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4 years ago

Cos (x + π/ 3) + cos (x - π/ 3) = 1 Solve for "x" on the interval [0, 2pi)

1 answer:

8 0

$\bf cos\left( x+\frac{\pi }{3} \right)+cos\left( x-\frac{\pi }{3} \right)=1\\\\
-----------------------------\\\\\
[cos(x)cos\left( \frac{\pi }{3} \right)\underline{-sin(x)sin\left( \frac{\pi }{3} \right)}] 
+ [cos(x)cos\left( \frac{\pi }{3} \right)\underline{+sin(x)sin\left( \frac{\pi }{3} \right)}]=1
\\\\\\$

$\bf cos(x)cos\left( \frac{\pi }{3} \right)+cos(x)cos\left( \frac{\pi }{3} \right)=1\implies 2cos(x)cos\left( \frac{\pi }{3} \right)=1
\\\\\\
2cos(x)\cdot \cfrac{1}{2}=1\implies cos(x)=1\implies \measuredangle x=cos^{-1}(1)
\\\\\\
\measuredangle x = 
\begin{cases}
0\\
2\pi 
\end{cases}$

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I need help with #39-42, please explain.

shusha [124]

For question 39 & 40, we need to use the below equation to complete the sentence

$l=m\sqrt{n}$

Question 39:

When ' n ' increase, the $\sqrt{n}$ will also increase and that multiplied with constant ' m ', the l will also increase.

Solution for question 39:

As $n$ increases and $m$ stays constant , $l$ increases

-------

Question 40:

Solving the equation for m, we get

$l = m\sqrt{n} \\ \\ m=\frac{l}{\sqrt{n}}$

When ' l ' increases, the numerator increase, the denominator stays constant because 'n' stays constant, for this condition, the fraction increases.

Solution for question 40:

As $l$ increase and $n$ stays constant, $m$ increases

------

For question 41 & 42, we need to use the below equation to complete the sentence

$r=s^2/t^2$

Question 41:

When $s$ is triped, the equation will be...

$r=(3s)^2/t^2=\frac{3^{2}s^{2}}{t^2} =9s^2/t^2$

Solution for question 41:

If $s$ is tripled and $t$ stays constant, $r$ is multiplied by 9

--------

Question 42:

When t is doubled, the equation will be...

$r=s^2/(2t)^2=\frac{s^2}{2^2 \cdot t^2}=\frac{s^2}{4t^2}\\ \\ r=0.25s^2/t^2 \; \; (or) \; \; \frac{1}{4} \cdot \frac{s^2}{t^2}$

Solution for 42:

If $t$ doubled and $s$ stays constant, $r$ is multiplied by 1/4 or 0.25

3 0

3 years ago

Which statement is best supported by the information in the box plots?

solmaris [256]

Answer:

B is the correct

Step-by-step explanation:

choose as brinliest

4 0

3 years ago

PLease help me ,really need help with explanation

mylen [45]

Check the picture below.

volume wise, we know the smaller pyramid is 1/8 th of the whole pyramid, so the volume of the whole pyramid must be 8/8 th.

Now, if we take off 1/8 th of the volume of whole pyramid, what the whole pyramid is left with is 7/8 th of its total volume, and that 7/8 th is the truncated part, because the 1/8 we chopped off from it, is the volume of the tiny pyramid atop.

Now, what's the ratio of the tiny pyramid to the truncated bottom?

$\stackrel{\textit{\Large Volumes}}{\cfrac{\textit{small pyramid}}{\textit{frustum}}\implies \cfrac{~~\frac{1}{8}whole ~~}{\frac{7}{8}whole}}\implies \cfrac{~~\frac{1}{8} ~~}{\frac{7}{8}}\implies \cfrac{1}{8}\cdot \cfrac{8}{7}\implies \cfrac{1}{7}$