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2 years ago

I dont understand this

Mathematics

2 answers:

blagie [28]2 years ago

7 0

Answer:

Pretty sure its 4

brainliest pls

weqwewe [10]2 years ago

3 0

Answer:

The answer is A.) 9

Step-by-step explanation:

You might be interested in

Simplify day 19 please

Genrish500 [490]

The answer is approximately 11.18.

3 0

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

1. The population of a small town has established a growth rate of 3% per year. If the

Rasek [7]

Answer:

17 years

Step-by-step explanation:

3% of 2000 = 60

3000-200 = 1000

1000 ÷ 60= 16.6666666667

Round to the nearest whole number: 17

8 0

3 years ago

Dahasolnce [82]

Answer:

C (3x4) + (5x2) + 20

Step-by-step explanation:

3 things that cost 4 dollars. 5 things that cost 2 dollars and one that cost 20.

3 0

3 years ago

A new park was designed to contain two circular gardens. Garden A has a diameter of 50 m, and garden B has a diameter of 70 m. T

Nastasia [14]

Answer:

$5,811.95\ m^2$ of fabric.

Step-by-step explanation:

-The amount of fabric needed is equivalent to the area of the two gardens.

-We calculate the combined areas as:

$A=A_s+A_b\\\\=\pi r^2+\pi R^2\\\\=\pi(25^2+35^2)\\\\=1850\pi \ m^2\\\\=5811.95\ m^2$

Hence, 5811.95 sq meters of fabric will be needed to cover the area of both gardens.

5 0

3 years ago