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3 years ago

12

Why do you think rates are usually written as unit rates?

2 answers:

stellarik [79]3 years ago

6 0

Coooooooooooooooooooooool

Elden [556K]3 years ago

6 0

It's so you can compare two rates

For example,
person A walks 10 miles in 2 hours
person B walks 40 miles in 4 hours

If you want to know who is the faster walker, then you divide the distance over the time
person A's speed = distance/time = 10/2 = 5 miles per hour
person B's speed = distance/time = 40/4 = 10 miles per hour

So we can see that person B is faster as 10 is larger than 5. This is only possible by comparing the unit rates of 5 mph (for person A) and 10 mph (for person B)

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2 years ago

a solid consists of cylinder surmounted by a right circular cone. The height of the cone is 2h. If the volume of the solid is 3

Mademuasel [1]

Answer:

height of cylinder = 4/3 h

Step-by-step explanation:

The solid has a cylinder surmounted with a cone .Therefore, the volume of the solid is the sum of the cone and the cylinder.

volume of the solid = volume of cylinder + volume of cone

volume of the solid = πr²h + 1/3πr²h

let

height of the cylinder = H

recall

the height of the cone = 2h

volume of the solid = πr²h + 1/3πr²h

3(1/3πr²2h) = πr²H + 1/3πr²2h

2πr²h = πr²H + 2/3 πr²h

πr²(2h) = πr²(H + 2/3 h)

divide both sides by πr²

2h = H + 2/3 h

2h - 2/3h = H

H = 6h - 2h/3

H = 4/3 h

height of cylinder = 4/3 h

8 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%7B%7D%5E%7B2%7D%20-%204%20%7D%7B%20%5Csqrt%7Bx%20%7B%7D%5E%7B2%7D%20-%206x%2

Nimfa-mama [501]

First of all, we can observe that

$x^2-6x+9 = (x-3)^2$

So the expression becomes

$\dfrac{x^2-4}{\sqrt{(x-3)^2}} = \dfrac{x^2-4}{|x-3|}$

This means that the expression is defined for every $x\neq 3$

Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask

$x^2-4 \geq 0 \iff x\leq -2 \lor x\geq 2$

Since we can't accept 3 as an answer, the actual solution set is

$(-\infty,-2] \cup [2,3) \cup (3,\infty)$

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2 years ago