hectictar

 f(x)  =  x² + bx + c

g(x)  =  x³ + wx² + yx + z

[f(x)]³ - [g(x)]² + f(x) - 1

(x²+bx+c)³ - (x³+wx²+yx+z)²   +   x²+bx+c   -   1

(x²+bx+c)(x²​+bx+c)(x²​+bx+c)  -  (x³+wx²+yx+z)(x³+wx²+yx+z)   +   x²+bx+c   -   1

x⁴ + ...

We could continue, but by now I can see that the first term of   [f(x)]³   will be   1x⁶   and the first term of   [g(x)]²   will be   1x⁶   . Since   [g(x)]²    is being subtracted,  the   1x⁶   will cancel each other and go away. The next biggest exponent comes from  x³ * wx²  =  wx⁵ .

So  5   is the maximum degree. 

\(\int(x+\frac4{x^2}-5x+6)\,dx \\~\\ =\int(\frac4{x^2}-4x+6)\,dx \\~\\ =\int \frac4{x^2}\,dx+\int-4x\,dx+\int6\,dx \\~\\ =4\int x^{-2}\,dx-4\int x\,dx+6\int 1\,dx\)       Combine like terms.

Applying the power rule gives us...

\(=4(\frac{x^{-1}}{-1})-4(\frac{x^2}{2})+6(x) +c\\~\\ =-4x^{-1}-2x^2+6x+c\)                 , where   c   is a constant.

Is a square a rectangle?

Yes! A square is a rectangle. (A square is the only shape that is both a rectangle and a rhombus!)

Can a rectangle be a square?

Yes, a rectangle can be a square, but a rectangle is not always a square.   

Question

For every 1,000 miles on the car, reduce its value by one-fifth of a percent.

So... after each 1,000 miles, it is worth   (100 - .02)%  =  99.8%  =  0.998   of its previous value.

So we can say....

car value  =  35,000 * 0.998ⁿ             , where  n  is the number of thousands of miles.

127.5 out of what number equals 15 out of 100 ?

\(\frac{127.5}{x}=\frac{15}{100} \\~\\ 127.5=\frac{15}{100}\,*\,x \\~\\ 127.5\,*\,\frac{100}{15}=x \\~\\ 850=x\)   Now we just need to solve this for x .

The two points are   ( 4 ,  5 )   and   ( 3 ,   6 )

                                  x₁ , y₁               x₂ , y₂

gradient, or   slope   =   (change in y's) / (change in x's)

                                 =   (y₁ - y₂) / (x₁ - x₂)

                                 =   (5 - 6) / (4 - 3)

                                 =   (-1) / (1)

                                 =   -1

Are you trying to make up your own problem where  t = 13  is the solution?

Let's start by saying something about  13  that is a true statement.

2 * 13 + 1  =  27           Also, there are two operations on the left side. This makes two steps.

Now replace  " 13 "  with  " t "  .

2 * t + 1  =  27

2t + 1  =  27

Now we have a problem where  t = 13  is the solution.   

tan( 30º )  =  25 / x               Multiply both sides of the equation by  x  .

x tan( 30º )  =  25                 Divide both sides of the equation by tan( 30º )  .

x  =  25 / tan( 30º )               And   tan( 30º ) = √3 / 3

x  =  25 / ( √3 / 3 )

x  =  25 * 3 / √3

x  =  75 / √3                         Multiply numerator and denominator by  √3  .

x  =  75√3 / 3                       Reduce fraction by  3 .

x  =  25√3

I remember this question from a while back....

Haha you're not dumb !! Glad you got it now!