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3 years ago

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π?

1 answer:

3 0

Recall that to get the x-intercepts, we set the f(x) = y = 0, thus

$\bf \stackrel{f(x)}{0}=-4cos\left(x-\frac{\pi }{2} \right)\implies 0=cos\left(x-\frac{\pi }{2} \right)
\\\\\\
cos^{-1}(0)=cos^{-1}\left[ cos\left(x-\frac{\pi }{2} \right) \right]\implies cos^{-1}(0)=x-\cfrac{\pi }{2}
\\\\\\
x-\cfrac{\pi }{2}=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}$

$\bf -------------------------------\\\\
x-\cfrac{\pi }{2}=\cfrac{\pi }{2}\implies x=\cfrac{\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{2\pi }{2}\implies \boxed{x=\pi }\\\\
-------------------------------\\\\
x-\cfrac{\pi }{2}=\cfrac{3\pi }{2}\implies x=\cfrac{3\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{4\pi }{2}\implies \boxed{x=2\pi }$

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Hailey spent $12 to buy $2 fish her cousin spent double the amount on fish each fish cost the same amount how many fish do haile

Alchen [17]

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3 years ago

Read 2 more answers

Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

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3 years ago

WILL MARK BRAINLIEST!

Artist 52 [7]

Answer:

Following are the responses to the given points:

Step-by-step explanation:

Dilation implies the triangle $\Delta XYZ$ stretched through the factor "2".

$m\angle Y = m\angle C = 90^{\circ} \leftarrow given \\\\$

right triangles:

$\Delta XYZ and \Delta ACB \\\\\angle X \cong \angle A \leftarrow given\\\\$

complementary angles:

$\angle X \ and\ \angle Z$

$m\angle Z = 90^{\circ} - m\angle X \\\\$

complementary angles:

$\angle A \ and\ \angle B$

$m\angle B = 90^{\circ} - m\angle A \\\\\therefore \\\\ \angle Z \cong \angle B \\\\\Delta XYZ \sim \Delta ACB \\\\$

Same triangles: proportional side are corresponding, congruence angles are respective.

$\sin \angle X = \frac{5}{5.59} \leftarrow given \\\\\sin\angle X = \frac{YZ}{XY} \\\\YZ = 5 (units) \rightarrow leg in \Delta XYZ \\\\XZ = 5.59 (units) \rightarrow hypotenuse \ in\ \Delta XYZ\\\\$

Calculating the length of leg XY:

$XY = \sqrt{((5.59)^2 - 52)} \cong 2.4996 (units)\\\\\frac{CB}{YZ} = 2 \leftarrow given \\\\CD = 2YZ = 2 \times 5 = 10 \ (units)\\\\\frac{AC}{XY} = 2 \leftarrow \ given\\\\AC = 2XY \cong 2 \times 2.4996 \cong 4.999\ (units)\\\\$