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alekssr [168]
3 years ago
7

The sum of the roots of the quadratic 5x^2 - 6x + 1 = 0 is

Mathematics
1 answer:
MatroZZZ [7]3 years ago
8 0

Answer:

here's your answer

hope this helped you

please mark as the brainliest (ㆁωㆁ)

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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
the driving distance between Manchester and London is 195 miles. Faris intends to travel from Manchester to London by coach. The
Dahasolnce [82]

Answer:

7.24pm

Step-by-step explanation:

196+50=3.9h

0.9h=0.9x60mnt=54mnt

3.9h=3h 54mnt

3:30pm+3h 54mnt

3:30pm+3h 54mnt=7.2pm

3 0
3 years ago
Can someone pls pls help me ?
Yakvenalex [24]

9514 1404 393

Answer:

  a = 9 meters

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  28 m = a + 2m + a + 8m

  18 m = 2a . . . . . . . . . . . . . . . . subtract 10m, collect terms

  9 m = a . . . . . . . . . . . . . . . divide by 2

The value of a is 9 meters.

8 0
3 years ago
How would you prove these two triangles conrguent?
Crank

Answer:

SSS

Step-by-step explanation:

4 0
3 years ago
Which expression is equivalent to log_5(x/4)^2?
viktelen [127]

For this case we must find an expression equivalent to:

log_ {5} (\frac {x} {4}) ^ 2

So:

We expanded log_ {5} ((\frac {x} {4}) ^ 2)by moving 2 out of the logarithm:

2log_ {5} (\frac {x} {4})

By definition of logarithm properties we have to:

The logarithm of a product is equal to the sum of the logarithms of each factor:

log (xy) = log (x) + log (y)

The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.

log (\frac {x} {y}) = log (x) -log (y)

Then, rewriting the expression:

2 (log_ {5} (x) -log_ {5} (4))

We apply distributive property:

2log_ {5} (x) -2log_ {5} (4)

Answer:

An equivalent expression is:

2log_ {5} (x) -2log_ {5} (4)

3 0
3 years ago
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