Choose the best estimate.<br> 589 - 473 =<br> 150<br> 100<br> 50<br> 200

Please help with this Math Question...

Nataly [62]

Answer: A

<u>Step-by-step explanation:</u>

f(x) = x³ + 4x² + 7x + 6

possible rational roots are ±{1, 2, 3, 6}

Try x = -2

-2 | 1 4 7 6

1 2 3 0 ← remainder is 0 so x = -2 is a root ⇒ (x + 2) = 0

The factored polynomial x² + 2x + 3 = 0 is not factorable so use the quadratic formula to find the roots.

a=1, b=2, c=3

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x=\dfrac{-(2)\pm\sqrt{(2)^2-4(1)(3)} }{2(1)}$

$x=\dfrac{-2\pm\sqrt{4-12} }{2}$

$x=\dfrac{-2\pm\sqrt{-8} }{2}$

$x=\dfrac{-2\pm2i\sqrt{2}}{2}$

$x = -1 \pm i\sqrt{2}$

$x = -1 + i\sqrt{2}$ $x = -1 - i\sqrt{2}$

$x - (-1 + i\sqrt{2})=0$ $x - (-1 - i\sqrt{2})=0$

The factors are:

$(x - 2)[x - (-1 + i\sqrt{2})][x - (-1 - i\sqrt{2})]$

5 0

2 years ago

3. What is the radius, in centimeters, of a circle that has a circumference of 16 centimeters?

ludmilkaskok [199]

Answer: 8cm I think-

3 0

2 years ago

Read 2 more answers

Let ρ = x3 + xe−x for x ∈ (0, 1), compute the center of mass.

hram777 [196]

The center of mass is mathematically given as

$\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$

<h3>What is the center of mass.?</h3>

Determine the center of mass in one dimension:

Represent the masses at the respective distances.

$\begin{|c|c|} Masses \ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ Located at \\\rho=x^{3}+x \cdot e^{-x} & \ \ \ \ x \in(0,1)$ \\\end$

We calculate the total mass of the system.

$\begin{aligned}m &=\int_{0}^{1} \rho \cdot d x \\& m =\int_{0}^{1}\left(x^{3}+x \cdot e^{-x}\right) \cdot d x \\&m =\left|\frac{x^{4}}{4}-(x+1) e^{-x}\right|_{0}^{1} \\&m =\left(\frac{5}{4}-\frac{2}{e}\right)\end{aligned}$

Step 03: Calculate the moment of the system.

$\begin{aligned}M &=\int_{0}^{1}(\rho \cdot x) \cdot d x \\& M=\int_{0}^{1}\left(x^{4}+x^{2} \cdot e^{-x}\right) \cdot d x \\&M =\left|\frac{x^{5}}{5}-\left(x^{2}-2 x+2\right) \cdot e^{-x}\right|_{0}^{1} \\&M=\left(\frac{11}{5}-\frac{5}{e}\right)\end{aligned}$

we calculate the center of mass.

$\begin{aligned}\bar{x} &=\left(\frac{M}{m}\right) \\& \bar{x}=\left\{\left(\frac{\left.11-\frac{5}{5}\right)}{\left(\frac{5}{4}-\frac{2}{e}\right)}\right\}\right.\\& \bar{x}=\left(\frac{11 e-25}{5 e}\right) \cdot\left(\frac{4 e}{5 e-8}\right) \\&\bar{x}=\left(\frac{44 e-100}{25 e-40}\right)\end{aligned}$