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anyanavicka [17]
3 years ago
9

Find the area of the polygon. All angles in the figure are right triangles.

Mathematics
1 answer:
svet-max [94.6K]3 years ago
7 0

Answer:

The area is 207 square feet

Step-by-step explanation:

*The area of the rectangle whose dimensions are 21 and 15 is 315 square feet

*The area of the rectangle whose dimensions are 12 and 9 is 108 square feet

*By subtracting the small area from the big area you will get the area of the polygon

*The area of the polygon = 315 - 108 = 207 square feet

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Set

\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta

The region R is given in polar coordinates by the set

R=\left\{(r,\theta)\mid2\le r\le3,0\le\theta\le\dfrac\pi2\right\}

So we have

\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_2^3r\sin(r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac\pi4(\cos4-\cos9)}

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3 years ago
Original price: $32 ;Markup: 12.5% ;what is Retail Price
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3 years ago
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stepladder [879]

Answer:

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Step-by-step explanation:

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3 0
3 years ago
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Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a samp
Anastaziya [24]
Given:
μ = $3.26 million, averaged salary
σ = $1.2 million, standard deviation
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Let x = random test value
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z = (x - μ)/ (σ/√n) = (4 - 3.26)/(1.2/10) = 6.1667

From standard tables,
P(z<6.1667) = 1
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In triangle RG shown below. m 63 and m 30 Which of the following is the<br> 63
Tatiana [17]

Answer:

The value of the hypotenuse is 69.77 meters.

Step-by-step explanation:

To determine, in triangle RG, the value of its hypotenuse if its sides measure 63 meters and 30 meters, the following calculation must be performed, applying the Pythagorean theorem:

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Therefore, the value of the hypotenuse is 69.77 meters.

7 0
3 years ago
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