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Anna11 [10]
2 years ago
14

The following three shapes are based only on squares, semicircles, and quarter circles.

Mathematics
1 answer:
grin007 [14]2 years ago
4 0

The perimeter of the shaded part is: 25.1 cm.

The area of the shaded part is: 36.6 cm².

<h3>How to Find the Perimeter and Area of the Shaded Part?</h3>

Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).

Parameters given are:

  • s = 8 cm
  • r = 8 cm

Plug in the values into the equation

Area = 8² - 2(8² - 1/4π(8²)).

Area = 64 - 2(64 - 50.3)

Area = 36.6 cm²

Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm

Learn more about perimeter and area on:

brainly.com/question/443376

#SPJ1

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\bf P=182e^{kt}\qquad &#10;\begin{cases}&#10;2002\impliedby \textit{8 years later}\\&#10;t=8\qquad P=186&#10;\end{cases}\implies 186=182e^{k8}&#10;\\\\\\&#10;\cfrac{186}{182}=e^{8k}\implies ln\left( \frac{93}{91} \right)=ln(e^{8k})\implies ln\left( \frac{93}{91} \right)=8k&#10;\\\\\\&#10;\cfrac{ln\left( \frac{93}{91} \right)}{8}=k\implies 0.0027\approx k\implies \boxed{P=182e^{0.0027t}}

what's the population in 2004?  well,  from 1994 to 2004 is 10 years later, so t = 10

plug that in, to get P for 2004
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3 years ago
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barxatty [35]

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Find the exact value of the following expression (without using a calculator): tan(Sin^-1 x/2)
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Answer:

tan(Sin^-1 x/2)=  \frac{x/2}{\sqrt{1-x^{2}/4 } }

Step-by-step explanation:

Let sin^-1 x/2= θ

then sinθ= x/2

on the basis of unit circle, we have a triangle with hypotenuse of length 1,   one side of length x/2 and opposite angle of θ.

          tan(Sin^-1 x/2) = tanθ

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as per trigonometric identities cosθ= √(1-sin^2θ)

           tanθ= sinθ/ √(1-sin^2θ)

substituting the value sinθ=x/2 in the above equation

             tanθ= \frac{x/2}{\sqrt{1-x^{2}/4 } }

now substituting the value sin^-1 x/2= θ in above equation

             tan(sin^-1 x/2) =  \frac{x/2}{\sqrt{1-x^{2}/4 } }

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3 0
3 years ago
Item 12
GalinKa [24]

Answer:

The maximum height of the water balloon occurs at x = 0.

The water balloon is in the air for 2 s.

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I'm confused since it does start at a height of 64, but I think it meant that it started lower then went up, so I would say that wouldn't be true.

The water balloon hits the ground in 64 s

it hits the ground at 2 seconds

4 0
3 years ago
Read 2 more answers
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