Deck of 52 cards contains 5suits: hearts, clubs, diamonds, and spades. each suit consists of cards numbered 2 through 10, a jack
1 answer:
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Answer:
is linearly dependent set.
Step-by-step explanation:
Given: is a linearly dependent set in set of real numbers R
To show: the set is linearly dependent.
Solution:
If is a set of linearly dependent vectors then there exists atleast one
such that
Consider
A linear transformation T: U→V satisfies the following properties:
1.
2.
Here, ∈ U
As T is a linear transformation,
As is a linearly dependent set,
for some
So, for some
Therefore, set is linearly dependent.
<h3>Answer: Largest value is a = 9</h3>
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Work Shown:
b = 5
(2b)^2 = (2*5)^2 = 100
So we want the expression a^2+3b to be less than (2b)^2 = 100
We need to solve a^2 + 3b < 100 which turns into
a^2 + 3b < 100
a^2 + 3(5) < 100
a^2 + 15 < 100
after substituting in b = 5.
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Let's isolate 'a'
a^2 + 15 < 100
a^2 < 100-15
a^2 < 85
a < sqrt(85)
a < 9.2195
'a' is an integer, so we round down to the nearest whole number to get
So the greatest integer possible for 'a' is a = 9.
------------------
Check:
plug in a = 9 and b = 5
a^2 + 3b < 100
9^2 + 3(5) < 100
81 + 15 < 100
96 < 100 .... true statement
now try a = 10 and b = 5
a^2 + 3b < 100
10^2 + 3(5) < 100
100 + 15 < 100 ... you can probably already see the issue
115 < 100 ... this is false, so a = 10 doesn't work