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const2013 [10]
3 years ago
14

What is 720° converted to radians? o 4 о o O 40

Mathematics
1 answer:
hoa [83]3 years ago
4 0

Formula: d° * π/180 = rad

d = number of degrees given

rad = radians

Solve with the given values.

720° * π/180 = rad

720° * 0.0174 = rad

12.559968... = rad

Round to the nearest hundredth.

12.559968... → 12.56

Therefore, the answer is approximately 12.56rads

Best of Luck!

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A. a is greater than zero
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What is the percentage change for 60 to 35
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60*x = 35
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x-5y= -30
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Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma
Paraphin [41]

Given:

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The total surface area is 96 cm cube.

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\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}

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\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}

Volume is,

\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}

Now, differentiate with respect to x,

\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}

Now,

\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}

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\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}

Since, the double derivative is negative.

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\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}

Answer: maximum volume of the cylinder is,

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1 year ago
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Answer:

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density is mass divided by volume:

density =  \frac{mass}{volume}

you can manipulate the formula by multiplying with volume:

density \times volume = mass

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volume =  \frac{mass}{density}

in this case:

volume =  \frac{25g}{11.4 \frac{g}{cm}  }  = 2.193 { \: cm}^{3}

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