a line perpendicular to y=-1/5x+1 and intersects the point (-5,1) what is the equation of this perpendicular line

Mathematics

1 answer:

nikitadnepr [17]3 years ago

3 0

Answer:

Step-by-step explanation:

y = -1/5x + 1

the slope here is -1/5.....a perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So our perpendicular slope will have to be 5.....(because I flipped -1/5, making it -5/1, then I switched the sign...making it 5/1 or just 5)

y = mx + b

slope(m) = 5

(-5,1)...x = -5 and y = 1

now we sub and find b, the y int

1 = 5(-5) + b

1 = - 25 + b

1 + 25 = b

26 = b

so ur equation for the perpendicular line is : y = 5x + 26

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Natalija [7]

Split up the interval [2, 5] into $n$ equally spaced subintervals, then consider the value of $f(x)$ at the right endpoint of each subinterval.

The length of the interval is $5-2=3$ , so the length of each subinterval would be $\dfrac3n$ . This means the first rectangle's height would be taken to be $x^2$ when $x=2+\dfrac3n$ , so that the height is $\left(2+\dfrac3n\right)^2$ , and its base would have length $\dfrac{3k}n$ . So the area under $x^2$ over the first subinterval is $\left(2+\dfrac3n\right)^2\dfrac3n$ .

Continuing in this fashion, the area under $x^2$ over the $k$ th subinterval is approximated by $\left(2+\dfrac{3k}n\right)^2\dfrac{3k}n$ , and so the Riemann approximation to the definite integral is

$\displaystyle\sum_{k=1}^n\left(2+\frac{3k}n\right)^2\frac{3k}n$

and its value is given exactly by taking $n\to\infty$ . So the answer is D (and the value of the integral is exactly 39).