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Naddika [18.5K]
3 years ago
8

Which equation is a line that is parallel to the x- axis and passes through the point (5,2)?

Mathematics
1 answer:
Natali [406]3 years ago
4 0

Answer:

y = 2

Step-by-step explanation:

Since the line is parallel to the x-axis,

the gradient, m = 0

From the point, we know that

x = 5

y = 2

So y = 2 is the line that parallel to x-axis

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Evaluate the integral ∫2−1|x−1|dx
defon

I think you might be referring to the definite integral,

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx

Recall the definition of absolute value:

|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x

Then |x-1|=x-1 if x\ge1, and |x-1|=1-x is x. So spliting up the integral at <em>x</em> = 1, we have

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx

The rest is simple:

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}

5 0
3 years ago
If a+b-c=d, if a-b+c=e, then a= ?
yaroslaw [1]
A + b = d+c 
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A band has 7 new songs and wants to put 5 of them on a demo cd. how many different arrangements of 5 songs are possible.
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Actually, this question first involves COMBINATIONS and then PERMUTATIONS.

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That means we can put each of the 5 song combinations into 120 "5 song sequences". 
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