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Juliette [100K]
3 years ago
7

How do animators use math

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
6 0
It allows the animator<span> to find unknowns from a simple set of equations and to work out aspects of geometric figures when you are dealing with objects that move and change. An </span>animator uses<span> linear algebra to show the way that an object is rotated and shifted and made larger and smaller—all major actions in </span>animation.
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Find the number of elements in A 1 ∪ A 2 ∪ A 3 if there are 200 elements in A 1 , 1000 in A 2 , and 5, 000 in A 3 if (a) A 1 ⊆ A
lina2011 [118]

Answer:

a. 4600

b. 6200

c. 6193

Step-by-step explanation:

Let n(A) the number of elements in A.

Remember, the number of elements in A_1 \cup A_2 \cup A_3 satisfies

n(A_1 \cup A_2 \cup A_3)=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)

Then,

a) If A_1\subseteq A_2, n(A_1 \cap A_2)=n(A_1)=200, and if A_2\subseteq A_3, n(A_2\cap A_3)=n(A_2)=1000

Since A_1\subseteq A_2\; and \; A_2\subseteq A_3, \; then \; A_1\cap A_2 \cap A_3= A_1

So

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-200-200-1000-200=4600

b) Since the sets are pairwise disjoint

n(A_1 \cup A_2 \cup A_3)=\\n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\200+1000+5000-0-0-0-0=6200

c) Since there are two elements in common to each pair of sets and one element in all three sets, then

n(A_1 \cup A_2 \cup A_3)=\\=n(A_1)+n(A_2)+n(A_3)-n(A_1\cap A_2)-n(A_1\cap A_3)-n(A_2\cap A_3)-n(A_1\cap A_2 \cap A_3)=\\=200+1000+5000-2-2-2-1=6193

8 0
3 years ago
5/6÷5=___<br><br>3/7÷6=___<br><br>5/8÷8=___<br><br>15/8÷5​=___
alexandr1967 [171]

Answer:

1/6

1/14

5/64

3/8

Step-by-step explanation:

Easiest and fastest way to evaluate these is to plug it into a calc.

7 0
3 years ago
What is the volume of the right rectangular prism, in cubic inches?
Natali5045456 [20]

Answer:

V=576

Step-by-step explanation:

6 0
3 years ago
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Eight friends are sharing 3 pizzas. The pizzas are the same size, and each person will eat the same amount. What fraction tells
Stolb23 [73]

\frac{8}{3}
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3 years ago
I need help with this!
Colt1911 [192]
The answer is 30 units
8 0
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