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Leya [2.2K]
3 years ago
7

a square is a figure with two pairs of parallel sides and four write angles. is the statement a good definition? if not find a c

ounterexample
Mathematics
2 answers:
Ahat [919]3 years ago
7 0
The statement is not a good definition.

A counterexample is a rectangle.

A rectangle has two pairs of parallel side and four right angles, but it is not a square.
sertanlavr [38]3 years ago
5 0
No, because that could easily be defining a rectangle as well as a square.

A square is a figure with two pairs of parallel sides of the same length, and four right angles.
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For what values of b are the vectors \langle -46, b, 10 \rangle and \langle b, b^2, b \rangle orthogonal
Jet001 [13]

Answer:

b = 6 or b = -6 (non-zero vectors)

b = 0 (zero vector)

Step-by-step explanation:

Two vectors \vec{a}=\langle a_1,a_2,a_3\rangle and \vec{b}=\langle b_1,b_2,b_3\rangle are orthogonal if their dot product is equal to 0, or in other words

a_1\cdot b_1+a_2\cdot b_2+a_3\cdot b_3=0

In your case,

\vec{a}=\langle -46, b, 10\rangle\\ \\\vec{b}=\langle b,b^2,b\rangle

Hence, if vectors a and b are orthogonal, then

-46\cdot b+b\cdot b^2+10\cdot b=0\\ \\-46b+b^3+10b=0\\ \\b^3-36b=0\\ \\b(b^2-36)=0\\ \\b(b-6)(b+6)=0\\ \\b=0\text{ or }b=6\text{ or }b=-6

Note, then if b = 0, then \vec{b}=\langle 0,0,0\rangle and zero-vector is orthogonal to any other vectors.

Thus, b = 6 or b = -6.

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3 years ago
What is 200 less than?
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201

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