Mathematics, 11.04.2020 18:17 daytonaspicola

The circumference of a sphere was measured to be 70 cm with a possible error of 0.5 cm. Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.)What is the relative error? (Round your answer to three decimal places.)

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Answer from: dedrell16

Therefore the error in the calculated volume is 130 cm^3 .

The relative error is 0.011.

Step-by-step explanation:

Given that,

The circumference of a sphere was 70 cm.

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

C= $2\pi r$

Differentiating with respect to r

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

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

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

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

$\triangle C=0.5$

$\therefore \triangle r= \frac{0.5}{2\pi}$

The volume of the sphere is $V=\frac43 \pi r^3$

$V=\frac43 \pi r^3$

Differentiating with respect to r

$\frac{dV}{dr}=\frac43 \pi r^2$

$\Rightarrow \frac{\triangle V}{\triangle r}=\frac43 \pi r^2$

$\Rightarrow \triangle V}=\frac43 \pi r^2\times \triangle r}$

Putting $\triangle r=\frac{0.5}{2\pi}$

$\Rightarrow \triangle V}=\frac43 \pi r^2\times \frac{0.5}{2\pi}$

$\Rightarrow \triangle V}=\frac13 \pi r^2$

$\Rightarrow \triangle V}=\frac1{3} \pi (\frac C{2\pi})^2$ $[\because r=\frac C{2\pi}]$

$\Rightarrow \triangle V}=\frac1{1 2} \times \frac{C^2}{\pi}$

$\Rightarrow \triangle V}=\frac1{1 2} \times \frac{70^2}{\pi}$ [ C=70 cm]

$\Rightarrow \triangle V}\approx 130 \ cm^3$

Therefore the error in the calculated volume is 130 cm^3 .

Relative error $=\frac{\triangle V}{V}$

$=\frac{\frac13 \pi (\frac{C}{2\pi})^2 }{\frac43 \pi (\frac C{2\pi})^3}$

$=\frac{1}{4 (\frac C{2\pi})}$

$=\frac{\pi }{4C}$

$\approx 0.011$

The relative error is 0.011.

Answer from: Quest

amount of oatypop that contains the prize = 40%

amount of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

= s +f s +f f s+ff f s+ff f f s+ infinity.where f= failure,s= success

= or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

= = 87.04 %

step-by-step explanation:

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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