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3 years ago

9

May I get help on this I am struggling with math

2 answers:

Travka [436]3 years ago

7 0

The answer is 10 milligrams of Medication A. When you divide 18 by 3 for Medication B, you get 6. Then you have to divide 60 by 6 and you get 10 milligrams.

Vesna [10]3 years ago

5 0

60/18 = A/3....60 in A to 18 in B = x in A to 3 in B
cross multiply because this is a proportion
(18)(A) = (60)(3)
18A = 180
A = 180/18
A = 10 milligrams <===

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Answer:

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3 years ago

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katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

Calculate the area of a square with sides of 5 inches.

Luda [366]

Answer:

A = 25 in²

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

<u>Geometry</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

Side length = 5 in

<u>Step 2: Solve for </u><em><u>A</u></em>

Substitute: A = (5 in)²
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And we have our final answer!

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3 years ago

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Alex Ar [27]

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2 years ago

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