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It's 29.

Also, there is a calculator on this page if you click home on the top of the page.

poor puppy

im doing awsome!

You first need a density (kg/m³) to do this.

5*10³*5*10² → 25*10³⁺² → 25*10⁵ → 2.5*10⁶ 

Since cos 45 = sin 45 the x-component velocity is the same as the y-component.

P(n) = 4ⁿ + 15n - 1.       P(1) = 18.   Divisible by 9

P(n+1) = P(n) + Q(n).      (A)         where Q(n) = 3*4ⁿ + 15

Q(n) = 3*4ⁿ + 15.    Q(1) = 27. Divisible by 9

Q(n+1) = 3*4ⁿ⁺¹ + 15.    Q(n+1) = 12*4ⁿ + 15  Q(n+1) = 9*4ⁿ + Q(n).

Hence if Q(n) divisible by 9 then Q(n+1) divisible by 9 

Hence Q(n) divisible by 9 (because Q(1) also divisible by 9)

So if P(n) divisible by 9 then P(n+1) divisible by 9 (because both terms on RHS of A are divisible by 9).

Since P(1) is also divisible by 9 then P(n) is divisible by 9.  QED.

There could be something obvious that I'm not seeing either, but failing that, a second induction proof to show that 4^k + 5 is divisible by 3 works.

Oh... is there no way to simplify that? It seems like a very messy answer. How about the second case with an i coefficient infront of the x^2 term? thanks

What does your teacher say is a "whole number" ?

I am pretty sure that 0.84 is not a whole number!

0.84  ≠  84

It can be written as a fraction, though.

This did NOT help. Your probobly from a different school so your learning different. I'M IN DIVISON FOR TWO TOPICS.  Hectictar try doing division and you might see (mabey not). And I think it might be 84. And this is NOT an answer.

0.84 cannot be expressed as a whole number.

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When the equation of the parabola is in this form:

y  =  ax² + bx + c

The  x-coordinate  of the turning point   =   - \(\frac{b}{2a}\)

----------

For example, if the equation of the parabola is

y  =  3x² + 4x + 1

The  x-coordinate  of the turning point   =   - \(\frac{4}{2(3)}\)   =   - \(\frac{2}{3}\)

Plug this in for  x  to find the value of the  y-coordinate.

y   =   3( - \(\frac{2}{3}\) )² + 4( - \(\frac{2}{3}\) ) + 1   =   - \(\frac13\)

So the turning point is  ( - \(\frac{2}{3}\),  - \(\frac{1}{3}\) )

Multiplying a number by  10  moves the decimal point to the right one place.

For example...      2 * 10  =  20     and     0.7 * 10  =  7

When we multiply  2.56  by  1,000,000,000 , we are multiplying  2.56  by  10 , 9 times.

So we need to move the decimal point to the right  9  places.

2.56 * 1,000,000,000  =  2,560,000,000.0

The decimal point goes at the very end of  2,560,000,000 , but it isn't necessary to write it since only zeros follow it.

I don't know.

LOL!!!!!!.....some people might call that "cheating"....I prefer the term, "research"

Well thank you!  

I did have a little hint after I saw what the answer was supposed to be from WolframAlpha though!!!

y  = - √ [ 2x -6]

First.....since we can't take the square root of something < 0....then  2x  - 6  must be ≥ 0

So

2x  - 6 ≥  0

2x ≥ 6

x ≥ 3     and this is the domain  →    [3, infinity )

The range is a little tougher

The  greatest  value that  y can be is when x = 3......which means that y = 0

Note that all x's greater than 3 produce  a larger and larger square root....but...the " - " out front means that  we gett larger and larger negative square roots......so......the range is actually  

( - infinity, 0 ]

See the graph here :  https://www.desmos.com/calculator/0mevks4btb

Note that as x increases, y decreases

I agree with AT.....that's a very nice factoring "trick,"  hectictar.....!!!

Could you also possibly do the domain and range of -sqrt(2x-6).

4^2x  - 5

This is an exponential.......the domain for an exponential is all real numbers  [ note....2x is defined for all real numbers....so.....4^2x  is, too....because the exponent is just a real number ]

The range is trickier.......if it was just    4^2x  the range would be  (0, infinity)

However.......the " - 5 "   part  shifts the graph down by 5 units.....so.....the range now becomes

(-5, infinity)

See the graph here :  https://www.desmos.com/calculator/szmhu8kwjm

Notice that graph almost touches   y = -5    [ but not quite  !!!]

Wow, good job Hecticar. Certainy wouldn't haven't gotten that.

First factor this.

x⁴ + x³ - 11x² + x - 12     Rearrange.

x³ + x + x⁴ - 11x² - 12       Factor  x  out of the first two terms and split the  -11x² .

x(x² + 1) + x⁴ + x² - 12x² - 12    Factor  x² out of  x⁴ + x²     and  -12  out of  -12x² - 12 .

x(x² + 1) + x²(x² + 1) - 12(x² + 1)     Factor  (x² + 1)  out of all the terms. 

(x² + 1)(x² + x - 12)    Factor the  x² + x - 12 .

(x² + 1)(x² + 4x - 3x - 12)

(x² + 1)(x(x + 4) - 3(x + 4))

(x² + 1)(x + 4)(x - 3)

To find out the  x  values that make this equal to zero, set each factor equal to zero and solve for  x .

x² + 1  =  0           x - 3  =  0           x + 4  =  0

x²  =  -1                 x  = 3                   x  =  -4

not real

We need to find the variation constant, k

So we have

P  = kA

8160  = 8k   divide both sides by 8

1020   = k

So

P =  1020 * 12   =  12,240 watts