-9x^3-72x^2+36=3x^3+x^2-3x+8 Add 9x^3 to both sides.
-72x^2 + 36 = 3x^3 + 9x^3 + x^2 - 3x + 8 Add 72x^2 to both sides
36 = 12x^3 + 73x^2 - 3x + 8 Subtract 36 from both sides.
0 = 12x^3 + 73x^2 - 3x - 28
It does factor, but it is not very nice.
(x + 6.06)(x - 6.09)(x + 0.632)
If there is any kind of error please report it in a note below.
Answer:
The answer is below
Step-by-step explanation:
The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.
![\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cor%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3DA%5C%5C%5C%5Cwhere%5C%20A%5C%20is%5C%20a%5C%20finite%5C%20value.%5C%5C%5C%5CGiven%5C%20that%20%5C%20f%28x%29%20%3D25000%281%2B0.025%29%5Ex%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%28%5Cinfty%29%3D%5Cinfty%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20f%28x%29%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281%2B0.025%29%5Ex%5D%3D%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B25000%281.025%29%5Ex%5D%5C%5C%3D25000%20%5Clim_%7Bx%20%5Cto%20-%5Cinfty%7D%20%5B%281.025%29%5Ex%5D%3D25000%280%29%3D0%5C%5C%5C%5C)
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)
d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.
The coordinates of the vertices of the triangle are
(–8, 8), (–8, –4), and<span> (10, –4)</span>.
Consider QR the base of the triangle. The measure of the base is b = 18 units, and the measure of the height is h = <span>12</span> units.
The area of triangle PQR is<span>108</span> square units.
Answer:
Step-by-step explanation:
$ 6.18 is what each pen costs
