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thanks so much to both the users who posted answers!

In the second answer, I'm just confused about where the dividing by sqrt(2) comes from, since sin(pi/4) and cos(pi/4) equal sqrt(2) over 2, not just sqrt(2)

Ok, got it. The diagonal of the square is an angle bisector, which means that ADB = 45 degrees. Using a little common sense, ADE is an angle bisector as well. How I figured this out was if the angle wasn't equal on both sides, then the square sides would overlap. So ADE = 22.5 degrees. I used trig on this part, but Tan 22.5 = 0.41421356237 about. So then I got a suspicion, so I plugged in \(\sqrt 2 -1\) into the calculator, and I got the same answer. So the answer is \(\sqrt 2 -1\) , which you need to find the sum, so 2 + 1 = 3. Sorry my method is a little unorthodox, but it's the best I could come up with. I tried doing something with the angle bisector theorem, and I got \(\frac {1}{\sqrt2} = \frac{AE}{EB}\), but I couldn't get any further than that.

Hope this helps!

The area of a triangle can be expressed as A = rs, where r is the radius of the incircle and s is the semiperimeter. The area of the triangle is 136, which you can find either by using Heron's formula or just dropping the altitude. We can find the semiperimeter pretty easily, \(\frac {17+17+16}{2} = \frac {50}{2} = 25\) . So we have \(136=25r\) so \(\frac {136}{25} =r\) .

Hope this helps!

I'm assuming you want to find X and Y. Add the two equations and the y's cancel out. So we have 4x = 36, so x = 9. Substitute this into either of the equations, and you can see that y = -18.

Hope this helps!

Wow, that's smart!!!!

Oops. Sorry I couldn't be more help! I misunderstood the question!

I assume you need the equation for the parabola

The vertex  lies at   (0, - 1.5)

Since the directrix is above the focus....the parabola turns downward

p =   l  -1 - - 1.5 l  = l .5 l  =     =   .5

So...we have this form

4p ( y + 1.5) =  - ( x - 0)^2

4(.5)(y + 1.5) = - x^2

2 ( y + 1.5) = -x^2

y + 1.5 =  -(1/2)x^2

y =   -(1/2) x^2 - 1.5

Here's the graph :  https://www.desmos.com/calculator/kqbcr8utzm

If it still isn't working, make a new account or something

3

a^(-1/2)  =  1 /a^1/2   = 1 / √a

b^3/2  =   √b^3  = b√b

So..we have

3 ( 1 /√a) ( b√b) =

   3b√b

_______               [ also could be written as 3b √ (b / a)  ]

    √a

x - 1/x =i*sqrt(2)

x^2187 - 1 / (x^2187) =

x^(2187+2187) - 1 / (x^2187) - Use substitution

(x^4374 -  1) / (x^2187) =i*sqrt(2)

\(\begin{align*} &x-1\equiv 1-x\pmod {12}\implies 2x\equiv 2\pmod{12},\\ &x-2\equiv 2-x\pmod{12}\implies 2x\equiv 4\pmod{12}. \end{align*}\)

Since \( 2x\) cannot be equivalent to both two and four in mod 12 we know that there are \(\boxed{0} \) solutions.

At 3 hrs

Intake  = 3(3)^2 + 2  = 29 gal/hr

draining = 4(3) - 1  =  11 gal/hr

So

The rate at which the amount of liquid is changing in the tank = [ 29 - 11]  =  18 gal / hr

So....1st answer

The rate at which the amount of liquid in the tank is changing at t = 3 hours is 18 gallons per hour.

The rate at which the amount of liquid in the tank is changing at t = 3 hours is 40 gallons per hour.

There are 40 gallons of liquid in the tank at t = 3 hours.

There are 18 gallons of liquid in the tank at t = 3 hours.

 those are my answer choices

(i - d)   is the rate the tank is being filled after x hours

For instance....after 2 hours   the tank is being filled at  3(2)^2 + 2 =  14 gal/hr

And it is being drained at 4(2) - 1 = 7 gal/hr

So.....the net is that it is being filled at 2 hours  =   14 - 7  =   7 gals/hr   

So

(i - d)(3)   is the rate that the tank is being filled at 3 hrs

Since i is how much liquid is being put in, and d is how much is being let out, i - d is how much liquid is in the container at any given time. So (i-d)(3) is how much liquid is in the container in gallons after three hours.

Hope this helps!

2^(-1/2)  =  1 / 2^(1/2)  =  1 / √2

a^-(3/2)  =  1 / (a)^(3/2) =   1/  √a^3  =   1 / [ a √a]

b^1/2 = √b

So, GM...putting this together, we have.....

(1 / √2) * 1/ [ ( a √a ) ]  ( √b ) =

      √b                        √b

________   =          _______

   a √a √2                  a √[2a]

Just Google or something. Type your number, then down on the bottom you'll see X^y. That's what you want.

Note that the side opposite x  =  e

And the side adjacent to x =  f

So

tangent x  = opp /adj    =     e / f

Notice that, in the right triangle on the right.....the adjacent side to x  is 2.5   and the hypotenuse is  5.4

The cos x = adjacent / hypotenuse

So

cos x  = 2.5 /5.4    

(f * g) (x)  means

f(x) * g(x)  =

[ x^4 - 9 ] [ x^3 + 9 ] =

x^4 * x^3 - 9*x^3 + 9*x^4  -9*9 =

x^7 + 9x^4 - 9x^3 - 81

(f - g)(x)  means

f(x)  - g(x)  =

[ 3x^5 + 6x^2 - 5 ] - [ 2x^4 + 7x^2 - x + 16 ] =

3x^5 + 6x^2 - 5  - 2x^4 - 7x^2 + x  - 16   =

3x^5 - 2x^4 - x^2 + x - 21

(f + g)(x)  means  f(x) + g(x)  = [ x^3 - x ] + [ x^3 + 2x^2 - 10 ]  =  2x^3 + 2x^2 - x - 10