What is the opposite of 1 / 3

A wire b units long is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle.

mezya [45]

1. Divide wire b in parts x and b-x.

2. Bend the b-x piece to form a triangle with side (b-x)/3

There are many ways to find the area of the equilateral triangle. One is by the formula A= $\frac{1}{2}sin60^{o}side*side= \frac{1}{2} \frac{ \sqrt{3} }{2} (\frac{b-x}{3}) ^{2}= \frac{ \sqrt{3} }{36}(b-x)^{2}$
A= $\frac{ \sqrt{3} }{36}(b-x)^{2}=\frac{ \sqrt{3} }{36}( b^{2}-2bx+ x^{2} )=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}$

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6

3. Let x be the circumference of the circle.

$2 \pi r=x$

so $r= \frac{x}{2 \pi }$

Area of circle = $\pi r^{2}= \pi ( \frac{x}{2 \pi } )^{2} = \frac{ \pi }{ 4 \pi ^{2} }* x^{2} = \frac{1}{4 \pi } x^{2}$

4. Let f(x)= $\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}+\frac{1}{4 \pi } x^{2}$

be the function of the sum of the areas of the triangle and circle.

5. f(x) is a minimum means f'(x)=0

f'(x)= $\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x$ =0

$\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0$

$(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) x=\frac{ \sqrt{3} }{18}b$

$x= \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

6. So one part is $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$ and the other part is b- $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

4 0

3 years ago

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Charity karthik spent $35 of his allowance and gave $5 to a charity. if the number of dollars he spends is proportional to the n

Vera_Pavlovna [14]

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Question 696338: Please I need help solving an algebra: solving proportions
CHARITY Karthik spent $35 of his allowance and gave $5 to a charity. If the number of dollars he spends is proportional to the number of dollars he gives to charitt, how much of much of a $100-allowance will he give to a charity?
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Answer by stanbon(74715) About Me (Show Source):
You can put this solution on YOUR website!
Karthik spent $35 of his allowance and gave $5 to a charity. If the number of dollars he spends is proportional to the number of dollars he gives to charitt, how much of a $100-allowance will he give to a charity?
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x/100 = 5/35
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6 0

3 years ago

Explain how you would write 423,090,709,000 in word form

vfiekz [6]

Four hundred twenty-three billion, ninety million, seven hundred nine thousand

Hope this helped:))

8 0

3 years ago

1.What is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron?

stiks02 [169]

1. Answer;

- Triangle

Explanation;

The cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron is a Triangle.

A tetrahedron also a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

2. Answers

- Triangle

Explanation;

The cross section formed by a plane that intersects three faces of a cube is a Triangle. A cross section is the shape we get when cutting straight through an object. The shape of the cross-section of a solid depends upon the orientation of the cutting plane to the solid.

7 0

3 years ago

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Warm up question, what is 5/6 + 5/6? Explain how you got the answer.

Helga [31]

Answer: 5/3

Step-by-step explanation:

6 0

2 years ago

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