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Alex_Xolod [135]
3 years ago
7

Explain how you can use the terms from the binomial expansion to approximate 0.985.

Mathematics
1 answer:
stiv31 [10]3 years ago
5 0

There are 5 + 1 = 6 terms in the binomial expansion of (1−0.02)5, and since the 4th term is approximately 0, the 5th and 6th terms are also approximately 0. So, approximate the value of 0.985 by adding the first three terms: 1 + (-0.1) + 0.004 = 0.904.


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12a+60 i think lol

Step-by-step explanation:

this is how i did it though:

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12a+60

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Step-by-step explanation:

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2 years ago
Solve for x<br> 20<br> 30<br> 40<br> 56
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Step-by-step explanation:

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Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)
vichka [17]

Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\

Apply substitution to get

y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right)  + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x)  + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x)  + \left(a - 6b\right)\cos(x) = \sin(x)\\\\

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a  -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0
2 years ago
b. Use de Moivre's Theorem to compute the following: b. ^3√(8cos(4π / 5) + 8isin(4π / 5)). This is the only one i need help with
pochemuha
De Moivre's Theorem states that if a complex number is written in the polar coordinate form [ r (cosθ + isinθ)] and you raise it to the power n, then this can be evaluated by raising the modulus (r) to the power and multiply the argument (θ) by the power.  This therefore would give r ⁿ  [cos (nθ) + i sin (nθ)].

let A =  ∛ <span>(8 cos (4π / 5) + 8 i sin (4π / 5))

</span>⇒  A = ∛ <span>(8 [cos (4π / 5) + i sin (4π / 5)])
</span>
Now by applying De Moivre's Theorem,

⇒ A = 8^{ \frac{1}{3} } [cos (\frac{4 \pi }{5} × \frac{1}{3}) + i sin (\frac{4 \pi }{5} × \frac{1}{3})

⇒ A = 2 [ cos (\frac{4 \pi }{15}) + i  sin (\frac{4 \pi }{15})

⇒ A = 2 [0.0117 +  i 0.01297 ] rads



4 0
3 years ago
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