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3 years ago

The prime factorization of N is 3^3 * 7^r. If N has exactly 16 positive integer factors, what is the value of R?

Mathematics

2 answers:

lord [1]3 years ago

8 0

Answer:

3^3 * 7^r has (3 + 1)*(r + 1) = 16 factors.

So r must be 3.

LenaWriter [7]3 years ago

3 0

Answer:

Step-by-step explanation:

N = 3^3 * 7^r

N has 16 integer factors

3^3 is 3 factors

That means 7^r must be 16-3 or 13 factor

7^r must be 13 terms

so 7^r must be 7*7*7..... *7 so that there are 13 term which means

r must be 13

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Ostrovityanka [42]

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Step-by-step explanation:

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3 years ago

A display case of glitter stickers are marked 15 for $2. If Cathy wants to buy 30 glitter stickers, how much will Cathy spend?

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3 years ago

Read 2 more answers

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:

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

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

$A = 4$

4 0

3 years ago