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1 year ago

54 students fit on a bus. There are 125

Mathematics

2 answers:

melomori [17]1 year ago

6 0

Answer:

Step-by-step explanation:

125 students ÷54 students (1 bus) =2.31 (buses)

3 buses.

vfiekz [6]1 year ago

3 0

Answer: 3 buses

Step-by-step explanation: If 54 students fit on a bus, and 125 students are in 8th grade,

You should divide.

125 divided by 54 is 2.31...

we can't have 2.31... buses, so we say 3 buses.

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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:

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

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3 years ago

What is the length of AB?

Bingel [31]

Answer:

ab is equal to 5

Step-by-step explanation:

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3 years ago

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Help please I gotta get my grade up!

DochEvi [55]

First step: you got to add y to both sides in the math problem Ex: 15x - y + y < 12 + y

Second step: simplify 15x < 12 + y

Third Step: This you got to divide both sides by 15 like this: 15x/15 < 12/15 + y/15

Last and Fourth step: Simplify and thats your answer x < 12 + y/15

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3 years ago

Which of the following statements best describes the graph of 3x − 2y = 4?

tigry1 [53]

<span>B.) It is a straight line joining the points (0, −2), (2, 1), and (−2, −5).

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3 years ago

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When simplified completely, the product of a monomial and a monomial is sometimesalwaysnever a monomial

Vaselesa [24]

Answer:

Always

Step-by-step explanation:

A mononomial's variable can only have exponents 0,1,2,3 etc so the product will also be a mononomial.

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3 years ago