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Crazy boy [7]
3 years ago
13

Ok this may be hard but I found this on my test ;--;

Mathematics
1 answer:
umka2103 [35]3 years ago
8 0

Answer:

-2383.83870968

Step-by-step explanation:

I hope this is right...

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Solve for (0,2π]<br> 2cos ß * sin ß = cos ß
Temka [501]

Given :

An equation, 2cos ß sin ß = cos ß .

To Find :

The value for above equation in (0, 2π ] .

Solution :

Now, 2cos ß sin ß = cos ß

2 sin ß = 1

sin ß = 1/2

We know, sin ß = sin (π/6)  or sin ß = sin (5π/6) in  ( 0, 2π ] .

Therefore,

\beta = \dfrac{\pi}{6}\ or\ \beta = \dfrac{5\pi}{6}

Hence, this is the required solution.

4 0
2 years ago
If
Dovator [93]

12^2=144

144 is divided by b which also is an odd interger, there only 2 numbers : 1 and 3

if b=3, a^2=48, then there will be no a available

if b=1 , a^2=144, then a is 12 and 12 can not be divided by 9

The answer is D

3 0
3 years ago
Which ruler gives the most precise METRIC measurement?
tester [92]
Millimeters as my science teacher has just said.
3 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csf%5Clim_%7Bx%20%5Cto%200%20%7D%20%5Cfrac%7B1%20-%20%5Cprod%20%5Climits_%
xxTIMURxx [149]

To demonstrate a method for computing the limit itself, let's pick a small value of n. If n = 3, then our limit is

\displaystyle \lim_{x \to 0 } \frac{1 - \prod \limits_{k = 2}^{3} \sqrt[k]{\cos(kx)} }{ {x}^{2} }

Let a = 1 and b the cosine product, and write them as

\dfrac{a - b}{x^2}

with

b = \sqrt{\cos(2x)} \sqrt[3]{\cos(3x)} = \sqrt[6]{\cos^3(2x)} \sqrt[6]{\cos^2(3x)} = \left(\cos^3(2x) \cos^2(3x)\right)^{\frac16}

Now we use the identity

a^n-b^n = (a-b)\left(a^{n-1}+a^{n-2}b+a^{n-3}b^2+\cdots a^2b^{n-3}+ab^{n-2}+b^{n-1}\right)

to rationalize the numerator. This gives

\displaystyle \frac{a^6-b^6}{x^2 \left(a^5+a^4b+a^3b^2+a^2b^3+ab^4+b^5\right)}

As x approaches 0, both a and b approach 1, so the polynomial in a and b in the denominator approaches 6, and our original limit reduces to

\displaystyle \frac16 \lim_{x\to0} \frac{1-\cos^3(2x)\cos^2(3x)}{x^2}

For the remaining limit, use the Taylor expansion for cos(x) :

\cos(x) = 1 - \dfrac{x^2}2 + \mathcal{O}(x^4)

where \mathcal{O}(x^4) essentially means that all the other terms in the expansion grow as quickly as or faster than x⁴; in other words, the expansion behaves asymptotically like x⁴. As x approaches 0, all these terms go to 0 as well.

Then

\displaystyle \cos^3(2x) \cos^2(3x) = \left(1 - 2x^2\right)^3 \left(1 - \frac{9x^2}2\right)^2

\displaystyle \cos^3(2x) \cos^2(3x) = \left(1 - 6x^2 + 12x^4 - 8x^6\right) \left(1 - 9x^2 + \frac{81x^4}4\right)

\displaystyle \cos^3(2x) \cos^2(3x) = 1 - 15x^2 + \mathcal{O}(x^4)

so in our limit, the constant terms cancel, and the asymptotic terms go to 0, and we end up with

\displaystyle \frac16 \lim_{x\to0} \frac{15x^2}{x^2} = \frac{15}6 = \frac52

Unfortunately, this doesn't agree with the limit we want, so n ≠ 3. But you can try applying this method for larger n, or computing a more general result.

Edit: some scratch work suggests the limit is 10 for n = 6.

6 0
2 years ago
Please answer please
loris [4]
4/5 + a = 1
=1/5

*try using cymath it helps!
6 0
3 years ago
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