Mathematics, 20.10.2020 16:01 lizzy2951

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of LaTeX: 50cm^3/hr. At what rate is it's diameter decreasing

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The rate at which grindstone diameter decreases is $-5/2\pi r \;{\rm cm/hr}$ and this can be determined by using the given data.

Given :

A 10 cm thick grindstone is initially 200 cm in diameter and it is wearing away at a rate of 50 $\rm cm^3/hr$ .

The following steps can be used in order to determine the rate at which grindstone diameter decreases:

Step 1 - According to the given data, the rate at which grindstone volume decreases is:

$\dfrac{dV}{dt} = 50\;{\rm cm^3/hr}$ --- (1)

Step 2 - The formula of the volume of the cylinder (grindstone) is given below:

$V = \pi r^2 h$

Step 3 - Differentiate the above expression with respect to 'r'.

$\dfrac{dV}{dr} = 2\pi r h$ --- (2)

Step 4 - So, using the expression (1) and (2) the rate at which grindstone diameter decreases is:

$\dfrac{dr}{dt}=\dfrac{\frac{dV}{dt}}{\frac{dV}{dr}}$

$\dfrac{dr}{dt}=\dfrac{-50}{2\pi r \times 10}\\$

$\dfrac{dr}{dt} = -\dfrac{5}{2\pi r }\; {\rm cm/hr}$

So, the rate at which grindstone diameter decreases is $-5/2\pi r \;{\rm cm/hr}$ .

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Answer from: rmjracingz2185

Complete question is;

A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm/hr. At what rate is its diameter decreasing?

Diameter is decreasing at the rate of 5/(2πr) cm/hr

Step-by-step explanation:

We are told the stone is wearing away at a rate of 50 cm/hr. This means the volume is decreasing. Thus;

dV/dt = -50 cm/hr

Now, a grindstone is in the shape of a cylinder. Thus, volume of grindstone is;

V = πr²h

dV/dr = 2πrh

Now,to find the rate at which the diameter is decreasing, we'll write;

dr/dt = (dV/dt)/(dV/dr)

dr/dt = -50/(2πrh)

We are given;

Diameter = 200 cm

Radius; r = 200/2 = 100 cm

Thickness; h = 10 cm

Thus;

dr/dt = -50/(2π × r × 10)

dr/dt = -5/(2πr) cm/hr

Answer from: Quest

answer: segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students. an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality. in the case of brown v. board of education, that standard was challenged and defeated. segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to education. this was being violated by states whose laws supported the segregation of schools. section 1 of the 14th amendment reads as follows:

all persons born or naturalized in the united states and subject to the jurisdiction thereof, are citizens of the united states and of the state wherein they reside. no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the united states; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

Answer from: Quest

Ithink it would be 160 people