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1 year ago

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Given that cos(theta) = -2 radical 5/5, and is in Quadrant II, what is cos(2theta)?

1 answer:

gtnhenbr [62]1 year ago

5 0

$cos \theta = \frac{ - 2 \sqrt{5} }{5}$

$cos 2\theta = 2cos {}^{2} \theta - 1 \\ cos2 \theta = 2( \frac{ - 2 \sqrt{5} }{5} ) {}^{2} - 1 \\ cos2 \theta = 2( \frac{20}{ \\ 25} ) - 1 \\ cos2 \theta = \frac{40 - 25}{25} = \frac{15}{25} = \frac{3}{5}$

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Algebra 2 (picture shown)

TEA [102]

Answer:

<em>M(13)=14.3 gram</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

The exponential function is used to model natural decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

$C(t)=C_o\cdot(1-r)^t$

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The element has an initial mass of Mo=970 grams, the decaying rate is r=27.7% = 0.277 per minute.

The equation of the model is:

$M(t)=M_o\cdot(1-r)^t$

$M(t)=970\cdot(1-0.277)^t$

Operating:

$M(t)=970\cdot 0.723^t$

After t=13 minutes the remaining mass is:

$M(13)=970\cdot 0.723^{13}$

Calculating:

M(13)=14.3 gram

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3 years ago

Write each of the following expressions without using the absolute value sign. |x−4| if x>4. PLEASE INCLUDE EXPLANATION!!!

kotykmax [81]

The answer is 3.141529

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3 years ago

Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of

victus00 [196]

Answer:

g(x), f(x) and h(x)

Step-by-step explanation:

Given

Interval: (0,3)

See attachment for functions f(x), g(x) and h(x)

Required

Order from fastest to slowest decreasing average rate of change

The average rate of change is calculated as:

$Rate = \frac{f(b) - f(a)}{b - a}$

In this case:

$(a,b) = (0,3)$

i.e.

$a = 0\\b=3$

For f(x)

$f(x) = 16(\frac{1}{2})^x$

$Rate = \frac{f(b) - f(a)}{b - a}$

$Rate = \frac{f(3) - f(0)}{3 - 0}$

$Rate = \frac{f(3) - f(0)}{3}$

Calculate f(3) and f(0)

$f(x) = 16(\frac{1}{2})^x$

$f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2$

$f(0) = 16(\frac{1}{2})^0 = 16 * 1 = 16$

So:

$Rate = \frac{f(3) - f(0)}{3}$

$Rate = \frac{2 - 16}{3}$

$Rate = -\frac{14}{3}$

For g(x)

$Rate = \frac{g(b) - g(a)}{b - a}$

$Rate = \frac{g(3) - g(0)}{3 - 0}$

$Rate = \frac{g(3) - g(0)}{3}$

From the table of g(x)

$g(3) = 1$

$g(1) = 27$

So:

$Rate = \frac{1 - 27}{3}$

$Rate = -\frac{26}{3}$

For h(x)

$Rate = \frac{h(b) - h(a)}{b - a}$

$Rate = \frac{h(3) - h(0)}{3 - 0}$

$Rate = \frac{h(3) - h(0)}{3}$

From the graph of h(x)

$h(3) = -3$

$h(0) = 4$

So:

$Rate = \frac{-3 - 4}{3}$

$Rate = -\frac{7}{3}$

So, the calculated rates of change are:

$f(x) = -\frac{14}{3}$ $= -4.67$

$g(x) = -\frac{26}{3}$ $=-8.67$

$h(x) = -\frac{7}{3}$ $=-2.33$

By comparison:

From the fastest decreasing to slowest, the order is: <em>g(x), f(x) and h(x)</em>

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3 years ago

Slove for y in terms of X x-2y=6

dolphi86 [110]

Answer: y = $\frac{1}{2}$ x−3

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2 years ago

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slamgirl [31]

you must switch the denominator and numerator of the second fraction, and then multiply. the answer is <u>5/6</u>

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3 years ago

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