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3 years ago

Find all solutions to the equation. cos x = -1/2

Mathematics

2 answers:

nikdorinn [45]3 years ago

5 0

Answer:

You didn't add the range. I'll use (0<x<2π)

cosx = -1/2

x=-cos-¹(1/2)

x= -60°

Cosine is negative in the second and 3rd quadrants

180-x ---- Second quadrant

x+180 ----- 3rd quadrant

Our answer

180-(-60)=240° or 4π/3 second quad

180+(-60) = 120° or 2π/3---- 3rd quad

ELEN [110]3 years ago

4 0

Answer:

Step-by-step explanation:

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3 years ago

Consider the initial value problem for the function y given by:

alex41 [277]

Answer:

Step-by-step explanation:

An implicit expression is a relation of the form y = f(x) where f is a a function with x as a variable.

$\frac{\mathrm{d} y}{\mathrm{d} t}=2y\left ( 1-\frac{y}{4} \right )\\\frac{\mathrm{d} y}{\mathrm{d} t}=\frac{y}{2}(4-y)$

On integrating both sides, we get

$\int \frac{dy}{y(4-y)}=\int \frac{1}{2}\,dt\\\frac{1}{4}\int \frac{1}{y}+\frac{1}{4-y}\,dy=\frac{1}{2}\,dt\\$

We know that $\int \frac{dy}{y}=\ln y$ .

Therefore,

$\int \frac{dy}{y(4-y)}=\int \frac{1}{2}\,dt\\\frac{1}{4}\int \frac{1}{y}+\frac{1}{4-y}\,dy=\int \frac{1}{2}\,dt\\\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}+C$

As $y(0)=1$ ,

$C=-\frac{\ln 3}{4}$

So, $\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}-\frac{\ln 3}{4}$

$\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}-\frac{\ln 3}{4}\\\ln y-\ln (4-y)=2t-\ln 3\\\ln \left ( \frac{y}{4-y} \right )=2t-\ln 3\\\frac{y}{4-y}=e^{2t-\ln 3}\\y=(4-y)e^{2t-\ln 3}\\y\left ( 1+e^{2t-\ln 3}\\ \right )=4e^{2t-\ln 3}\\y=\frac{4e^{2t-\ln 3}}{1+e^{2t-\ln 3}}$

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4 years ago

△ABC has vertices A(–2, –2), B(1, –1), and C(2, 0). Find the image of △ABC after a dilation centered at the origin with a scale

Vitek1552 [10]

Answer:

see explanation

Step-by-step explanation:

since the dilatation is centred at the origin , then multiply each of the coordinates of A, B, C by the scale factor 2, that is

A' = (2(- 2), 2(- 2) ) = A'(- 4, - 4 )

B' = (2(1), 2(- 1) ) = B'(2, - 2 )

C' = (2(2), 2(0) ) = C'(4, 0 )

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3 years ago