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2 years ago

Tìm kiếm x y z x-1/y =1 y-1/z =1 z-1/x =1

Mathematics

1 answer:

const2013 [10]2 years ago

3 0

y - 1/z = 1 ==> y = 1 + 1/z

z - 1/x = 1 ==> z = 1 + 1/x

==> y = 1 + 1/(1 + 1/x) = 1 + x/(x + 1) = (2x + 1)/(x + 1)

x - 1/y = x - (x + 1)/(2x + 1) = (2x ² - 1)/(2x + 1) = 1

==> 2x ² - 1 = 2x + 1

==> 2x ² - 2x - 2 = 0

==> x ² - x - 1 = 0

==> x = (1 ± √5)/2

If you start solving for z, then for x, then for y, you would get the same equation as above (with y in place of x), and the same thing happens if you solve for x, then y, then z. So it turns out that x = y = z.

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2 years ago

Please help answer the question.

muminat

Answer:

a. $\dfrac{y^8}{x^{10}}$

Step-by-step explanation:

First step is ti distribute the exponent outside the parenthesis. According to the law of exponents, you need to distribute it to each variable.

$\left(\dfrac{x^{-4}y}{x^{-9}y^5}\right)^{-2}\\\\=\dfrac{x^{(-4\times-2)}y^{(1\times-2)}}{x^{(-9\times-2)}y^{(5\times-2)}}\\\\=\dfrac{x^{8}y^{-2}}{x^{18}y^{-10}}$

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$=\dfrac{x^8y^{-2}}{x^{18}y^{-10}}\\\\=\dfrac{x^8y^{10}}{x^{18}y^{2}}\\\\$

Next, when it comes to division, we subtract the exponents of the numerator and the denominator of similar variables.

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2 years ago

The resting heart rate of US females 20 years old or older is normally distributed with a mean of 75 bpm (beats per minute). Sup

Sergio [31]

Answer:

69 bpm

Step-by-step explanation:

Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve. Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.

Next we use the formula for z score to determine the x value representing this woman's heart rate:

x - mean x - 75 bpm

z = ----------------- = -0.43073 = --------------------

std. dev. 15

Thus, x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm

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2 years ago