the original line has a slope of -6/7, so the line perpendicular is 7/6. we swap the numerator and denominator, and if the starting slope is positive, the perpendicular slope would be negative, and the other way around.

3 0

2 years ago

How does adding the log together automatically mean that it is a factorial?

andreyandreev [35.5K]

Answer: The answer is given below.

Step-by-step explanation: We are given an equality involving logarithm and we are to show the implication of L.H.S. to R.H.S.

We will be using the following two properties of logarithm:

$(i)~\log_ba=\dfrac{1}{\log_ab},\\\\\\(ii)~log_ab+\log_ac=\log_a(bc).$

The proof is as follows:

$L.H.S.\\\\\\=\dfrac{1}{\log_2N}+\dfrac{1}{\log_3N}+\dfrac{1}{\log_4N}+\cdots+\dfrac{1}{\log_{100}N}\\\\\\=\log_N2+\logN3+\log_N4+\cdots+\log_N100\\\\=\log_N\{2.3.4...100\}\\\\=\log_N\{1.2.3.4...100\}\\\\=\log_N{100!}\\\\=\dfrac{1}{\log_{100!}N}\\\\=R.H.S.$

Hence proved.

6 0

3 years ago

For what values of k does the graph of y=-2x^2+5x+k not cut the x axis

goldenfox [79]

The answer is 4 because there r three 3 2s

6 0

3 years ago