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Alinara [238K]
3 years ago
7

Guided Practice

Mathematics
1 answer:
s2008m [1.1K]3 years ago
6 0

Answer:

A.

1.125%; 0.375%

Step-by-step explanation:

Quarterly interest rate is 4.5 / 4 = 1.125%.

Monthly rate is 4.5 / 12 = 0.375%.

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If y is a differentiable function of x, then the slope of the tangent to the curve xy-2y 4y^2=6 at the point where y=1 is
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3. Let U and V be subspaces of a vector space W. Prove that their intersection UnV is also a subspace of W
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Answer:  The proof is done below.

Step-by-step explanation:  Given that U and V are subspaces of a vector space W.

We are to prove that the intersection U ∩ V is also a subspace of W.

(a) Since U and V are subspaces of the vector space W, so we must have

0 ∈ U and 0 ∈ V.

Then, 0 ∈ U ∩ V.

That is, zero vector is in the intersection of U and V.

(b) Now, let x, y ∈ U ∩ V.

This implies that x ∈ U, x ∈ V, y ∈ U and y ∈ V.

Since U and V are subspaces of U and V, so we get

x + y ∈ U  and  x + y ∈ V.

This implies that x + y ∈ U ∩ V.

(c) Also, for a ∈ R (a real number), we have

ax ∈ U and ax ∈ V (since U and V are subspaces of W).

So, ax ∈ U∩ V.

Therefore, 0 ∈ U ∩ V and for x, y ∈ U ∩ V, a ∈ R, we have

x + y and ax ∈ U ∩ V.

Thus, U ∩ V is also a subspace of W.

Hence proved.

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3 years ago
How many pairs of intersecting line segments are shown?
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The answer is 24! You can find this out by just counting them.
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Find the
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