Lesson 3−23 - 23−2 Some Attributes of Polynomial Functions a. f(x)=5x−x3+3x5−2f ( x ) = 5 x - x ^ { 3 } + 3 x ^ { 5 } - 2f(x)=5x−x3+3x5−2 b. f(x)=−22x3−8x4−2x+7f ( x ) = - frac { 2 } { 2 } x ^ { 3 } - 8 x ^ { 4 } - 2 x + 7f(x)=−22​x3−8x4−2x+7

Find the linear approximation of the function $f(x)=\sqrt{1-x}$ at $a=0$ and use it to approximate the numbers $\sqrt{0.9}$ and $\sqrt{0.99}$.

A baseball team plays in a stadium that holds 55,000 spectators. With ticket prices at 10, the average attendance had been 27,000. When ticket prices were lowered to10,the average attend ance had been 27,000.When ticket prices were lowered to 8, the average attendance rose to 33,000. How should ticket prices be set to maximize revenue?

Determine whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

Equations differential systems
$x_1^{\prime }=-2x_1-x_2$
$x_2^{\prime }=4x_1-2x_2-2t^{-3}$

f​ increased by 45 is equal to 88

The equations
${\displaystyle Ax+By+C=0}$
and
${\displaystyle x\cos \alpha +y\sin \alpha -p=0}$
will represent one and the same straight line if their corresponding coefficients are proportional:
${\displaystyle \frac{\cos \alpha }{A}}={\displaystyle \frac{\sin \alpha }{B}}={\displaystyle \frac{-p}{C}}=k(\text{say})$
So that
${\displaystyle \cos \alpha =Ak}$
${\displaystyle \sin \alpha =Bk}$
${\displaystyle -p=Ck}$
Now,
${\displaystyle A^2{k}^2+B^2{k}^2=1}$
${\displaystyle k^2=d\frac{1}{A^2+B^2}}$
${\displaystyle k=\pm d\frac{1}{\sqrt{A^2+B^2}}}$
If ${\displaystyle C>0}$, then
${\displaystyle k=-d\frac{1}{\sqrt{A^2+B^2}}}$
Here I don't understand the portion after "If ${\displaystyle C>0}$, then……"

Solve the equations and inequalities. ${\displaystyle a.a^2+12a+36=0}$
${\displaystyle b.a^2+12a+36<0}$
${\displaystyle c.a^2+12a+36\le 0}$
${\displaystyle d.a^2+12a+36>0}$
${\displaystyle e.a^2+12a+36\ge 0}$