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3 years ago

(Sphere has a volume of 40 cubic meters and is reduced by a scale factor

Mathematics

1 answer:

djyliett [7]3 years ago

5 0

Answer: $10\ m^3$

Step-by-step explanation:

Given

The volume of Sphere is $40\ m^3$

It is reduced by a scale factor of one-fourth i.e. Volume is reduced to one-fourth of the original volume

The new volume is given by

$\Rightarrow V_{new}=\dfrac{V}{4}=\dfrac{40}{4}\\\\\Rightarrow V_{new}=10\ m^3$

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jeka94

Answer:

Zeroes : 1, 4 and -5.

Potential roots: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

Step-by-step explanation:

The given equation is

$x^3-21x=-20$

It can be written as

$x^3+0x^2-21x+20=0$

Splitting the middle terms, we get

$x^3-x^2+x^2-x-20x+20=0$

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Splitting the middle terms, we get

$(x-1)(x^2+5x-4x-20)=0$

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Using zero product property, we get

$x-1=0\Rightarrow x=1$

$x-4=0\Rightarrow x=4$

$x+5=0\Rightarrow x=-5$

Therefore, the zeroes of the equation are 1, 4 and -5.

According to rational root theorem, the potential root of the polynomial are

$x=\dfrac{\text{Factor of constant}}{\text{Factor of leading coefficient}}$

Constant = 20

Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.

Leading coefficient= 1

Factors of leading coefficient ±1.

Therefore, the potential root of the polynomial are $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .

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3 years ago

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3 years ago

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Answer:

x = ± 4 $\sqrt{6}$

Step-by-step explanation:

Given

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x = ± $\sqrt{96}$ = ± $\sqrt{16(6)}$ = $\sqrt{16}$ × $\sqrt{6}$ = ± 4 $\sqrt{6}$

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3 years ago