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alex41 [277]
2 years ago
5

Ian drew this example of a five-pointed star. He wants to create a computer program to draw five-pointed stars in general. To do

this, he needs to know about the relationships between the internal acute angles at the points of the star. What is the sum of the angles at its five points (in degrees)? Justify your answer.
Mathematics
1 answer:
Sunny_sXe [5.5K]2 years ago
3 0

The sum of the angles at its five points is 900 degrees.

<h3><u>Geometry </u></h3>

Since Ian drew a five-pointed star, to determine what is the sum of the angles at its five points in degrees, the following calculation must be performed:

  • Five pointed star = 5 triangles
  • 1 triangle = 180 degrees in its interior angles
  • 180 x 5 = 900

Therefore, the sum of the angles at its five points is 900 degrees.

Learn more about geometry in brainly.com/question/11298860

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A sector of a circle has a central angle of 45 . Find the area of the sector if the radius of the circle is 15 cm.
prohojiy [21]

Answer:

A = 28.125 * pi cm^2

A = 88.357  cm^2


Step-by-step explanation:

Area of a sector is 1/2 r^2 theta  where theta is in radians

convert 45 degrees to radians

theta = 45 * pi/180 = pi/4

A = 1/2 * 15^2 * pi/4

A =1/2 * 225 * pi/4

A = 28.125 * pi cm^2

A = 88.357  cm^2


6 0
3 years ago
MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t
ioda

Answer:

We would have

                                    l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}

where " l " is  length, " w"  is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

         Surface area for a box with no top = lw+2lh+2wh = 64

where " l " is  length, " w"  is width and "h" is height.

 Step 2.

Remember as well that

                              Volume of the box = l*w*h

Step 3

 We can now use lagrange multipliers.  Lets say,

                                    F(l,w,h) = lwh

and

                                g(l,w,h) = lw+2lh+2wh = 64

By the lagrange multipliers method we know that                            

 

                                                     \nabla F  = \lambda \nabla g

Step 4

Remember that

                          \nabla F  = (wh,lh,lw)

and

                      \nabla g = (w+2h,l+2h , 2w+2l)

So basically you will have the system of equations

                              wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

                                   lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)

Then you would get

                      l\lambda (w+2h) = w\lambda (l+2h) =  h\lambda (2w+2l)

You can get rid of \lambda from these equations and you would get

                         lw+2lh = lw+2wh =  2wh+2lh

And from those equations you would get

                                             l = w =2h

Now remember the original equation

                                    lw+2lh+2wh = 64

If we plug in what we just got, we would have

                                 l^{2} + l^{2} + l^2   =  64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}

                       

                                                 

7 0
3 years ago
Write the standard number for 800,000 + 4,000 + 600 + 40 + 2.
murzikaleks [220]

Answer:

804,642

Step-by-step explanation:

800,000 + 4,000 + 600 + 40 + 2.

Add the terms

804,642

4 0
3 years ago
Write a multiplication equation and a division equation for each statement or diagram. Eight $5 bills are worth $40. There are 9
OLga [1]

Answer:

Eight $5 bills are worth $40.  5x8=40                40/5=8

There are 9 thirds in 3 ones. 3x3=9                    9/3=3

A tape diagram of 5 equal parts. Each part is labeled one fifth. Above the bar is a bracket, labeled 1, that spans the entire length of the bar.  

5x 0.20=1                       5/1= 0.20

Step-by-step explanation:


5 0
3 years ago
Read 2 more answers
H(x)=2x-4/3<br> o h^-1(x)= 3x-12/2<br> o h^-1(x)= 3/(2x-4)<br> o h^-1(x)= 3x+4/2
Fed [463]

Answer:

\large\boxed{h^{-1}(x)=\dfrac{3x+4}{2}}

Step-by-step explanation:

h(x)=\dfrac{2x-4}{3}\to y=\dfrac{2x-4}{3}\\\\\text{Exchange x to y and vice versa}:\\\\x=\dfrac{2y-4}{3}\\\\\text{Solve for y:}\\\\\dfrac{2y-4}{3}=x\qquad\text{multiply both sides by 3}\\\\2y-4=3x\qquad\text{add 4 to both sides}\\\\2y=3x+4\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+4}{2}

7 0
3 years ago
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