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Fofino [41]
3 years ago
5

Find the area of the shaded region. Leave the answer in terms of

title=" \pi " alt=" \pi " align="absmiddle" class="latex-formula"> and in simplest radical form

Mathematics
1 answer:
mash [69]3 years ago
6 0
16^2 - π8^2
256 - 64π
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Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.
Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral \int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx, we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}

= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} }  \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du }  \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}]  \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\

= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C

substitute u = 1-2x⁵ into the result

= \dfrac{1}{40(1-2x^5)^4} +C

Hence\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx = \dfrac{1}{40(1-2x^5)^4} +C

5 0
3 years ago
Simplify <br> -2.5·4<br><br><br><br> thanks hhhhhhhhh
ICE Princess25 [194]

Answer:

-10

Step-by-step explanation:

-2.5 times 4

-10

4 0
3 years ago
Read 2 more answers
I need answer ASAP<br> If f(x) = 2x+1 and g(x) = 3x-2 Find f[g(1)] =
Nadya [2.5K]

Answer:

f[g(1)] = 3

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>

  • Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 2x + 1

g(x) = 3x - 2

<u>Step 2: Find g(1)</u>

  1. Substitute in <em>x</em>:                    g(1) = 3(1) - 2
  2. Multiply:                               g(1) = 3 - 2
  3. Subtract:                              g(1) = 1

<u>Step 3: Find f[g(1)]</u>

  1. Substitute in g(1):                    f[g(1)] = 2(1) + 1
  2. Multiply:                                   f[g(1)] = 2 + 1
  3. Add:                                         f[g(1)] = 3
7 0
3 years ago
In order for figure EFGH to be a trapozoid, which of the following must be true?
kicyunya [14]
You must connect all the letters to create the shape of a trapezoid


7 0
3 years ago
If 3/4 is the dividend and -2/5 is the divisor then what is the quotient ?
Alexxx [7]

Answer:

\dfrac{-15}{8}

Step-by-step explanation:

<h3>Fraction division:</h3>

\sf \dfrac{3}{4} \ \div \dfrac{-2}{5}

 Use KCF method.

  • Keep the first fraction.
  • Change division to multiplication
  • Flip the second fraction.

       \sf \dfrac{3}{4} \ \div \dfrac{-2}{5}=\dfrac{3}{4}*\dfrac{-5}{2}

                      \sf = \dfrac{3*(-5)}{4*2}\\\\ =\dfrac{-15}{8}

4 0
11 months ago
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