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2 years ago

6.

Mathematics

2 answers:

Whitepunk [10]2 years ago

4 0

Answer:

28°

Step-by-step explanation:

For this problem, we are given the leg length opposite the angle x and the hypotenuse. This perfectly describes the trig function, sine. We can set up an equation:

opposite / hypotenuse = sin(x°)

We can substitute in the sides:

7 / 15 = sin(x°)

Now, to find x, we can evaluate the inverse of sin or arcsin on the ratio 7 / 15

arcsin(7 / 15) = x° = 27.81813928°

This rounds to 28°

coldgirl [10]2 years ago

3 0

Step-by-step explanation:

$\sin(x) = \frac{7}{15} \\ x = { \sin}^{ - 1} ( \frac{7}{15} ) \\ x = 27.8 \degree$

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<h3>Answer: -19, -15, -9, -1, 9 (choice A)</h3>

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Explanation:

If we plug in x = -2, then we get,

y = x^2 + 7x - 9

y = (-2)^2 + 7(-2) - 9

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If you repeat those steps for x = -1, then you should get y = -15

Then x = 0 leads to y = -9

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The outputs we get are: -19, -15, -9, -1, 9 which is choice A

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Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions

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I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take $z=y'$ , so that $z'=y''$ and we're left with the ODE linear in $z$ :

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$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0$

$\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0$

All the coefficients of the series vanish, and setting $x=0$ in the power series forms for $y$ and $y'$ tell us that $y(0)=a_0$ and $y'(0)=a_1$ , so we get the recurrence

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so that the solution to the ODE is

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We also require the solution to satisfy $y(0)=a_0$ , which we can do easily by adding and subtracting a constant as needed:

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