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svetlana [45]
3 years ago
15

The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

Mathematics
1 answer:
Firdavs [7]3 years ago
6 0

Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:

<em>y</em> = -1 - <em>x</em>  ==>  <em>x</em> = -1 - <em>y</em>

<em>y</em> = <em>x</em> - 1  ==>  <em>x</em> = 1 + <em>y</em>

So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.

This means the area is given by the integral,

\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy

The integral with respect to <em>x</em> is trivial:

\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy

For the remaining integral, integrate term-by-term to get

\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

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Step-by-step explanation:

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5 0
2 years ago
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Hamburgers cost $3 and hotdogs cost $2. The total cost of buying b hamburgers and d hotdogs can be expressed by C=3b+2d. How can
Temka [501]
C = 3b+2d is the same as 3b+2d = C

Let's isolate d. To do this, we first need to subtract 3b from both sides

3b+2d = C
3b+2d-3b = C-3b
2d = C-3b

Then divide both sides by 2

2d = C-3b
2d/2 = (C-3b)/2
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Take note of the parenthesis as they are very important. We want to divide ALL of C-3b over 2. We don't want to just divide -3b over 2.

The answer choices you have aren't 100% clear but I have a feeling your teacher meant to say d = (C-3b)/2 instead of d = C-3b/2 for choice A

If that assumption is correct, then the answer is choice A.
7 0
3 years ago
My Than purchased a bicycle costing RS 56oo from a dealer at 51 discount and a sold a profit of 10%. If he had soll it at sy dis
Alisiya [41]

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3 years ago
X/2 is greater than or equal to -4
irga5000 [103]
\frac{x}{2}≥-4

Pretend the greater than or equal to sign is an equal sign, we will substitute it back in later.

x/2 = -4
Multiply both sides by 2 to get x alone
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3 years ago
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Kay [80]

Answer:

x= -8     x=2

Step-by-step explanation:

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Subtract 10 from each side

x^2 +6x -16 =0

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Using the zero product property

x+8 =0    x-2 =0

x= -8     x=2

8 0
3 years ago
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