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3 years ago

10

Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is

the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft

1 answer:

miv72 [106K]3 years ago

8 0

Plug in 30ft for L and 2310 for n so you will get 2310=7(30)(h)... h would equal 11ft

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Find all solutions to cosx cos3 x-sinx sine3x= 0 on the interval {0,2pi}

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$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
\boxed{cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}})}
\\ \quad \\
cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\
------------------------$

$\bf cos(x)cos(3x)-sin(x)sin(3x)=0\implies cos(x+3x)=0
\\\\\\
cos(4x)=0\implies cos^{-1}[cos(4x)]=cos^{-1}(0)\implies 4x=cos^{-1}(0)
\\\\\\
4x=
\begin{cases}
\frac{\pi }{2}\\\\
\frac{3\pi }{2}
\end{cases}\implies 
\begin{cases}
4x=\cfrac{\pi }{2}\implies &\measuredangle x=\cfrac{\pi }{8}\\\\
4x=\cfrac{3\pi }{2}\implies &\measuredangle x=\cfrac{3\pi }{8}
\end{cases}$

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