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Leviafan [203]
3 years ago
15

Convert 6 20 into a decimal

Mathematics
1 answer:
lakkis [162]3 years ago
6 0

Answer:

6.20

wait what do u mean

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The graph of a function h is shown below find h(2).
Fantom [35]

Answer:

i cant really see it but i think the answer is 5

Step-by-step explanation:

when you look at the graph go to where x is 2 then keep going up and whatever point it hits thats the answer

3 0
2 years ago
Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
If 2a-b:2a+b=1:2find the value of a:b​
weqwewe [10]

Answer & Step-by-step explanation:

2a - b : 2a + b = 1 : 2

2a - b = 1

-                         Elimination

2a + b = 2

-b - (b) = -1

-2b = -1

b = 0.5

---------------------------------------------------------------------------------

2a + b = 2           Substitution

2a + 0.5 = 2

2a = 1.5

a = 0.75

--------------------------------------------------------------------------------------

a:b

0.75 : 0.5

or

3/4 : 1/2

Hope this helps!!!

 

3 0
3 years ago
H E L P!!!!!!!!!!!!!!!!!!!
LenaWriter [7]

Answer:

a

Step-by-step explanation:

4 0
3 years ago
Find the value of x.
OverLord2011 [107]

Answer:

5

Step-by-step explanation:

4 0
2 years ago
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