

Triangle CZY is a right triangle with Z the right angle and angle C = 66^o   --->   tan(66)  =  x / h

Triangle CZX is a right triangle with angle XCZ = 80^o   --->   tan(80)  =  (x + 800) / h

We now have:  tan(66)  =  x/h   --->   x  =  h·tan(66)

                         tan(80)  =  (x + 800)/h   --->   x + 800  =  h·tan(80)   --->   x  =  h·tan(80) - 800

Combining these two equations:  h·tan(66)  =  h·tan(80) - 800

                                   h·tan(66) -  h·tan(80)  =  -800

                                      h(tan(66) - tan(80))  =  -800

                                                                   h  =  -800 / (tan(66) - tan(80))

                                                                   h  =  233.6'

Careful :  10 mg is a mass    .01 ml is a volume      this applies to WATER , but not most other substances

First:  Find the y-value when x = 3:  y  =  (3·3)/(32 - 1)  =  9/8   --->   (3, 9/8)

Second:  Find the first derivative of y:

     y'  =  [ (x2 - 1)·(3)  -  (3x)·(2x) ] [ (x2 - 1)2 ]  =  [ -3x2 - 3 ] / [ (x2 - 1)2 ]

Third:  Find the value of the first derivative when x = 3:  y'  =  [ -3(3)2 - 3 ] / [ ((3)2 - 1)2 ]  =  -15/32

Fourth:  Find the slope of the normal (perpendicular) at that point:  slope  =  32/15

Fifth:  Find the equation of the normal by using the point-slope form:  point = (3, 9/8)  m  =  32/15

      y - 9/8  =  (32/15)(x - 3)

1st question: #1 is correct

2nd question: #3 is correct

3rd question: #3 is correct

You can reread the sentences out loud and see which one sounds best, that's quite helpful

If there are only 3 types of birds, that means that the sum of two types of birds equals 6. Which means there are 3 birds of each type. 3 * 3= 9 birds.

In your previous question, I explained how parentheses are used in a sentence, maybe you can use that to answer these questions.

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Edit:

The first sentence is written correctly.

Parentheses act like comma's for an appositive in a sentence encloses additional, unneeded information.

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X= Price of adults

1/2X= Price of kids

7 * 1/2X + 3X= 13/2X= $63

X=126/13= $9.692307692

1/2X= 63/13= $4.846153846

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1,  2, 2

LOL!!!!

 6.97824×10^6   =   6978240   min

In  one  year   we  have

365 * 24 * 60  =  525,600 min 

So  we  have

6978240 / 525600  =     [ 13   +  101/365 ] years    =

13 years 101 days =

13 years 3 months 11 days

:D thanks a lot! Have a good day!
(I was going to say have a "chill" day but then I decided it was too cringy so :)

So we have

2(11)^2 + 4(11)  + 9  + 3(12)^2 + 10 (12) + 11  =

242 + 44 + 9  + 432 + 120 + 11  =

858    (base 10)

100%  -  11% = 89% of the value of the car retained after 1 year

5,000 =22,400 x 0.89^n

0.89^n =5,000 / 22,400

n = log(5,000/22,400) / log(0.89)

n = 12.87 years = ~12.9 years.

hey thank you i need help 

(1/2) / 8   =   x  / 72      cross-multiply

72 (1/2)  =  8x

36  =   8x       divide both sides  by  8

36/8  = x  =  9/2  =  2.25 in

2x - y - z = 0      (1)
x -2z = 1  ⇒   x = 1 + 2z      (2)
x + y -5z = 3       (3)

Sub  (2)  into (1)  and (3)  for   x    and we  have that

2 (1 + 2z) - y - z  =  0  ⇒  -y + 3z =  -2    ( 4)

(1 + 2z) + y  -5z  = 3  ⇒     y - 3z  = 2     (5)

If we add  (4) and (5)   we  get  that 0 = 0

This means  that we have infinite solutions here  for x,y and  z

Using (5)  we  have  that   y = 2 + 3z

So....holding  z constant  we  have that

(x , y , z)   =   ( 1 + 2z , 2 + 3z , z )

Yup, thanks! *thumbs up*

oh ok. I'm never been good at math, like ever, so :| 

Kinda makes sense though. Thanks for answering :D