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2 years ago

14

The following function defines a recessive sequence:

1 answer:

irga5000 [103]2 years ago

5 0

$f(0)=-4\\f(1)=12\\\\f(n)=-3f(n-1)-2f(n-2)\\\\f(2)=-3f(2-1)-2f(2-2)=-3f(1)-2f(0)=-3\cdot12-2\cdot(-4)\\=-36+8=-28\\\\f(3)=-3f(3-1)-2f(3-2)=-3f(2)-2f(1)=-3\cdot(-28)-2\cdot12\\=84-24=60\\\\Answer:A)\ -4;\ 12;-28;\ 60;...$

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Andreyy89

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3 years ago

A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

pentagon [3]

Answer:

$V=298.5cm^3$

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

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from this formula we clear the radius r:

$r^2=\frac{SA}{4\pi}\\ \\r=\sqrt{\frac{SA}{4\pi} }$

and we substitute the known value of the surface area, and also the value of $\pi$ :

$r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm$

and now that we know the radius we find the volume:

$V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3$

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2 years ago

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2 years ago

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Step-by-step explanation:

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2 years ago