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3 years ago

Does anyone know how to solve this?

Mathematics

1 answer:

masya89 [10]3 years ago

3 0

Answer:

b = -125/9

Step-by-step explanation:

1 + log5 ( -9b) = 4

Subtract 1 from each side

1 -1+ log5 ( -9b) = 4-1

log5 ( -9b) = 3

Raise each side to the base 5

5^ log5 ( -9b) = 5^3

This will cancel the log5

-9b = 125

Divide each side by 9

-9b/-9 = 125/-9

b = -125/9

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Use an appropriate substitution to solve the equation

Yuri [45]

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This ODE is in standard Bernoulli form, so we can divide through both sides by $y^5$ to get

$y^{-5}y'-\dfrac8xy^{-4}=\dfrac1{x^{20}}$

Substitute $z=y^{-4}$ , so that $z'=-4y^{-5}y'$ . Then the ODE can be written as a linear one in $z$ :

$-\dfrac14z'-\dfrac8xz=\dfrac1{x^{20}}$
$z'+\dfrac{32}xz=-\dfrac4{x^{20}}$

Multiplying both sides by $x^{32}$ gives

$x^{32}z'+32x^{31}z=-4x^{12}$
$(x^{32}z)'=-4x^{12}$
$x^{32}z=\displaystyle-4\int x^{12}\,\mathrm dx$
$x^{32}z=-\dfrac4{13}x^{13}+C$
$z=-\dfrac4{13x^{19}}+\dfrac C{x^{32}}$

Back-substitute to solve for $y$ :

$\dfrac1{y^4}=-\dfrac4{13x^{19}}+\dfrac C{x^{32}}$
$y^4=\dfrac1{Cx^{-32}-\frac4{13}x^{-19}}$
$y=\left(\dfrac{x^{32}}{C-\frac4{13}x^{13}}\right)^{1/4}$
$y=\dfrac{x^8}{(C-\frac4{13}x^{13})^{1/4}}$

Given that $y(1)=1$ , you have

$1=\dfrac{1^8}{(C-\frac4{13}1^{13})^{1/4}}$
$1=\dfrac1{(C-\frac4{13})^{1/4}}$
$1=\left(C-\dfrac4{13}\right)^{1/4}$
$1=C-\dfrac4{13}$
$C=\dfrac{17}{13}$

so that the particular solution is

$y=\dfrac{x^8}{(\frac{17}{13}-\frac4{13}x^{13})^{1/4}}$

4 0

3 years ago

Pls help will give brainliest!!! pls I dont understand

SCORPION-xisa [38]

Answer:z=10yd

y=38 degrees

x=90 degrees

w=180-128= 52 degrees

u=6.2yd

v=7.9yd

Step-by-step explanation:

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3 years ago

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Ksenya-84 [330]

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

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3 years ago

For Triangle PQM, where M is the Right Angle and PQ is the Hypotenuse. You know side PM = 8, side PQ = 17, Side MQ = 15. Find An

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Answer:

61.9°

Step-by-step explanation:

tan p = opposite/ adjacent

tan p = 15/8

$tan^{-1}$ (15/8)

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3 years ago

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Volgvan

Answer:

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7 0

3 years ago