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weeeeeb [17]
3 years ago
10

A machine coats metal spheres with a plastic coating. The metal spheres have a radius of 9 mm. The spheres formed by the metal a

nd plastic coating have a radius of 12 mm.
How much plastic coating is on each sphere?
Use 3.14 to approximate pi and express your final answer in hundredths.
Mathematics
1 answer:
HACTEHA [7]3 years ago
7 0
Find the volumes of the two spheres and subtract.

V = 4/3 * pi * r^3

V = 4/3 * 3.14 * 9^3

Simplify exponent:

V = 4/3 * 3.14 * 729

Multiply:

V = 3052.08

V = 4/3 * pi * r^3

V = 4/3 * 3.14 * 12^3

Simplify exponent:

V = 4/3 * 3.14 * 1728

Multiply:

V = 7234.56

Subtract the two volumes:

7234.56 - 3052.08 = 4182.48
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Evaluate the given expression at x= -4<br> -3x + 2x^2 + 2
Mkey [24]

Answer:

\huge{ \boxed{ \bold{ \text{46}}}}

Step-by-step explanation:

If the value of variables of algebraic expression are given, the value of the term or expression can easily obtained by replacing the variables with numbers.

\text{ \underline{ Given}} :  \text{x =  - 4}

\text{ \underline{ To \: find}} :  \sf{value \: of \:  - 3x + 2 {x}^{2}  + 2}

\text{  Plug \: the \: value \: of \: x}

➝ \:  \sf{ - 3 * (- 4 )+ 2 *  {( - 4)}^{2}  + 2}

\text{Remember!} :  \text{Multiplying \: a \: negative \: integer \: by \: negative \: integer \: gives \: a \: positive \: integer.}

➝\sf{12 + 2 *  {( - 4)}^{2}  + 2}

\text{Evaluate \: the \: power}

➝\text{12 + 2 * 16 + 2}

\text{Multiply \: the \: numbers}

➝\text{12 + 32 + 2}

\text{Add \: the \: numbers}

➝  \boxed { \text{46}}

\text{Hope \: I \: helped!}

\text{Best \: regards!}

~\text{TheAnimeGirl}

7 0
3 years ago
Read 2 more answers
If anyone knows about definite integrals for calculus then please I request help! I
kicyunya [14]

Answer:

\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Fundamental Theorem of Calculus 1]:                                     \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Property [Multiplied Constant]:                                                         \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

U-Substitution

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution.</em>

  1. Set <em>u</em>:                                                                                                             \displaystyle u = 4x^{-2}
  2. [<em>u</em>] Differentiate [Basic Power Rule, Derivative Properties]:                       \displaystyle du = \frac{-8}{x^3} \ dx
  3. [Bounds] Switch:                                                                                           \displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.

<u>Step 3: Integrate Pt. 2</u>

  1. [Integral] Rewrite [Integration Property - Multiplied Constant]:                 \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx
  2. [Integral] U-Substitution:                                                                              \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du
  3. [Integral] Exponential Integration:                                                               \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}
  4. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)
  5. Simplify:                                                                                                         \displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)

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

Unit: Integration

4 0
2 years ago
Find the volume of a cone with a base radius of 6 yd and a height of 12 yd
anygoal [31]

Answer:

452.38934 yd^3

Step-by-step explanation:

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3 years ago
*PART D QUESTIONS ONLY*
BlackZzzverrR [31]

Answer:

look at the pictures

Step-by-step explanation:

7 0
2 years ago
Simplify the following:<br> 3x+2y+7-5x+7y
const2013 [10]
<span>3x+ 2y+7 -5x+7y
= -2x + 9y + 7

hope it helps</span>
3 0
3 years ago
Read 2 more answers
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