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Ulleksa [173]
3 years ago
6

2(-3/2 + 4 ÷ -11) A=-43/9 B=-49/11 C=-20/11 D=-10/9​

Mathematics
1 answer:
Vladimir [108]3 years ago
6 0

Answer:

-41/11

Step-by-step explanation:

4/-11=-4/11

-3/2+(-4/11)=-3/2-4/11=-41/22

2(-41/22)=-41/11

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The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. A) Use differentials to estimate the max
siniylev [52]

Answer:

A) The maximum error in the calculated surface area: 25cm^2

Relative error: 0.013

B) The maximum error in the calculated volume: 162cm^2

Relative error: 0.019

Step-by-step explanation:

A) The formula for the surface area is:

A=4\pi r^2

The measured value is the circumference which is equal to:

C=2\pi r

then the radius is:

r=\frac{C}{2\pi}

Substituting in the formula of the surface:

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

Using the formula to calculate the error:

dy=f'(x)dx

Where x is the variable measured and y is a function of x(y=f(x)).

dA=f'(C)dC\\dA=\frac{2C^{(2-1)}}{\pi}dC\\dA=\frac{2C}{\pi}dC

We have C=80cm and dC=0.5cm

dA=\frac{2C}{\pi}dC\\dA=\frac{2(80)}{\pi}(0.5)\\dA=\frac{160}{\pi}(0.5)\\dA=50.9296(0.5)\\dA=25.4648\approx25cm^2

The relative error is the maximum error divide by the total area. The total area is: A=\frac{C^2}{\pi}=\frac{(80)^2}{\pi}=\frac{6400}{\pi}=2037.1833cm^2

\frac{dA}{A}=\frac{25.4648}{2037.1833} =0.0125\approx0.013

B) The formula for the volume is:

V=\frac{4}{3} \pi r^3

Using r=\frac{C}{2\pi}

V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (\frac{C}{2\pi})^3\\V=\frac{4}{3} \pi (\frac{C^3}{8\pi^3})\\V=\frac{1}{3}(\frac{C^3}{2\pi^2})\\V=\frac{C^3}{6\pi^2}

The maximum error is:

dV=\frac{3C^{3-1}}{6\pi^2}dC\\dV=\frac{C^{2}}{2\pi^2}dC\\dV=\frac{(80)^{2}}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=(324.2278)(0.5)\\dV=162.1139\approx162cm^2

The calculated volume is:

V=\frac{C^3}{6\pi^2}\\V=\frac{(80)^3}{6\pi^2}\\V=\frac{512000}{6\pi^2}\\V=8646.0743

The relative error is:

\frac{dV}{V}=\frac{162.1139}{8646.0743}=0.0188\approx0.019

3 0
3 years ago
Greatest common factor for 17 and 42
Musya8 [376]
Since 17 isnt a factor of 42 the only factor is 1
5 0
3 years ago
Help? don't know what to pick, and please dont choose randomly
Yakvenalex [24]

Answer:

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6 0
3 years ago
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Ket [755]

Answer:

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7 0
3 years ago
Major arc CBD measures 300°. Which is the radian measure of its corresponding central angle? radians radians radians radians
morpeh [17]

Answer:

\frac{5}{3}\pi\ radians

Step-by-step explanation:

we know that

If the measures of the major arc CBD is equal to 300 degrees

then

the measure of its corresponding central angle  is equal to  300 degrees

so

Convert degrees to radians

Remember that

180\°=\pi \ radians

so by proportion

Convert 300\° to radians

\frac{\pi}{180}\frac{radians}{degrees} =\frac{x}{300}\frac{radians}{degrees}\\ \\x=300\pi /180\\ \\x=\frac{5}{3}\pi\ radians

7 0
3 years ago
Read 2 more answers
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