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Effectus [21]
3 years ago
8

The positions of two divers from the water’s surface after a dive are shown:

Mathematics
1 answer:
Travka [436]3 years ago
8 0

Answer:

Step-by-step explanation:

the 4 one

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Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into
Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = (\frac{60\pi }{\pi+4}) in

b)the length of the wire for the square = (\frac{240}{\pi+4}) in

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

         b=\frac{y}{4}

Area of the square which is L² can now be said to be;

A_S=(\frac{y}{4})^2 = \frac{y^2}{16}

On the otherhand; let the radius (r) of the  circle be;

2πr = 60-y

r = \frac{60-y}{2\pi }

Area of the circle which is πr² can now be;

A_C= \pi (\frac{60-y}{2\pi } )^2

     =( \frac{60-y}{4\pi } )^2

Total Area (A);

A = A_S+A_C

   = \frac{y^2}{16} +(\frac{60-y}{4\pi } )^2

For the smallest possible area; \frac{dA}{dy}=0

∴ \frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0

If we divide through with (2) and each entity move to the opposite side; we have:

\frac{y}{18}=\frac{(60-y)}{2\pi}

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

y= \frac{240}{\pi+4}

∴ since y= \frac{240}{\pi+4}, we can determine for the length of the circle ;

60-y can now be;

= 60-\frac{240}{\pi+4}

= \frac{(\pi+4)*60-240}{\pi+40}

= \frac{60\pi+240-240}{\pi+4}

= (\frac{60\pi}{\pi+4})in

also, the length of wire for the square  (y) ; y= (\frac{240}{\pi+4})in

The smallest possible area (A) = \frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

4 0
3 years ago
Matt he bought five book he needed 9 how many more he needed
Dimas [21]

Answer:

5

Step-by-step explanation:

4 0
2 years ago
What are the parallel sides of a trapezoid​
saul85 [17]

Answer:

Parallel means that the lines will never cross. If we look at a  traditional trapezoid, the top side and the bottom side are straight lines that will never cross one another. The left and right sides are slanted towards one another, to they are not parallel.

Hope this helped. : )

3 0
3 years ago
Lutfen soruyu cevaplayın ​
elena-s [515]

Answer:

huh????

Step-by-step explanation:

what did you try to say

8 0
2 years ago
John wanted to estimate the product of 5.2 and 6.7. What is the best estimate for his problem?
NNADVOKAT [17]
Round 5.2 down to 5 and Round 6.7 to 7.
5+7=12
8 0
3 years ago
Read 2 more answers
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