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4vir4ik [10]
3 years ago
7

PLEASE HELP ASAP! The quotient of two rational numbers is positive. What can you conclude about the signs of the dividend and th

e divisor?
Mathematics
2 answers:
miskamm [114]3 years ago
4 0

Answer:

Step-by-step explanation:

Both dividend and divisor have same sign -  

(i) both have positive sign  or

(ii) both have negative sign

Eg:

(i) \frac{10}{2}=5

(ii)\frac{-10}{-2}=5

Anon25 [30]3 years ago
3 0

Answer:

They either both have to be positive or negative.

Step-by-step explanation:

1 / 1 = 1

-1 / -1 = 1

This gets you positive, when both dividend and divisors are positive or negative.

-1 / 1 = -1

1 / -1 = -1

This gets you negative, when both dividend and divisors are different signs.

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Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.
mafiozo [28]

Answer:

A = 4

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

y = \frac{2}{x}

y'=-2\cdot x^{-2}

The numerical value of the slope is:

y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}

The component of the y-axis is:

y = \frac{2}{9}

Now, the tangent line has the following mathematical model:

y = m \cdot x + b

The value of the intercept is found by isolating it within the equation and replacing all known variables:

b = y - m \cdot x

b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}

Thus, the tangent line is:

y = -\frac{2}{81}\cdot x + \frac{4}{9}

The vertical distance between a point of the tangent line and the origin is given by the intercept.

d_{y} = \frac{4}{9}

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

-\frac{2}{81}\cdot x + \frac{4}{9}=0

-\frac{2}{9}\cdot x + 4 = 0

x = 18

d_{x} = 18

The area of the triangle is computed by this formula:

A = \frac{1}{2}\cdot d_{x}\cdot d_{y}

A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )

A = 4

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vova2212 [387]

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