09909909 2345555333333333333333333333333333333333333333333333333333333
9514 1404 393
Answer:
970
Step-by-step explanation:
It turns out that the radical terms cancel, so the result is an integer. You can find the integer value using your calculator. It is ...
(5 +2√6)³ +1/(5 +2√6)³ = 970
_____
The cube of 'a' is ...
(5+2√6)³ = 5³ +3·5²·2√6 +3·5·(2√6)² +(2√6)³
= 125 +3·50√6 +3·120 +48√6
a³ = 485 +198√6
The reciprocal of this is ...
b³ = 1/a³ = 1/(485 +198√6) = (485 -198√6)/(485² -6·198²) = (485 -198√6)/1
b³ = 485 -198√6
Then the sum is ...
a³ +b³ = (485 +198√6) +(485 -198√6) = 970
The <u>different</u> selections of<u> one</u> meat and <u>one</u> vegetable are possible are 18 selections.
Since the Hickory Stick has a selection of 3 meats and 6 vegetables, the number of ways we can select <u>one </u>meat out of 3 is ³C₁ = 3.
Also, the number of ways we can select <u>one </u>vegetable out of 6 is ⁶C₁ = 6.
So, the total number of selections of <u>one</u> meat and <u>one</u> vegetable is ³C₁ × ⁶C₁ = 3 × 6
= 18 selections
So, the <u>different</u> selections of<u> one</u> meat and <u>one</u> vegetable are possible are 18 selections.
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Answer:
4.25x ≤ 50
Number of drink = 11
Step-by-step explanation:
Given:
Amount of gift card = $50
Each drink cost = $4.25
Find:
Number of drink
Computation:
Assume;
Number of drink = x
So,
4.25x ≤ 50
x ≤ 11.76
so,
Number of drink = 11
The width used for the car spaces are taken as a multiples of the width of
the compact car spaces.
Correct response:
- The store owners are incorrect
<h3 /><h3>Methods used to obtain the above response</h3>
Let <em>x</em><em> </em>represent the width of the cars parked compact, and let a·x represent the width of cars parked in full size spaces.
We have;
Initial space occupied = 10·x + 12·(a·x) = x·(10 + 12·a)
New space design = 16·x + 9×(a·x) = x·(16 + 9·a)
When the dimensions of the initial and new arrangement are equal, we have;
10 + 12·a = 16 + 9·a
12·a - 9·a = 16 - 10 = 6
3·a = 6
a = 6 ÷ 3 = 2
a = 2
Whereby the factor <em>a</em> < 2, such that the width of the full size space is less than twice the width of the compact spaces, by testing, we have;
10 + 12·a < 16 + 9·a
Which gives;
x·(10 + 12·a) < x·(16 + 9·a)
Therefore;
The initial total car park space is less than the space required for 16
compact spaces and 9 full size spaces, therefore; the store owners are
incorrect.
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