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4 years ago

Line segment MN is shown below. If point P(x,y) partitions the line segment

Mathematics

1 answer:

Nina [5.8K]4 years ago

7 0

Answer:

P (-1 , 0)

Step-by-step explanation:

M (-6 , 2) N (9 , -4) P (x , y)

horizontal distance of M and N = 9 - (-6) = 15

vertical distance of M and N = 2 - (-4) = 6

1/3 from x coordinate of M (-6): -6 + 15/3 = -1 This is x coordinate of point P

1/3 from y coordinate of M (2): 2 - 6/3 = 0 This is y coordinate of point P

P (x , y) i.e P (-1 , 0)

check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385

distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77

MP / PN = 5.385 / 10.77 = 0.5 = 1/2

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3 years ago

What is the value of x in theequation 2.5 (6x - 4) = 10 + 4 (1.5 +0.5 x)?

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Answer:

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Step-by-step explanation:

Let's solve your equation step-by-step.

2.5(6x−4)=10+4(1.5+0.5x)

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2.5(6x−4)=10+4(1.5+0.5x)

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Step 2: Subtract 2x from both sides.

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3 years ago

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Answer:

A.Both of the students did the problem correctly.

Step-by-step explanation:

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Read 2 more answers

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worty [1.4K]

The full range is $-\pi$ (length $2L=2\pi$ ), so the half range is $L=\pi$ . The half range sine series would then be given by

$f(x)=\displaystyle\sum_{n\ge1}b_n\sin\dfrac{n\pi x}L=\sum_{n\ge1}b_n\sin nx$

where

$b_n=\displaystyle\frac2L\int_0^Lf(x)\sin\dfrac{n\pi x}L\,\mathrm dx=\frac2\pi\int_0^\pi(\pi-x)\sin nx\,\mathrm dx$

Essentially, this is the same as finding the Fourier series for the function

$\begin{cases}g(x)=\begin{cases}\pi-x&\text{for }0$

Integrating by parts yields

$b_n=\dfrac2\pi\left(\dfrac\pi n-\dfrac{\sin n\pi}{n^2}\right)=\dfrac2n$

So the half range sine series for this function is simply

$f(x)=\displaystyle\sum_{n\ge1}\frac{2\sin nx}n$

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