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The attached diagram represents the Venn diagram of the sets
<h3>How to draw the Venn diagram?</h3>The sets are given as:
- The universal set, U = The set of integers.
- A = The set of even integers.
- B = The set of odd integers.
- C = The set of multiples of 3.
- D= The set of prime numbers
From the above representation, we have the following highlights:
- Set A and set B will not intersect, because no number can be even and odd
- Set C and set D will intersect set A because they have common elements 6 and 2, respectively
- Set C and set D will intersect set B because they have common elements 3 and 3, respectively
Using the above highlights, we can now draw the Venn diagram
See attachment for the Venn diagram
Read more about Venn diagram at:
#SPJ1
Part (a)
<h3>Answer: 12.1</h3>-----------------------
Work Shown:
We'll apply the sine rule since we have a known opposite side of AB = 10 and an unknown hypotenuse we want to find BD.
Focus on triangle ABD
sin(angle) = opposite/hypotenuse
sin(D) = AB/BD
sin(56) = 10/x
x*sin(56) = 10
x = 10/sin(56)
x = 12.062179
x = 12.1
Make sure your calculator is in degree mode.
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Part (b)
<h3>Answer: 15.1</h3>-----------------------
Work Shown:
Draw an xy coordinate grid.
Place point A at the origin (0,0).
Point B is 10 units above this, so B is at (0,10).
Point C is at (18,10) since we move 18 units to the right of B.
Point D is at approximately (6.745085, 0). The 6.745085 is from solving tan(56) = 10/x for x.
Refer to the diagram below.
Apply the distance formula for the points C and D.
Segment CD is roughly 15.1 cm long.
