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BartSMP [9]
3 years ago
14

(Please Hurry!) Which expression is equivalent to the following complex fraction?

Mathematics
1 answer:
galben [10]3 years ago
6 0

Answer:

The expression equivalent to the given complex fraction is

\frac{-2x+5y}{3x-2y}

Step-by-step explanation:

An easy way to solve the complex fraction is to solve the numerator and denominator separately.

Numerator:

\frac{-2}{x} + \frac{5}{y}\\ = \frac{-2y + 5x}{xy}

Denominator:

\frac{3}{y} + \frac{-2}{x}\\ = \frac{3x - 2y}{xy}

Solving the complex fraction:

[\frac{-2}{x} + \frac{5}{y}] / [\frac{3}{y} + \frac{-2}{x}]\\= [\frac{-2y + 5x}{xy}] / [\frac{3x - 2y}{xy}]

=\frac{-2y + 5x}{xy} * \frac{xy}{3x - 2y}

Common terms in the numerator and denominator cancels each other(Cross multiplication) :

= \frac{-2y + 5x}{3x - 2y}

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The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP dt = P(a
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Step-by-step explanation:

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What’s the height of the can?
kondaur [170]

Answer:

5 inches

Step-by-step explanation:

The formula to find the surface area of a cylinder is A = 2πrh + 2πr²  

Since we need the height we will need to solve for h

  • First we can subtract 2πr² from both sides to get A - 2πr² = 2πrh
  • Then we can divide both sides by 2πr to get h=\frac{A-2\pi r^{2}  }{2\pi r}

Now we can plug in our known values and solve for h

  • Here we were given the diameter, d, however this formula is in terms of the radius, r.
  • The diameter is equivalent to double the radius, d = 2r
  • Therefore the radius is equivalent to half the diameter, r=\frac{1}{2} d
  • Plugging in d to solve for r we get r=\frac{1}{2}(2) which simplifies to r = 1

The two variables for this equation we have no obtained, A = 12π and r = 1, so we can plug them into our equation to solve for the height

  • h=\frac{12\pi -2\pi (1)^{2}  }{2\pi (1)}=h=\frac{12\pi -2\pi  }{2\pi }=\frac{10\pi }{2\pi } =5
  • The height is 5 inches
4 0
3 years ago
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