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3 years ago

What will be the reciprocal of 5/3?

Mathematics

2 answers:

NNADVOKAT [17]3 years ago

8 0

The reciprocal of 5/3 is 3/5.

Hope I helped!

Mrac [35]3 years ago

6 0

the reciprocal of 5/3 is 3/5

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WILL GET BRAILIEST FOR CORRECT ANSWER

Alex Ar [27]

Answer:

x = ± $\sqrt{20}$

Step-by-step explanation:

Given

x² = 20 ( take the square root of both sides )

x = ± $\sqrt{20}$

which can be simplified to

x = ± 2 $\sqrt{5}$

[ ± means plus or minus ]

5 0

3 years ago

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is

Hitman42 [59]

Answer:

red 420 times

Step-by-step explanation:

The results show red (18) out of ( 18+10+7+19+6)

18 / 60

18/60 * 1400 = 420 times

7 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

4 years ago

Do you know how to use the Pythagorean identity?

goblinko [34]

The Pythagorean theorem or identity is given by

H²=P²+B²
P²=H²-B²
B²=H²-P²

Where

B is base of right angle traingle
H is Hypotenuse
P is perpendicular

8 0

2 years ago

A candy store in the mall orders 1000 boxes a month each box of candy weighs 45.9 grams . What is the total weight in grams of t

Degger [83]

Answer:

45900 grams

Step-by-step explanation:

All you need to do is multiply 45.9 grams by 1000 for the total combined weight of every box combined to get.

45.9 x 1000 = 45900

4 0

3 years ago