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CANNOT BE!! YOUR QUESTION IS WRONG!!!. Check your question carefully. Tell me your answer and I will show you how your question is wrong!

Use exactly the same procedure as in your last question about $5,000 credit card loan.

All you have to do is to change the numbers and copy everything else exactly the same!

Note that...

\(\sin^2(w)+\cos^2(w)=1\quad\rightarrow\quad \frac{\sin^2(w)}{\sin^2(w)}+\frac{\cos^2(w)}{\sin^2(w)}=\frac{1}{\sin^2(w)}\quad\rightarrow\quad 1+\cot^2(w)=\csc^2(w)\)

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\(\begin{array}\ \csc^3(w)&=&\frac{\cot^3(w)+\cot(w)}{\cos(w)}\\~\\ &=&\frac{\cot(w)(\cot^2(w)+1)}{\cos(w)}\\~\\ &=&\frac{\cot(w)(1+\cot^2(w))}{\cos(w)}\\~\\ &=&\frac{\cot(w)\csc^2(w)}{\cos(w)}\\~\\ &=&\frac{1}{\cos(w)}\cdot\cot(w)\cdot\csc^2(w)\\~\\ &=&\frac{1}{\cos(w)}\cdot\frac{\cos(w)}{\sin(w)}\cdot\csc^2(w)\\~\\ &=&\frac{1}{\sin(w)}\cdot\csc^2(w)\\~\\ &=&\csc(w)\cdot\csc^2(w)\\~\\ &=&\csc^3(w) \end{array} \)

A horizontal asymptote is the line that a function approaches as x goes to infinity or negative infinity. So although the function crosses the x axis at (-1, 0), it's not what the function approaches as x goes to infinity or negative infinity. It's why something like this could happen. 

Answer is wrong.

I'm not familiar with credit cards and how they charge interest. First, you must remember that 1% is a WEEKLY rate. I would prorate it for any number of days. The easiest thing to do is to take the balance at the end of each day and calculate the interest on it for 1 day a time.So, $1,300 x 0.01/7 =$1.86 at the end of day 1. I believe if they calculate it daily, then that means that the 1% WEEKLY rate is compounded daily. The balance at end of day 1 should be: $1,301.86. Then this balance is carried to day 2 as $1,301.86 x 0.01/7=$1,303.72 - balance at the end of day 2......and so on.

Try this method and see if it gives you the correct answer. Good luck.

You can do the following:
27% / 12 =0.0225 - This is your monthly interest rate. But your monthly payment is 3.5% of principal. So you can take the net of the two: 0.035 - 0.0225 =0.0125. Then you would use this rate to amortize the loan for t number of months as follows:
Balance =PV x [1 - 0.0125]^t
Balance =$5,000 x 0.9875^t
$0.01 =$5,000 x 0.9875^t
By the way, to bring down the balance of the loan to 1 cent, it would take about 366 months, or about 30.5 years!!.

\(log(x+2)^2=0\\ 2log(x+2)=0\\ log(x+2)=0\\ 10^{log(x+2)}=10^0\\ x+2=1\\ x=-1 \)

check

∠A   =   180° - 40° - 55°   =   85°

Since  ∠A  is the largest angle in triangle BAD, the side opposide ∠A must be the largest side in triangle BAD. That is...

BD  >  AB    and

BD  >  AD

∠C   =   180° - 75° - 55°   =   50°

Since ∠CBD is the largest angle in triangle CBD, the side opposite ∠CBD must be the largest side in triangle CBD. That is...

CD  >  BC    and

CD  >  BD

So  CD  must be the longest segment.

1/7  of the deer caught  had tags

Thus....we might assume that the 90 tagged ones represent 1/7  of  the total poplation

So....the total population  is    7 * 90   =     630

sin (xy)  = x + y

Use the Chain Rule on the left

cos(xy) *[ xy' +  y ]  =  1  + y'

cos(xy) * xy' + cos(xy)*y  =  1 + y'      ....collect the y' terms on the left.....

xy' cos(xy) - y'  =   1  -  y* cos(xy)

y '   [ x*cos (xy)  - 1 ]  =  1 - y* cos(xy)

y ' =    [  1  - y* cos(xy) ]

          _____________

              x* cos(xy) - 1

\(y=\frac16x^2+2x+11\)

                                                Multiply through by  6 .

\(6y=x^2+12x+66\)

                                                Subtract  66  from both sides of the equation.

\(6y-66=x^2+12x\)

                                                Add  36  to both sides to complete the square on the right side.

\(6y-30=x^2+12x+36\)

                                                Factor the right side as a perfect square trinomial.

\(6y-30=(x+6)^2\)

                                                Factor  6 out of the terms on the left side.

\(6(y-5)=(x+6)^2\)

Now that the equation is in this form we can see that the vertex is  (-6, 5) .

Thanks  ....!!!!

Thanks so much, hectictar!!!!!!

y  =   (-5/8)x^2 - 3x  + 4

y  - 4   =  (-5/8)x^2  - 3x       complete the square on the right

y  - 4  =  (-5/8)  [ x^2  +  24/5x + 576/100  -  576/100]

y  - 4  =  (-5/8) [ x + 24/10]^2  + 18/5

y - 4  -  18/5  =  (-5/8)[x + 24/10]^2

(y  - 38/5)  = (-5/8)[ x + 24/10]^2     multiply both sides by -8/5

(-8/5) (y - 38/5)  = ( x + 24/10)^2

The vertex is (   -24/10, 38/5)  =    ( -12/5, 38/5)

Using the form

4p (y - k)  =  (x - h)^2

4p   =  -8/5

p  = -2/5

This parabola  turns downward so the equation of the directrix  is

y  = 

38/5 - p    

38/5 -  (-2/5)   =   

8

So    y  =  8 

The sides of the first triangle are either  10, 10, 20   or  10, 20, 20 .

The sides cannot be  10, 10, 20  because for them to be sides of a triangle, this must be true:

10 + 10  >  20

20 > 20   This is not true, so the sides of the triangle cannot be  10, 10, 20 .

So the sides of the first triangle are  10, 20, 20 .

The shortest side of this triangle is  10  inches.

The shortest side of a similar triangle is  50  inches.

Each side of the similar triangle is  5  times the side of the first triangle.

The sides of the larger triangle are  10 * 5, 20 * 5, 20 * 5

The sides of the larger triangle are  50, 100, 100

the perimeter of the larger triangle  =  50 + 100 + 100  =  250    (inches)

Goodness, I'm sorry about that.

Nice work Chris!

Quilly, if this is what you intended, and I expect it is, then you need to learn to use BRACKETS

I read it as you had written it which is     y=     1/3     +    3sin(theta)

And so there is no way I could have given this answer!

You are lucky that CPhill has been practicing his forensic mathematics!

r  =      1  / [3 + 3 sin θ]

3r  =  1 / [ 1 + sinθ]

3r  =  1 / [ 1  +  y /r]

3r  =  r /  [ r + y]

r + y  =  1/3

r  =  (1/3)  - y

√[x^2 + y^2]  =  (1/3) - y       square both sides

x^2  + y^2   =  1/9  - (2/3)y + y^2

x^2  =  1/9 - (2/3)y

9x^2 =  1  + 6y

6y  =   -9x^2 + 1

y  = (-3/2)x^2  + 1/6

This is a parabola  ...  see  here  :  https://www.desmos.com/calculator/m0v1m8zsrd

The graph of the function $f$ is shown below. How many solutions does the equation $f(f(x)) = 6$ have?

Let's see...

f(1)=6    and f (-2)=6

so when is   f(x)=1     or   f(x))=-2

f(x)=1      4 times             [ because the line graph crosses the line y=1  four times. ]

f(x)=-2     2 times

So there are 6 answers to     f(f(x)=6

A circle is centered at (11, −9)  and has a radius of 12.

What is the equation of the circle?

The equation of a circle is  

\((x-h)^2+(y-k)^2=r^2\\where\;\;\\ (h,k) \text{ is the centre and r is the radius}\)

This should be ample info for you to do it yourself.  Just do the substitutions.