1 year ago

The graph represents the piecewise function: f(x) = What is the domain and range of the function? Domain: Range:

Mathematics

2 answers:

masha68 [24]1 year ago

5 0

Answer:

Domain: all reall numbers

Range: all real numbers greater than or equal to 0

Step-by-step explanation:

White raven [17]1 year ago

4 0

Answer:

domain: All real numbers

Range: all real numbers greater than or equal to 0

Step-by-step explanation:

Edge 2020

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FrozenT [24]

Answer:

Therefore the maximum error in the surface area of the sphere is 22.27 cm².

Therefore the relative error is 0.014 (approx).

Step-by-step explanation:

Given that, The circumference of a sphere was 70 cm with the possible error 0.5 cm.

The circumference of the sphere is C $=2 \pi r$

∴C $=2 \pi r$ $\Rightarrow r =\frac{C}{2\pi}$

Differentiating with respect to r

$\frac{dC}{dr}= 2 \pi$

$\Rightarrow dr=\frac{dC}{2\pi}$

$\Rightarrow dr= \frac{0.5}{2\pi}$ [ relative error = dC= 0.5]

The surface area of the sphere is S= $4\pi r^2$

∴S= $4\pi r^2$

Differentiating with respect to r

$\frac{dS}{dr}=4\pi \times 2r$

$\Rightarrow dS=8\pi r dr$

dS will be maximum when dr is maximum.

Putting the value of r and dr

$\Rightarrow dS= 8\pi \times \frac{C}{2\pi} \times \frac {0.5}{2\pi}$

$\Rightarrow dS=\frac{C}{\pi}$

$\Rightarrow dS= \frac{70}{\pi}$ [ ∵ C= 70 ]

⇒dS= 22.27 (approx)

Therefore the maximum error in the surface area is 22.27 cm².

Relative error $=\frac{dS}{S}$

$=\frac{\frac{C}{\pi}}{4\pi r^2}$

$=\frac{\frac{C}{\pi}}{4\pi (\frac{C}{2\pi})^2}$

$=\frac{1}{C}$

$=\frac{1}{70}$

=0.014 (approx)

Therefore the relative error is 0.014 (approx).

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1 year ago