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Crank
3 years ago
12

Help please geometry !

Mathematics
1 answer:
Leona [35]3 years ago
4 0
If you use the same technique from the first question, you can do:

5x+2=3x+42
2x=40
x=20

For the rest of the questions, please use the same technique if they are vertical because I can't solve all of the questions for you sorry.
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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
the price per share of a stock decreased from $90 per share to $36 per share. by what percent did the price of the stock decreas
givi [52]

Answer:

60%

Step-by-step explanation:

we know that

the price per share of a stock decreased from $90 per share to $36 per share

In this problem

$90 represent the 100%

so

using proportion

Find out what percentage represent the difference of ($90-$36)

($90-$36)=$54

Let

x ----> the percentage of the difference

\frac{100\%}{\$90}=\frac{x}{\$54}\\\\x=54(100)/90\\\\x=60\%

8 0
3 years ago
What percent of 12 is 7?<br> Please show work :)
SVETLANKA909090 [29]
It’s 3 hope this helps
5 0
2 years ago
Read 2 more answers
Leah's house has a media room with a large flat-screen television to watch movies. The media room television has a width of 8 fe
Naddik [55]
The Answer Would Be 64 because if you divide 8/4.5 its equal to 64/36.
8 0
3 years ago
Find the perimeter of a rectangle with a width of (x - 3) and a length of 4x ​
Firdavs [7]

Step-by-step explanation:

        4x

   __________

   |                     |

x-3|                    |     x-3

   |                     |

   |__________

           4x

Add all sides together to get perimeter

2(4x)+2(x-3)=10x-6

7 0
2 years ago
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