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3 years ago

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Mathematics

2 answers:

galben [10]3 years ago

7 0

Answer:

Step-by-step explanation:

dsp733 years ago

4 0

Answer: 50 probably

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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

What is .22 divided by 88.66

Nana76 [90]

Answer:

0.00248139

Step-by-step explanation:

8 0

3 years ago

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A jug contains some orange juice. After pouring 240 milliliters of the orange juice into a cup, there are 875 milliliters of ora

zubka84 [21]

Answer:

1,115 mL

Step-by-step explanation:

The original amount of OJ is what we're trying to find, so that will be our variable, x. Now, keep in mind the order of events to write the correct equation. We started with the x amount of OJ, then 240 mL was taken away, to leave us with 875 mL. So, x - 240 = 875. Then we solve this by adding 240 to both sides to get the x alone. This gives us x=1,115 mL!

4 0

3 years ago

Could someone please tell me or explain how to solve these types of equations?? you don’t have to do these problems specifically

Lunna [17]

Okay so you know a straight line is equal to 180 degrees, so you set them up in an algebraic equation. (5x+2)+48=180 subtract 48 first to get 5x+2=132 Subtract the 2 this time to get 130. Now you end up with 5x=130. Here you divide 130 by 5 to get X=26. If you just need to find the degree of that angle tho you can stop after the first subtraction because the math tells you (5x+2)=132 degrees.

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2 years ago

ANSWER NEEDED QUICKLY, RIGHT ANSWER WILL RECEIVE BRAINLIEST ♦️

Oksi-84 [34.3K]

111km

the ratio is 1:15 so you do 7.4×15

7 0

3 years ago

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