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likoan [24]
3 years ago
9

Find the value of x.

Mathematics
1 answer:
Nadusha1986 [10]3 years ago
7 0

Answer:

71.79 degrees

Step-by-step explanation:

The cosine is (adjacent side to angle) / (hypotenuse)

so the cosine of x = 5/16

to get x you multiply cosine by its inverse

(cos^-1 x)(cos x) = (cos^-1 x)(5/16)

= 71.79 degrees

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Josh plays a game where he flips a coin and rolls a number cube. List all of the possible outcomes below.
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Heads 1
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3 0
3 years ago
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Recall that two angles are complementary if the sum of their measures is 90 degrees°. Find the measures of two complementary an
raketka [301]

Answer:

18° and 72°

Step-by-step explanation:

let x be the measure of one angle then the other is 3x + 18

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8 0
3 years ago
Weight of 8 bags of sugar is 400 kg. The weight of 30 such bags will be ------------------------------------
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1500 kg

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3 years ago
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Let f be the function defined by f(x) = e^(x) cos x.
Pavel [41]
(a)

The average rate of change of f on the interval 0 ≤ x ≤ π is

   \displaystyle
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(b)

f(x) = e^{x} cos x \implies f'(x) = e^x \cos(x) - e^x \sin(x) \implies \\ \\
f'\left(\frac{3\pi}{2} \right) = e^{3\pi/2} \cos(3\pi/2) - e^{3\pi/2} \sin(3\pi/2) \\ \\
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The absolute minimum value of f occurs at a critical point where f'(x) = 0 or at endpoints.

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f'(x) = e^x \cos(x) - e^x \sin(x) \\ \\
0 = e^x \big( \cos(x) - \sin(x)\big)

Use zero factor property to solve.

e^x \ \textgreater \  0\forall x \in \mathbb{R} so that factor will not generate solutions.
Set cos(x) - sin(x) = 0

\cos (x) - \sin (x) = 0 \\
\cos(x) = \sin(x)

cos(x) = 0 when x = π/2, 3π/2, but x = π/2. 3π/2 are not solutions to the equation. Therefore, we are justified in dividing both sides by cos(x) to make tan(x):

\displaystyle\cos(x) = \sin(x) \implies 0 = \frac{\sin (x)}{\cos(x)} \implies 0 = \tan(x) \implies \\ \\
x = \pi/4,\ 5\pi/4\ \forall\ x \in [0, 2\pi]

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\displaystyle f(5\pi/4) = e^{5\pi/4} \cos(5\pi/4) = e^{5\pi/4}  \frac{-\sqrt{2}}{2} = -e^{\pi/4}  \frac{\sqrt{2}}{2}

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g is a differentiable function; therefore, it is a continuous function, which tells us \lim_{x \to \pi/2} g(x) = g(\pi/2) = 0.

When we observe the limit  \displaystyle \lim_{x \to \pi/2} \frac{f(x)}{g(x)}, the numerator and denominator both approach zero. Thus we use L'Hospital's rule to evaluate the limit.

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\displaystyle\lim_{x \to \pi/2} \frac{f(x)}{g(x)} = \frac{-e^{\pi/2}}{2}</span>

3 0
3 years ago
I kind of don’t get this could someone explain and answer this question I would really appreciate :)
amm1812

Answer:

its the fourth one

sts3ps oe

3 0
3 years ago
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