-x^6 -5x^5 +16x^4 +80x^3 =0 solve for x

Molodets [167]

2(3x + 4) / 2(2x + 2)
Cancel the factored 2s

3x + 4 / 2x + 2

You may need to further factor the denominator, depending on the teacher.

3x + 4 / 2(x + 1)

6 0

2 years ago

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If A, B, and C are collinear, and AB = 18, AC = 41, what is a possible measure of BC?

ikadub [295]

Step-by-step explanation:

As ANC are collinear,

AB+BC=AC

so,

18+BC = 41

BC = 41-18

BC = 23 is the answer.

8 0

3 years ago

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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving

harina [27]

Answer:

The volume of the solid is 714.887 units³

Step-by-step explanation:

* Lets talk about the shell method

- The shell method is to finding the volume by decomposing

a solid of revolution into cylindrical shells

- Consider a region in the plane that is divided into thin vertical

rectangle

- If each vertical rectangle is revolved about the y-axis, we

obtain a cylindrical shell, with the top and bottom removed.

- The resulting volume of the cylindrical shell is the surface area

of the cylinder times the thickness of the cylinder

- The formula for the volume will be: V = $\int\limits^a_b {2\pi xf(x)} \, dx$ ,

where 2πx · f(x) is the surface area of the cylinder shell and

dx is its thickness

* Lets solve the problem

∵ y = $x^{\frac{5}{2}}$

∵ The plane region is revolving about the y-axis

∵ y = 32 and x = 0

- Lets find the volume by the shell method

- The definite integral are x = 0 and the value of x when y = 32

- Lets find the value of x when y = 0

∵ $y = x^{\frac{5}{2}}$

∵ y = 32

∴ $32=x^{\frac{5}{2}}$

- We will use this rule to find x, if $x^{\frac{a}{b}}=c, then=== x=c^{\frac{b}{a}}$ , where c

is a constant

∴ $x=(32)^{\frac{2}{5}}=4$

∴ The definite integral are x = 0 , x = 4

- Now we will use the rule

∵ $V = \int\limits^a_b {2\pi}xf(x) \, dx$

∵ y = f(x) = x^(5/2) , a = 4 , b = 0

∴ $V=2\pi \int\limits^4_0 {x}.x^{\frac{5}{2}}\, dx$

- simplify x(x^5/2) by adding their power

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{7}{2}}} \, dx$

- The rule of integration of $x^{n} is ==== \frac{x^{n+1}}{(n+1)}$

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{9}{2}}} \, dx=2\pi[\frac{x^{\frac{9}{2}}}{\frac{9}{2}}]$ from x = 0 to x = 4

∴ $V=2\pi[\frac{2}{9}x^{\frac{9}{2}}]$ from x = 0 to x = 4

- Substitute x = 4 and x = 0

∴ $V=2\pi[\frac{2}{9}(4)^{\frac{9}{2}}-\frac{2}{9}(0)^{\frac{9}{2}}}]=2\pi[\frac{1024}{9}-0]$

∴ $V=\frac{2048}{9}\pi=714.887$

* The volume of the solid is 714.887 units³

5 0

3 years ago

When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is called _____

zlopas [31]

Answer:

Cross section

Step-by-step explanation:

Cross section refers to the new two dimensional face exposed when we slice through a three dimensional objects.

It can also be the surface or shape exposed by making a straight cut through something, especially at right angles to an axis.

Cross section is the plane surface(two-dimensional objects) formed by cutting across a solid shape (three-dimensional shape) especially perpendicular to its longest axis.

8 0

3 years ago

What is the square root of 789?

Alexeev081 [22]

No even square
28.089

5 0

3 years ago