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4 years ago

Which of the following expressions can be used to complete the equation below Secx / 1+cot^2x=

Mathematics

1 answer:

svlad2 [7]4 years ago

3 0

Answer: D) Tan x sin x

<u>Step-by-step explanation:</u>

$\dfrac{sec}{1+cot^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{1}{1+cot^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{1}{1+(\frac{cos}{sin})^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{1}{(\frac{sin^2}{sin^2})+(\frac{cos^2}{sin^2})}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{sin^2}{sin^2+cos^2}\\\\\\=\dfrac{1}{cos}\cdot \dfrac{sin^2}{1}\\\\\\=\dfrac{sin\cdot sin}{cos\cdot 1}\\\\\\=\boxed{tan\cdot sin}$

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a. $\boxed{y-602=\frac{2}{3}(x-3)}$

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

$P_{1}(3,602) \\ \\ P_{2}(6,604) \\ \\ P_{3}(q,606) \\ \\ P_{4}(12,608)$

It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

$y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line$

Finding (m):

$Using: \\ \\ P_{1}(x_{1},y_{1}) \rightarrow P_{1}(3,602) \\ \\ P_{2}(x_{2}, y_{2}) \rightarrow P_{2}(6,604) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{604-602}{6-3} \\ \\ m=\frac{2}{3}$

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$(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}$

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The x-axis represents the <em>Number of Months </em>the pine tree was expected to grow.
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Since the slope o a line is:

$Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}$

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

The y-intercept can be found setting $x=0$ . So, from our equation:

$y-602=\frac{2}{3}(x-3)} \\ \\ \\ If \ x=0: \\ \\ y-602=\frac{2}{3}(0-3) \\ \\ y-602=-2 \\ \\ Solving \ for \ y: \\ \\ y=602-2 \\ \\ y=600$

So the y-intercept is $y=600$ and<em> represents the height of the tree at the moment Ariel started to record the heights.</em>

<h2>Learn more:</h2>

Slope Intercept form: brainly.com/question/4192440

#LearnWithBrainly

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