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Dafna1 [17]
2 years ago
15

Could anyone help me with this?

Mathematics
1 answer:
inn [45]2 years ago
5 0

Answer:

93.4 cm²

Step-by-step explanation:

Area of the shaded region = area of the square - area of half of the circle

Area of the shaded region = s² + ½(πr²)

Where,

r = 6.2 cm

s = length of square = diameter of circle = 2*r = 2*6.2

s = 12.4 cm

Plug in the values

Area of the shaded region = 12.4² - ½(π × 6.2²)

= 153.76 - 60.381411

= 93.378589

≈ 93.4 cm² (nearest tenth)

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A piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral trian
padilas [110]

Answer:

a.  8

b. 7

Step-by-step explanation:

Let x be the length of wire for the square and y = 8 -x (eq. 1) be the length of the wire for the equilateral triangle.

We know the x is the total length of the wire used, hence the length of a side of the square will be \frac{x}{4} . The area of the square will be: (\frac{x}{4}) ^ 2

Similarly for the equilateral triangle, perimeter is y. Hence the area will be \frac {\sqrt {3}\ y^2}{4}.

The total area of both shapes will be:  A = (\frac{x}{4})^2 + \frac{\sqrt {3} \ y^2}{4}

We will substitute the value of y from eq. 1:

A = (\frac{x}{4})^2 + \frac{\sqrt {3} \ (8-x)^2}{4}

We find the derivative of the above function to find maximum and minimum: f'(x) = 0 ⇒ A'(x) = 0

A' = \frac{x}{8} - \frac{\sqrt {3} \ (8-x)}{2}

A' = \frac{x}{8} - \frac{\sqrt {3} \ (8-x)}{2} = 0\\\\\frac{x}{8} - \frac{8\sqrt{3} -\sqrt{3} x}{2} =0\\\\x - 4(8\sqrt{3} -\sqrt{3}x)=0\\\\x-32\sqrt3 - 4\sqrt3 x = 0\\\\x - 4\sqrt3 = 32 \sqrt3 \\\\(1 - 4\sqrt3)x = 32 \sqrt3 \\\\x = \frac{32 \sqrt3 }{(1 - 4\sqrt3)}\\\\x =6.99 \approx 7.00

We find A''(7) to check whether x = 7 is the minimum or maximum of the function.

A'' = \frac {1}{8} +\frac {\sqrt {3}}{2} \\\\A'' = 0.99 \approx 1.00

Hence, x = 7 is the minimum and x = 8 will be the maximum

8 0
3 years ago
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