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Otrada [13]
3 years ago
12

AYUDA POR FAVOR, ES URGENTE ​

Mathematics
1 answer:
Alika [10]3 years ago
6 0

Answer:

212

Step-by-step explanation:

13 * 17 = 221

221- 9 = 212

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2 years ago
What is the slope intercept of -4 and y-intercept -1
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Points are given corresponding to (-8,0) and (0,-11), and you want line's equation in the form y=mx+b. Understand, you already have b=-11. If you too understand ...

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3 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
Which statements are correct interpretations of this graph?
gogolik [260]
Looking at the graph, we know that A. 3 boxes are filled every 4 min and D. 0.75 boxes are filled per minute are the correct answers.
Hope this helps~
7 0
3 years ago
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Simplify the expression. (p^9)^−2
EastWind [94]
<span><span> p9/p3</span> </span>Final result :<span> p6 </span>Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "p3"   was replaced by   "p^3".  1 more similar replacement(s).

Step by step solution :<span>Step  1  :</span><span> p9 Simplify —— p3 </span>Dividing exponential expressions :

<span> 1.1 </span>  <span> p9</span> divided by <span>p3 = p(9 - 3) = p6</span>

Final result :<span> p<span>6</span></span>
6 0
3 years ago
Read 2 more answers
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