Dan Perkins goat is attached to the corner of the 14-foot-by-7-foot pump house by a 14-foot length of rope. The goat eats the gr
1 answer:
<span>This pattern consists of three-fourths of a circle of radius 14 feet and one-fourth of a circle of radius 7 feet. What area of grass can Dan Perkins goat eat?</span>
We know that the formula for the area of the pitch circle are:
where alpha is the pinch of circle, r is radius, and pi is mathematics constant approximately equal 3,14
We know that the formula for the area of the pitch circle are:
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Answer:
Step-by-step explanation:
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Let's use FOIL (first, outer, inner, last) to solve this. We'll multiply the terms by one another in that fashion.
Rearrange in decreasing exponents.
Answer:
(A) Set A is linearly independent and spans . Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors , we are to decide which of the given statements is true:
In Matrix , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans . Thus it is basis for
.