Why does a stream or river change direction when going down a steep mountain

The circumference of a sphere was measured to be

professor190 [17]

To solve this problem we will apply the concepts related to the calculation of the surface, volume and error through the differentiation of the formulas given for the calculation of these values in a circle. Our values given at the beginning are

$\phi = 76cm$

$Error (dr) = 0.5cm$

The radius then would be

$\phi = 2\pi r \\76cm = 2\pi r\\r = \frac{38}{\pi} cm$

And

$\frac{d\phi}{dr} = 2\pi \\d\phi = 2\pi dr \\0.5 = 2\pi dr$

PART A ) For the Surface Area we have that,

$A = 4\pi r^2 \\A = 4\pi (\frac{38}{\pi})^2\\A = \frac{5776}{\pi}$

Deriving we have that the change in the Area is equivalent to the maximum error, therefore

$\frac{dA}{dr} = 4\pi (2r) \\dA = 4r (2\pi dr)$

Maximum error:

$dA = 4(\frac{38}{\pi})(0.5)$

$dA = \frac{76}{\pi}cm^2$

The relative error is that between the value of the Area and the maximum error, therefore:

$\frac{dA}{A} = \frac{\frac{76}{\pi}}{\frac{5776}{\pi}}$

$\frac{dA}{A} = 0.01315 = 1.31\%$

PART B) For the volume we repeat the same process but now with the formula for the calculation of the volume in a sphere, so

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

$V = \frac{4}{3} \pi (\frac{38}{\pi})^3$

$V = \frac{219488}{3\pi^2}$

Therefore the Maximum Error would be,

$\frac{dV}{dr} = \frac{4}{3} 3\pi r^2$

$dV = 2r^2 (2\pi dr)$

$dV = 4r^2 (\pi dr)$

Replacing the value for the radius

$dV = 4(\frac{38}{\pi})^2(0.5)$

$dV = \frac{2888}{\pi^2} cm^3$

And the relative Error

$\frac{dV}{V} = \frac{ \frac{2888}{\pi^2}}{ \frac{219488}{3\pi^2} }$

$\frac{dV}{V} = 0.03947$

$\frac{dV}{V} = 3.947\%$

3 0

3 years ago

Two students race up a flight of steps together. "Student A" reaches the top of the steps 2 seconds ahead of

oksano4ka [1.4K]

Um student a because they were there a few seconds ahead

3 0

3 years ago

In a solution, the substance that does the dissolving is called Blank Space __________.

Finger [1]

The answer is Solvent. The reason is in the wording, 'the substance that does the dissolving.' A solvent does the dissolving, a solute is something that can be dissolved.

4 0

3 years ago

In which of the following is positive work done by a person on a suitcase

MrRa [10]

pendajo sMh so stupid

4 0

3 years ago

•<br> What happens to similar charged<br> particles and differently charged<br> particles

mixas84 [53]

Answer:

Like charges repel

Different charges attract

Explanation:

When particles of similar charges are brought together, they repel each other and increase the distance of separation. Repulsion occurs because both two electrons have negative electrical charge forcing their lines of force to repel. However, when particles of opposite charges are brought nearer to each other, they attract each other and reduce the distance of separation.

8 0

3 years ago