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umka21 [38]
3 years ago
13

Please explain how to get the answer.

Mathematics
2 answers:
katen-ka-za [31]3 years ago
7 0
Alrighty..

Volume of sphere = 4/3 x (pi)x r^3 .where r is the radius of a circle ..in this case the radius for the smaller circle. and the Volume of the larger one would be 4/3 x (pi)x R^3 .
so when they say the volume if the larger one is Twice the smaller one they're bascially telling you that (4/3x(pi)xR^3 = <span>2 x </span>(4/3x(pi)xr^3) 

When you multiply the formula by two you'd get <span>4/3x(pi)xR^3=</span> 8/3 x (pi)x r^3 

Now solve accordingly by taking 4/3 to the other side.. you'll get sth like this 

(pi)R^3 = 2(pi)r^3  
Cancel the pi out 
 
now you have R^3 = 2r^3  divide the equation now by r^3 
 R^3/r^3 =2
you can also write this as (R/r)^3 = 2 
take the power cube to the other side to get cube root of 2!!!
therefore R/r= cube root of 2 

Hope this helped! :)


Maru [420]3 years ago
3 0
2r=R

Because 2 of "r" make 1 R
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Hello again! This is another Calculus question to be explained.
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Answer:

See explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

Functions

  • Function Notation
  • Exponential Property [Rewrite]:                                                                   \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Property [Root Rewrite]:                                                           \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Differentiation

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Derivative Property [Multiplied Constant]:                                                           \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

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Derivative Rule [Chain Rule]:                                                                                 \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

We are given the following and are trying to find the second derivative at <em>x</em> = 2:

\displaystyle f(2) = 2

\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}

When we differentiate this, we must follow the Chain Rule:                             \displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]

Use the Basic Power Rule:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]

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We can rewrite the 2nd derivative using exponential rules:

\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}

To evaluate the 2nd derivative at <em>x</em> = 2, simply substitute in <em>x</em> = 2 and the value f(2) = 2 into it:

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When we evaluate this using order of operations, we should obtain our answer:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

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Now that we have the common ratio, lets find the  explicit formula of our sequence. To do that we are going to use the formula: a_{n}=a_{1}*r^{n-1}. We know that a_{1}=4; we also know for our previous calculation that r=-5. So lets replace those values in our formula:
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Finally, to find the 9th therm in our sequence, we just need to replace n with 9 in our explicit formula:
a_{9}=4*(-5)^{9-1}
a_{9}=4*(-5)^{8}
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We can conclude that the 9th term in our geometric sequence is <span>1,562,500</span>
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