The formula for the nth square number is S_n = n^2. Use the formula to find the 11th square number.

Mathematics

1 answer:

Klio2033 [76]3 years ago

4 0

Answer:

121.

Step-by-step explanation:

$S_{11} = 11^{2} = 121.$ So, the 11th square number is 121.

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What is y in the first line if the line passing though (-1,y) and (1,0) perpendicular to the line passing (8,4) and (-1,1) ?

malfutka [58]

Answer:

$6$ .

Step-by-step explanation:

A line that goes through $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ where $x_{0} \ne x_{1}$ would have a slope of $m = (x_{1} - x_{0}) / (y_{1} - y_{0})$ .

The slope of the line that goes through $(8,\, 4)$ and $(-1,\, 1)$ would thus be:

$\begin{aligned}m_{2} &= \frac{1 - 4}{(-1) - 8} \\ &= \frac{(-3)}{(-9)} \\ &= \frac{1}{3}\end{aligned}$ .

Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is $(-1)$ .

Thus, if $m_{1}$ and $m_{2}$ denote the slope of the first and second lines in this question, $m_{1}\, m_{2} = (-1)$ since the two lines are perpendicular to one another. Since $m_{2} = (1/3)$ , the slope of the first line would be: