2 years ago

Help,,,,,,,,,, please

Mathematics

1 answer:

alexandr402 [8]2 years ago

6 0

Answer:

Statement and reason in below

Step-by-step explanation:

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A Bar of steel is 340 cm long Issa cuts two 55cm lengths of the bar He then cuts the rest into as many 40cm lengths as possible

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Answer:

5 bars

Step-by-step explanation:

340-(55+55)

230÷40

5.75

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Answer:

4 cu. units

Step-by-step explanation:

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Evaluate each expression |31|-|-1|

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That would be evaluated to 31+1 because you have to keep change flip. Keep the 31, change the symbol to addition, then flip the negative 1 to a positive number.

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If sinx+sin^2x=1 then what is the value of cos^12x+3cos^10x+3cos^8x+cos^6x

mr_godi [17]

$\sin x+\sin^2x=1\implies\sin x=1-\sin^2x=\cos^2x$

$\cos^{12}x+3\cos^{10}x+3\cos^8x+\cos^6x=\sin^6x+3\sin^5x+3\sin^4x+\sin^3x$
$=\sin^3x(\sin^3x+3\sin^2x+3\sin x+1)$
$=\sin^3x(\sin x+1)^3$

Let $y=\sin x$ . Then

$\sin^2x+\sin x-1=0\iff y^2+y-1=0\implies y=-\varphi,y=\varphi-1$

where $\varphi=\dfrac{1+\sqrt5}2\approx1.61803$ is the golden ratio.

$\begin{cases}y=-\varphi\\y=\varphi-1\end{cases}\implies\begin{cases}\sin x=-\varphi\\\sin x=\varphi-1\end{cases}$

Since $|\sin x|\le1$ for all real $x$ , we can omit the first equation, leaving us with

$\sin x=\varphi-1\approx0.61803$

$\cos^{12}x+3\cos^{10}x+3\cos^8x+\cos^6x=\sin^3x(\sin x+1)^3$
$=(\varphi-1)^3\varphi^3$
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where the last equality follows from the fact that $\varphi=1+\dfrac1\varphi$ .

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Angelina_Jolie [31]

Answer:

ssa

Step-by-step explanation:

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