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3 years ago

What is the value of R in this circuit

Mathematics

1 answer:

goblinko [34]3 years ago

5 0

See that messy ugly fraction on the right side of the equation ? Let's make it easier to write.

If we multiply the top and bottom of the fraction by the same thing, we won't change the value of the fraction. Let's multiply top and bottom by R .

The fraction 1 / (1/R + 1/2R)

Multiply top and bottom by R :

The fraction = R / (1 + 1/2) .

But that's just R/1.5 .

So 20 = R/1.5

Multiply each side of this equation by 1.5 , and you have . . .

30 = R

This is not even a problem about electrical circuits or resistors. This is a problem about handling complicated fractions to make them less messy.

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A piece of cardboard has the dimensions (x + 15) inches by (x) inches with the area of 60 in 2 . Write the quadratic equation th

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Answer:

$x^2 + 15x - 60 = 0$

The actual dimension is 18.28 by 3.28

Step-by-step explanation:

Given

Dimension:

$(x + 15)\ by\ x$

$Area = 60in^2$

Required

Determine the quadratic equation and get the possible values of x

Solving (a): Quadratic Equation.

The cardboard is rectangular in shape.

Hence, Area is calculated as thus:

$Area = Length * Width$

$60= (x + 15) * x$

Open Bracket

$60= x^2 + 15x$

Subtract 60 from both sides

$x^2 + 15x - 60 = 0$

Hence, the above represents the quadratic equation

Solving (b): The actual dimension

First, we need to solve for x

This can be solved using quadratic formula:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 1$

$b = 15$

$c = -60$

So:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-15 \± \sqrt{15^2 - 4*1*-60}}{2*1}$

$x = \frac{-15 \± \sqrt{225 + 240}}{2}$

$x = \frac{-15 \± \sqrt{465}}{2}$

$x = \frac{-15 \± \21.56}{2}$

Split:

$x = \frac{-15 + 21.56}{2}$ or $x = \frac{-15 - 21.56}{2}$

$x = \frac{6.56}{2}$ or $x = \frac{-36.36}{2}$

$x = 3.28$ or $x = -18.18$

But length can't be negative;

So:

$x = 3.28$

The actual dimensions: $(x + 15)\ by\ x$ is

$Length =3.28 +15$

$Length =18.28$

$Width = x$

$Width =3.28$

The actual dimension is 18.28 by 3.28

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