Write the geometric sequence in function notation.

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

Marie and fe work in a flower shop 6 hours on weekend to add their daily allowance in school. They spends 2 1/3 hours for making

Shkiper50 [21]

Answer:

2 1/6 hours

Step-by-step explanation:

2 1/3 + 1 1/2 + x = 6

convert all mixed numbers to improper fractions

7/3 + 3/2 + x = 6/1

change all numbers to have a common denominator

14/6 + 9/6 + x = 36/6

combine like terms

23/6 + x = 36/6

subtract 23/6 from both sides

x = 13/6

convert improper fraction to mixed number

2 1/6

7 0

4 years ago

Can I get help with these too? Thank you!!!!!

Anastasy [175]

For ABC:

The interior angle of C is 180 - 142 = 38
The three interior angles add up to 180°
(2x - 15) + (x - 5) + 38 = 180
3x - 20 + 38 = 180
3x + 18 = 180
3x = 162
x = 54

The measure of angle ABC = x - 5 = 54 - 5 = 49

For JKL:
The interior angle of L is 180 - 100 = 80°
The 3 interior angles add up to 180°
(2x + 27) + (2x - 11) + 80 = 180
4x + 16 + 80 = 180
4x + 96 = 180
4x = 84
x = 21

The measure of angle JKL is 2x - 11 = 2(21) - 11 = 42 - 11 = 31°

7 0

3 years ago

rene charges $2.25 for gasoline plus $8.50 per hour for mowing lawns what is x the number of hours he has to mow lawns to earn t

Black_prince [1.1K]

2.25 + 8.50x = 50

8.50x = 50 - 2.25

8.50x = 47.75
——— ———
8.50. 8.50

x = 5.6 hours

Hope that helps :)

4 0

4 years ago

Plz hurry

Delicious77 [7]

Answer:

me too jaja

Step-by-step explanation:

8 0

3 years ago