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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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mixas84 [53]

 

P = 12 + 6 + 8,5 = 18 + 8,5 = 26,5 mm

A = 12 × 4 / 2 = 48 / 2 = 24 mm²



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3 years ago
Lyle is sewing for a project. Find the total cost if he purchases: pattern $5.98, fabric $16.39, thread $2.25, and Velcro $1.29.
sesenic [268]
$25.91 is the correct answer
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Which place value contains the 7 in the quotient of 8,928 divided by 24?
Ainat [17]

Answer: 7 is in tens place

Step-by-step explanation: 8928 ÷ 24 = 372

Ones place - 2

Tens place - 7

Hundreds place - 3

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2 years ago
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Can someone help me with this math problem ?? Pls it’s for my final !
Airida [17]

Answer:

221.87 feet

Step-by-step explanation:

Given that,

A 525 ft cable runs from the top of an antenna to the ground.

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Using trigonometry,

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θ = 25°

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\sin\theta=\dfrac{P}{H}\\\\P=H\sin\theta\\\\P=525\times \sin(25)\\\\P=221.87\ ft

So, the height of the antenna is equal to 221.87 feet.

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3 years ago
An ice cream shoppe charges $1.19 for a scoop of ice cream and $0.49 for each topping. Jeb paid $4.55 for a three scoop sundae.
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He bought 3 scoops, each costing $1.19
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