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3 years ago

X^3-2x^2+5x-10=0 how do you solve or factor this polynomial?

1 answer:

7 0

$\bf x^3-2x^2+5x-10=0\implies \stackrel{\textit{doing some grouping}}{(x^3-2x^2)+(5x-10)}=0 \\\\\\ \stackrel{\textit{common factoring}}{x^2\underline{(x-2)}+5\underline{(x-2)}}=0\implies \stackrel{\textit{more common factoring}}{\underline{(x-2)}(x^2+5)}=0 \\\\[-0.35em] ~\dotfill\\\\ x-2=0\implies x=2~~~~\textit{\large\checkmark} \\\\[-0.35em] ~\dotfill\\\\ x^2+5=0\implies x^2=-5\implies x=\sqrt{-5}\implies x=i\sqrt{5}\quad \bigotimes$

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A box with a square base and no top is to be built with a volume of 1638416384 in33. Find the dimensions of the box that require

julsineya [31]

Answer:

$512\ \text{in}^2$

Step-by-step explanation:

x = Length and width of base

y = Height of box

Volume of the box is $16384\ \text{in}^3$

$x^2y=16384\\\Rightarrow y=\dfrac{16384}{x^2}$

Surface area is given by

$s=x^2+4y\\\Rightarrow s=x^2+4\times \dfrac{16384}{x^2}\\\Rightarrow s=x^2+\dfrac{65536}{x^2}$

Differentiating with respect to x we get

$s'=2x-\dfrac{131072}{x^3}$

Equating with 0 we get

$0=2x^4-131072\\\Rightarrow x=(\dfrac{131072}{2})^{\dfrac{1}{4}}\\\Rightarrow x=16$

$s''=2+\dfrac{393216}{x^4}$

at $x=16$

$s''=2+\dfrac{393216}{16^4}=8>0$

So the function is minimum at x = 16

$y=\dfrac{16384}{x^2}=\dfrac{16384}{16^2}\\\Rightarrow y=64$

The material required is

$s=x^2+4y=16^2+4\times 64\\\Rightarrow s=512\ \text{in}^2$

The minimum amount of material required is $512\ \text{in}^2$ .

6 0

3 years ago

Help quick please

GaryK [48]

Answer:

Growth

Step-by-step explanation:

since the (1.05) is bigger than 1 it is growth but if it was lower then 1 it would be decay .

3 0

3 years ago

What is the surface area of the storage chest? Round your answer to the nearest tenth.

Firdavs [7]

Answer:

1093.5 square inches

Step-by-step explanation:

Surface Area of the storage chest :

⇒ 2 (LW + WH + LH)

L = length
W = width
H = height

=============================================================

Given :

⇒ L = 26 in.

⇒ W = 7.5 in.

⇒ H = 10.5 in.

===========================================================

Solving :

⇒ Surface Area = 2(26 × 7.5 + 7.5 × 10.5 + 26 × 10.5)

⇒ Surface Area = 2(195 + 78.75 + 273)

⇒ Surface Area = 2(546.75)

⇒ Surface Area = 1093.5 square inches

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3 years ago

How can I construct a triangle using these three angles?? Please help I'll give 25 points

satela [25.4K]

Use a protractor to measure the degrees of the angles. Then, join them together.

6 0

3 years ago

Is 12.89 irrational

STatiana [176]

No. It's the ratio of 1,289 to 100 .

Also, it can be written as a fraction with whole numbers
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Also, it can be written down on paper completely, using
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Any one of these three facts makes it a rational number.

7 0

4 years ago