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3 years ago

Use the compound angle formulae to find the following in surd form: tan 225°

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

8 0

Answer:

On the trig unit circle,

tan 225 = tan (45 + 180) = tan 45 = 1

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

The equation of the tangent to the curve x^2 = 4y at the point on the curve where x=-2 is?

aleksandrvk [35]

$x^2 = 4y \Rightarrow y= \frac{x^2}{4}$
$\frac{dy}{dx} = \frac{2x}{4} = \frac{x}{2}$

(x = -2) $\frac{dy}{dx} = \frac{x}{2} = \frac{-2}{2} = -1$
(x = -2) $y= \frac{x^2}{4}= \frac{(-2)^2}{4} = 1$

$y-y_1=m(x-x_1)$
$y-1 = -1(x--2)
$
$y-1 = -1(x+2)$
$y-1 = -x-2$
$y=-x-1 = -(x+1)$

7 0

4 years ago

Read 2 more answers

What is the average rate of change from -3 to 0 of the function represented by the graph?

lbvjy [14]

Average rate of change = change in y ÷ change in x

We already know the change in x because we are measuring the x values from -3 to 0.

change in x = 0-(-3) = 3

To find the change in y find the difference between the corresponding y-values when x=0 and when x=-3.

change in y = 0.5-2 = -1.5

average rate of change = -1.5/3 = -0.5

answer: -0.5

3 0

3 years ago

FREE BRAINLIST

Fiesta28 [93]

Answer:

Hello

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Step-by-step explanation:

6 0

3 years ago

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Suppose that a box contains 8 cameras and that 4 of them are defective. A sample of 2 cameras is selected at random. Define the

maria [59]

Answer:

P(x) = 8Cx * p^x * (1 - p)^(8 - r) ; r = 0, 1, 2

Step-by-step explanation:

Given that:

Total Number of cameras (n) = 8

Defective cameras = 4

X: number of defective cameras

For a binomial distribution :

P(x) = nCx * p^x * (1 - p)^(n - x)

Probability of success (p) on each trial is the same = (total number of samples / number of defective samples) = 8/4 = 0.5

If 2 samples are chosen at random :

Then, the binomial probability distribution will be :

P(x) = 8Cx * p^x * (1 - p)^(8 - r) ; r = 0, 1, 2

5 0

3 years ago

Use the compound angle formulae to find the following in surd form: tan 225°​​

Use the compound angle formulae to find the following in surd form: tan 225°