Find the greatest common factor of the following monomials. 45s^6t^5 6s^2t^3 12s^4t^4

1 answer:

3 0

$45s^6t^5=3\cdot\boxed{3}\cdot5\cdot \boxed{s^2}\cdot s^4\cdot\boxed{ t^3}\cdot t^2\\\\6s^2t^3=2\cdot\boxed{3}\cdot \boxed{s^2}\cdot \boxed{t^3} \\\\12s^4t^4=2\cdot2\cdot\boxed{3}\cdot \boxed{s^2}\cdot s^2\cdot \boxed{t^3}\cdot t\\\\GCF(45s^6t^5;\ 6s^2t^3;\ 12s^4t^4)=3s^2t^3$

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The scores on a quiz are normally distributed. The mean of the quiz is 93 and the standard deviation is 4.2. By using the Empiri

xz_007 [3.2K]

Answer:

any score that lies between 88.8 and 97.2 is within one std. dev. of the mean

Step-by-step explanation:

One std. dev. above the mean would be 93 + 4.2, or 97.2. One std. dev. below the mean would be 93 - 4.2, or 88.8.

So: any score that lies between 88.8 and 97.2 is within one std. dev. of the mean.

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2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.

likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4 + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

$y = ^+_- \sqrt{-x^2+4x+4} -5$

Thus

$f(x) = \sqrt{-x^2+4x+4} - 5$

$g(x) = -\sqrt{-x^2+4x+4} - 5$

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

$\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0$