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3 years ago

What is... –9v + 1 = –8v − 7

Mathematics

2 answers:

almond37 [142]3 years ago

6 0

Answer:

v=8

Step-by-step explanation:

–9v + 1 = –8v − 7

Add 9v to each side

–9v+9v + 1 = –8v+9v − 7

1 = v-7

Add 7 to each side

1+7 = v-7+7

8 =v

sveta [45]3 years ago

5 0

Answer:

V=6

Step-by-step explanation:

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Pls help asap<br> if square x = -7 ; then x = - 49

natima [27]

Should be false because -7 x -7 is not -49 it is 49

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3 years ago

What is the answer to this question

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4 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:

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

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

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4 years ago

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mariarad [96]

Answer:

2+2 is 4 minus one thats 3 quick math, everyday men on the block smo** trees, see yo girl in da park dat gurl was an ocus, n the ting went ggggrrraaa paa paa paa paa paa grrrrrraaa n a boom boom boom boom boom!!!!!

Step-by-step explanation:

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3 years ago

The sales tax on a $350 computer is $ 22.75. find the sales tax rate.

likoan [24]

Set up an equation to solve for the tax rate, x:

$350(x) = 22.75\\x = \frac{22.75}{350}\\x = 0.065\\x = 6.5%$

We can conclude that the tax rate on the computer was 6.5 percent.

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3 years ago