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sladkih [1.3K]
2 years ago
11

Find the measure of angle 1

Mathematics
2 answers:
NARA [144]2 years ago
4 0

Answer:28

Step-by-step explanation:

sergejj [24]2 years ago
4 0
Answer: 28!

Step By Step Explanationm
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What is 78,400,000 expressed in scientific notation?
Virty [35]

Answer:

7.84  ×  10 ^7

Step-by-step explanation:

6 0
3 years ago
<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
The parkview middle school football team will be playing in the state championship the coach has free tickets to it will be dist
denis23 [38]

Answer:

the answer is 17.3 repeated

Step-by-step explanation:

because 52 divided by 3

8 0
2 years ago
15 POINTS 8m+4m+7m-2n what’s the answer
Romashka-Z-Leto [24]

To simplify combine like terms:

8m + 7m = 15m

4n - 2n = 2n


Simplified: 15m + 2n

6 0
3 years ago
Read 2 more answers
Sam is handing out advertisements for an upcoming event. He starts with a box of 5,000 advertisements and hands out 12 advertise
lawyer [7]

Answer:

n = 5,000 - 12t ​

Step-by-step explanation:

Sam is handing out advertisements for an upcoming event.

No of advertisements = 5000

No of advertisements per minute is 12.

We need to find the equation that best models the relationship between the amount of time t, Sam spends handing out advertisements and the number of advertisements, n, remaining.

5000 is fixed and there are 12 advertisements per minute. Let the equation is given by :

n = 5,000 - 12t ​

Hence, the correct option is (d).

7 0
3 years ago
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