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ioda
2 years ago
13

Prove that f(x) = x^3 – 1000x^2 + x – 1 is ω(x^3) and o(x^3).

Mathematics
1 answer:
liq [111]2 years ago
5 0
F(x) = x 3 − 1000x^2 + x − 1

> x3 − 1000x^ 2

= (x − 1000)x^2

> (.9x)x^2

= .9x^3

Therefore, f(x) is Ω(x^3 ) with C = .9, k = 10, 000. Also, for all x > 0:
 
f(x) = x^3 − 1000x^2 + x − 1

< x^3 + 1000x^3 + x^3 + x^3

= 1002x^3

Therefore, f(x) is O(x^3 ) with C = 1002, k = 1. 
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A rectangle that had the perimeter of 70 and the area of 250 has enlarged; its sides became twice as long. what is the new area
aliya0001 [1]
The perimeter of the original rectangle is:
 P = 2w + 2l = 70
 The area of the original rectangle is:
 A = w * l = 250
 Then, by modifying the length of its sides we have:
 Perimeter:
 P '= 2 (2w) +2 (2l)
 Rewriting:
 P '= 2 (2w + 2l)
 P '= 2P
 P '= 2 (70)
 P '= 140
 Area:
 A '= (2w) * (2l)
 Rewriting:
 A '= (2) * (2) (w) * (l)
 A '= 4 * w * l
 A '= 4 * A
 A '= 4 * 250
 A '= 1000
 Answer:
 
the new area and the new perimeter are:
 
P '= 140
 
A '= 1000
3 0
2 years ago
11. In a certain town the ratio of the number of cars to that of taxis is 15:4. If
Bess [88]

Answer: 645 cars

Step-by-step explanation:

Divide 172 by 4 to find the multiple which is 43 so if 4 was multiplied by 43 to get 172 taxis you must multiply 15 by 43 which gives 645

4 0
2 years ago
Read 2 more answers
Carys is checking her tax bill for the last year.
mariarad [96]
£18240

since the amount she earned falls within the range of the tax rate 40%, multiply her earnings by 0.4.

£45600*0.4= 18240
3 0
2 years ago
Read 2 more answers
What is equivalent to -3(3y-2x)+2(5x-4y)
aev [14]
-9y+6x+10x-8y
to expand brackets, you multiply the number outside by the numbers inside. first -3x3= -9. 
-2 by -3 is 6
2 by 5 is 10
2 by -4 is -8
4 0
2 years ago
Read 2 more answers
Fred and George ate 23 apples in July, 46 apples in August, 69 apples in September, and 92 apples in October. If this trend cont
VARVARA [1.3K]
The answer is 115

The sequence of the total apples look like this:

23 _ 46 _ 69_92_X

In which x is the total amount of apples eaten in the october.

From the sequence above we can see that each months gred and george consume additional of 23 apples

proof:
46 - 23 = 23
69 - 46 = 23
92 - 69 = 23

So, the amount of apples they will eat in November is:
92 + 23 = 115



4 0
2 years ago
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