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den301095 [7]
3 years ago
14

Sin x degrees= 4/15 HELLLPPPPPPPPP PLEASEEEEEEEEE!!!!!

Mathematics
2 answers:
Colt1911 [192]3 years ago
7 0

Answer:

x = 0.2699 or 15 .47°

Step-by-step explanation:

Given  : sin x = \frac{4}{15}.

To find : find  x.

Solution : We have given that

sin x = \frac{4}{15}.

Taking inverse of sin

sin^{-1} sin x = sin^{-1}(\frac{4}{15} ).

x = sin^{-1}(\frac{4}{15} ).

x = 0.2699 or 15 .47°

Therefore, x = 0.2699  or 15 .47°

Umnica [9.8K]3 years ago
3 0
From here, just make it inverse:

sin^{-1} ( \frac{4}{15}) = x
x=15.46600995.....
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Center: (2,8), Radius: 3
Rzqust [24]

Answer:

I’m not sure what this question is asking, but I’ll write an equation of this circle you are describing. Here, the x coordinate of the center is h, the y coordinate is k, and radius is r in the equation : (x-h)^2+(y-k)^2=r^2, meaning the equation in this situation is the following: (x-2)^2+(y-8)^2=9

Step-by-step explanation:

5 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
Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.
aksik [14]

Answer:

4w+120.

Step-by-step explanation:

She downloads 4 songs for every week which is represented as 4w, and she started with 120 songs which is represented as +120.

6 0
2 years ago
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Montano1993 [528]

Answer:

Step-by-step explanation:

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side length = 3

side length^2 = 3 * 3 = 9

The area of a circle is much harder to reason out. You could start with the area of a square and use the diameter is 3 units. But the corners are rounded and you don't know off hand what the area of one of them is, let alone all 4. You are given a formula for circles area, but you have no real idea what the formula actually means. Does it take the corner area into account? At the beginning levels, we don't know.

3 0
2 years ago
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You can rake a 20 square meter lawn in 10 minutes. If your mother asks you to rake your own lawn, which is 30 square meters, how
arsen [322]
20 square meter lawn..............................10 min
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3 years ago
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