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3 years ago

Please answer with steps

Mathematics

1 answer:

egoroff_w [7]3 years ago

7 0

9514 1404 393

Answer:

n = 99

Step-by-step explanation:

The sum of logarithms is the log of a product. Here, the sum of terms is ...

log(2/1) +log(3/2) +log(4/3) + ... +log((n+1)/n)

= log((2/1)(3/2)(4/3)×...×((n+1)/n)) = log(n+1)

So, the question reduces to ...

log(n+1) = 2

Taking antilogs, we have ...

n +1 = 10^2 = 100

n = 99

The value of n that makes the sum 2 is 99.

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What is the slope of the line that is perpendicular to the line that passes through (-2, 7) and (4, 9)? Type a numerical answer

kodGreya [7K]

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Therefore $m_{2}$ = -3.

Step-by-step explanation:

i) let us say the slope of the line passing through (-2,7) and (4,9) is $m_{1}$ .

ii) to find the slope of the line passing through two points ( $x_{1}$ , $y_{1}$ ) and ( $x_{2}$ , $y_{2}$ ) we use the formula m = $\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }$ . Therefore we can say that $m_{1}$ = $\dfrac{9 - 7}{4 - (-2)}$ = $\dfrac{1}{3}$ .

iii) let us say the slope of the perpendicular line to the line passing through (-2,7) and (4,9) is $m_{2}$

iv) from the formula for the slopes of a line and the line perpendicular to it which is given by $m_{1}$ × $m_{2}$ = -1, therefore $m_{2}$ = -1 ÷ $m_{1}$ = -3. Therefore $m_{2}$ = -3

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3 years ago

Please answer with steps​

Please answer with steps