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correction

Berichtigung

 #1 asinus

Hallo Gast!

Es wird gesagt, Wilhelm Tell habe einen Apfel vom Kopf seines Sohnes mit einem Pfeil getroffen.  Wenn der Pfeil mit einer Anfangsgeschwindigkeit von 60 m / s abgeschossen wurde und der Junge  20 m entfernt war, mit welchem Abflugwinkel hat Bill zielen müssen? (Es sei angenommen, dass  Pfeil und Apfel zunächst auf gleicher Höhe über dem Boden sind.)

v = 60 m/s

a = 20 m

c = Flugstrecke des Pfeiles

h = Fallstrecke des Pfeiles

t = Flugzeit

α = Abflugwinkel

c = v * t

t = c / v

c = a / cos α

h = (g / 2) * t²

h = a * tan α

a * tan α = (g / 2 ) * t²

t = √(2a * tan α / g)

v * t = a / cos α

t = a / v * cos α

√(2a * tan α / g) = a / v * cos α

2a * tan α / g = a² / v² * cos² α                 cos² α = 1 / (1 + tan² α)

2a * tan α / g = a² * (1 + tan² α ) / v²

40m * tan α / 9,81m/s² = 400m² * s² * (1 + tan² α) / 3600 m²

tan α = x

4,0775 * x = 0,1111 * (1 + x²)

0,1111 * x² - 4,0775x + 0,1111 = 0

x² - 36,6957x + 1 = 0

x(1;2) = 18,34875 +- √(336,6766 - 1)

x(1;2) = 18,34875 +- 18,32148

x1 = 0,02727 = tan α1

α1 = 1,56°

x2 = 36,67023 = tan α2

α2 = 88,44°

Bill can shoot under 1,56° or 88,44°

Greetings asinus :- )

!

I'm assumng that we have a square base with a side length of 5....if so, we have

V = (1/3)(area of the base) (height)  =   (1/3)(5^2)(8)  about  66.67  cubic units

We can use the Pythagorean Theorem for this :

sqrt [50^2  - 35^2 ] =  height   = about 35.7 ft.

'x' to the 1.04 root will give you that (the key that is two to the left of the '7' key)

the awnser is 61.03277808 it is a geometry type of question

four

1,999,999,998!

-3/4(x+5)  =

(-3/4)*x    +   (-3/4) * 5  =

(-3/4)x  - 15/4

it is: 170 2/3

w ​3 ​​=512

I think it should be written like this:

w^3=512 take the cubic root of both sides

w=512^(1/3)=8

w^3  = 512       take the cube root of both sides

w  =   8

Google it!?

Actually....if we wanted to stretch a point...it could be factored as:

 [ √2sinx + 1 ]   [ √2sinx - 1 ]

However.....I assumed you wanted to "simplify"  it rather than "factor"  it......

    14515  139/467

Thank you!

$ 0.85  

arctan (7/24) = 16.26 degrees

There's no "factoring"  involved, Shades......but we can express it in a more simple form.....

2sin^2x - 1   =

2sin^2x  - [ sin^2x + cos^2x]  =

sin^2x  - cos^2x =

-cos(2x)

2/15   

Yes, thank you very much! I had a factoring question that I wrote, but it didn't appear on the forum, so if you could answer this one too, I would greatly appreciate it: http://web2.0calc.com/questions/factoring_2753    

I think this is supposed to be :

sin x / (1 + cos x) + (1 + cos x)/sin x = 2 csc x    

get a common denominator on the left   = sinx (1 + cos x)

[ sinx (sinx)   + ( 1 + cosx)^2 ] /  [ sinx (1 + cosx)]

[sin^2x + 1 + 2cosx + cos^2x] / [ sinx(1 + cosx)]

[sin^2x + cos^2x + 1 + 2cosx] / [ sinx(1 + cosx)]  

{remember : sin^2x + cos^2x  = 1}

[ 1 + 1 + 2 cosx] / [sinx (1 + cosx)]

[2 + 2cos x]  /  [ sinx (1 + cos x) ]        factor out 2 on top

2(1 + cosx)  / [sinx ( 1 + cosx)]         "cancel "   the (1 + cos x) on top/bottom

2 / sinx  =

2 (1 / sinx)  =

2csc x         and this =  the right hand side

Thank you thank you :)

It might be easier to answer 5, first, before answering 4

5. The profit function is -0.0001x^2 + 8x - 50000  which is an "upside-down" parabola.....it's form is   -ax^2 + bx  - c.......this type of parabola will always have a maximum........the x co-ordinate of the max is found by :

x = -b / -2a   where    a  = 0.0001   and b = 8....so we have

-8 / [ -2(0.0001)]  =   40000

So.....this means that 40,000 books sold will maximize the profit

To find what that profit is  just put  40000 back into    -0.0001x^2 + 8x - 50000   and you should get 110,000  [dollars]  as the max profit  

4. We can find the roots of -0.0001x^2 + 8x - 50000........by setting it to 0

Thus    -0.0001x^2 + 8x - 50000  = 0

I used a computer algebra system to solve this and obtained ≈ 6833 and ≈ 73166 as roots

This means that from x ≈ 6733 to x  ≈ 40,000, the curve will be "rising" and the derivative will be positive [the profit will be increasing until it hits the max value of x = 40000]

Likewise.....from x  ≈ 40000 to x  ≈ 73166, the curve will be "falling" and the dervative will be negative [the profit will be decreasing until  it falls to 0 at 73166 books produced]

what happens to 4-5sqrt(2) when multiplied by 2

2[4 - 5sqrt(2)]=8 - 10sqrt(2)

Thank you very much!!!! :)