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Ainat [17]
2 years ago
15

What is the 2nd equivalent fraction to 1/11

Mathematics
1 answer:
alisha [4.7K]2 years ago
6 0
2/22.
i think
sorry if it’s wrong
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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
Read 2 more answers
Order of operations what should be done first to evaluate 6+ (-5-7) ÷ 2 -8(3)
Maru [420]

Answer:-24

Step-by-step explanation:

6+(-5-7) ➗ 2-8(3)

6-12 ➗ 2-24

6-6-24

0-24=-24

3 0
3 years ago
Select the correct answer from each drop-down menu. Right triangle ABC is represented with the right angle at vertex B. Base BC
Svetradugi [14.3K]

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

<h3>How to get the measures of the other two sides of the right triangle?</h3>

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

  • sin(a) = (adjacent cathetus)/(hypotenuse).
  • tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

  • hypotenuse = AC
  • opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

brainly.com/question/2217700

#SPJ1

6 0
2 years ago
How can you tell if a mixture is homogenous or heterogeneous?
irinina [24]

A homogeneous mixture has the same uniform appearance and composition throughout. Many homogeneous mixtures are commonly referred to as solutions. A heterogeneous mixture consists of visibly different substances or phases. The three phases or states of matter are gas, liquid, and solid.

4 0
3 years ago
Veronica spent a minimum of $65 on a doll and accessories for the doll. The doll cost $26 and the accessories cost $13 each. Wri
ANEK [815]

Answer:  13x+26 \ge 65

If you solve for x, you get x \ge 3 which means she bought at least 3 accessories.

=========================================================

Explanation:

x = number of accessories, some nonnegative whole number

13x = amount spent on accessories only

For instance, let's say she bought 5 accessories. This means she spent 13x = 13*5 = 60 dollars on those five items.

This is on top of the $26 Veronica paid for the doll itself (without the accessories). In total, she spent 13x+26 dollars for the doll (26) and the accessories (13x) combined.

We're told she spent a minimum of $65, which means that she spent 65 or more dollars.

So the total cost (13x+26) must be equal to 65 or larger than 65.

We write that as 13x+26 \ge 65 which sets up the inequality.

----------------------------

Let's solve for x

13x+26 \ge 65\\\\13x \ge 65-26\\\\13x \ge 39\\\\x \ge 39/13\\\\x \ge 3\\\\

So x can be equal to 3, or larger than it.

The lowest value x can be is 3.

Meaning that she bought at least 3 accessories (ie she bought 3 or more accessories).

3 0
3 years ago
Read 2 more answers
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