Four square pieces of corkboard are lined up to make a rectangle. The area of the entire corkboard is
1 answer:
9514 1404 393
Answer:
a) attached
b) 100 square inches, 1/4 of the total
c) square root of area
d) multiply by 4
Step-by-step explanation:
a) A diagram is attached
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b) If the total area consists of 4 squares of the same size, then the area of one square will be 1/4 of the total area. 1/4 of 400 square inches is 100 square inches, the area of one square.
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c) The area of a square is the square of the side length. You find the side length by finding the square root of the area. √(100 in²) = 10 in, the side length of each square.
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d) The rectangle is 4 squares laid side by side, so its length is 4 times the side length of one square: 4×10 in = 40 in.
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Let r be a radius of a given circle and α be an angle, that corresponds to a sector.
The circle area is
and denote the sector area as 
.
Then
(the ratio between area is the same as the ratio between coresponding angles).
.
The circle area is
Then
Answer:
True. See the explanation and proof below.
Step-by-step explanation:
For this case we need to remeber the definition of linear transformation.
Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:
1) T(x+y) = T(x) + T(y)
2) T(cv) = cT(v)
For all vectors and for all scalars
. And A is called the domain and B the codomain of T.
Proof
For this case the tranformation proposed is t:
Where
For this case we have the following assumption:
1) The transpose of an nxm matrix is an nxm matrix
And the following conditions:
2)
And we can express like this
3) If and
then we have this:
And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.