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Pavlova-9 [17]
3 years ago
7

Calculate the length a to two decimal places.

Mathematics
2 answers:
Anton [14]3 years ago
7 0
Obtuse scalene triangle.
<span>
Sides: </span>a = 7   b = 9   c = 3.31

<span>Area: </span>T = 10.324

<span>Perimeter: </span>p = 19.31
<span>
Semiperimeter: </span>s = 9.655

<span>Angle </span>∠ A = α = 43.868° = 43°52'6″ = 0.766<span> rad</span>
<span>
Angle </span>∠ B = β = 117° = 2.042<span> rad</span>
<span>
Angle </span>∠ C = γ = 19.132° = 19°7'54″ = 0.334<span> rad</span>

<span>Height: </span>ha<span> = 2.9</span>5
<span>
Height: </span>hb<span> = 2.29</span>4
<span>
Height: </span>hc<span> = 6.23</span>7

<span>Median: </span>ma<span> = 5.80</span>8
<span>
Median: </span>mb<span> = 3.11</span>9
<span>
Median: </span>mc<span> = 7.89</span>1


<span>Inradius: </span>r = 1.069
<span>
Circumradius: </span>R = 5.05

<span>Vertex coordinates: </span>A[3.31; 0] B[0; 0] C[-3.178; 6.237]
<span>
Centroid: </span>CG[0.044; 2.079]
<span>
Coordinates of the circumcenter: </span>U[1.655; 4.772<span>]

</span>
ivolga24 [154]3 years ago
6 0

Answer:

13.68

Step-by-step explanation:

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A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria
Luda [366]

The maximum and the minimum total area inclosed are 6.25m² and 2.72m²

What is an area?

⇒ The area is the region bounded by the shape of an object.

Calculation:

Let x is the length of the piece of wire for the equilateral triangle, whose side will then be (x/3) m long.

⇒  (10 - x) = length of the remaining piece for the square, whose side will then be (10 - x)/4 m long.

h = height of the equilateral triangle = h = a×√3/2 = (x/3)×(√3/2)

(Where a is the side of the triangle)

A(x) = Total area of the square formed + Total area of the triangle formed

Then    A(x) = [(10 - x)/4]²+ (1/2)(x/3)(x/6)√3

                   = [(100 - 20x + x²)/16] +  (√3/36)x² .

           

The maximum total area enclosed :

⇒ The entire 10m length should be allocated to the square because a square produces more area per unit of its perimeter than does a triangle.

Thus if all square, then x=0 and A(0)  = [2.5]² = 6.25 m² = Maximumarea

If all triangle, then x = 10  and  A(10) = (1.732/36)(100) = 4.811 m² .

So, the maximum area occurs when it's all used to make a square of side 2.5 m.

The minimum total area enclosed is :

⇒ We want a relatively small square and a small triangle.

 We are going to Find x by setting the derivative of A(x) to zero.

d[ A(x)]/dx  =   [(-20 + 2x)/16] + (2√3/36)x = 0

                  =  -5/4  + (1/8)x  +  (√3/18)x  = 0

                 x =  5/[4 (1/8 + √3/18)]  = 5/[ 4(0.125 + 0.09622)] = 5/(0.88489)  ⇒5.65 m perimeter of the triangle                  

             

and (10 - x) = 4.35 = perimeter of square

And  

A(5.65) = [4.35/4]² +  (√3/36)(5.65)²

             = 1.1827 from the square+1.5358 from the triangle

             =  2.719m² total area = Minimum area

⇒ On rounding off it will be 2.72m²

Hence the maximum and the minimum areas are 6.25m² and 2.72m²

Learn more about the area here:

brainly.com/question/25292087

#SPJ1

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Questions:  A piece of wire 10m long is cut into two pieces. one piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a. a maximum? b. minimum?

8 0
1 year ago
Solve each system of equations algebraically. For each one, explain what the solution (or lack thereof) tells you
Paul [167]

Answer:

a: no solutions

b: (2, 3)

Step-by-step explanation:

a:

In both equations, the slope of x is the same, but the y-intercept is not, which means they are parallel. Therefore, this system of equations has no solutions.

b:

Since both of the equations are equal to y, we can set them equal to each other:

\frac{1}{2}x^2+1= 2x-1\\x^2 + 2 = 4x - 2\\x^2-4x+4=0

We can solve by factoring (by finding a number that multiplies to 4 and adds up to -4):

(x-2)^2 = 0

x = 2

Now, to find y, plug-in x to any of the equations:

y = 2*2-1 = 3

Therefore, the solution to this system of equation is (2, 3)

I hope this helped.

4 0
3 years ago
1 -12.166 + (-1.54)​
castortr0y [4]

Answer:

-12.706

Step-by-step explanation:

First we distribute: 1 - 12.166 - 1.54

Then we subtract: -12.706

8 0
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Please help asap!!! 16 points
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You are given a table in which each row represents the coordinates of points.  For example, in the first line, we have x=-7 and y=5.  Work through the four given equations, one at a time, subbing -7 for x and 5 for y; is the equation still true?  If yes, then you have found the correct answer.  B is the exception; I'd suggest you check out equations A, C and D first, before focusing on B.

Example:  D:  (5)-5 = 2((-7) + 7) leads to 0 = 0.  Is that true?  If so, D is likely the correct answer. 
3 0
3 years ago
Please help. Will mark Brainliest to whoever gets it right! :)
levacccp [35]

Answer:

A's average speed is 100. I did this same thing and passed my grade.

6 0
3 years ago
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