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3 years ago

How does an indirect proof differ from a regular proof ?

Mathematics

2 answers:

Vlad [161]3 years ago

6 0

Answer and Step-by-step explanation:

Regular proof is a method of proving the statement directly.

In this method, we just proved it by using direct formula or theorem.

whereas,

Indirect proof is a way of proving by contradiction.

In this method we assume first that the given statement is false, then it is proved correct by contradiction.

ss7ja [257]3 years ago

3 0

Answer:

Regular proof is all about known facts that is for e.g X must be true, while in indirect proof you assume X is true

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Y_Kistochka [10]

Answer:

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2 years ago

Simplify to create an equivalent expression. 2(3r+7)−(2+r)

tamaranim1 [39]

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4 years ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

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3 years ago

Mary was making $25,000 per year. Her boss gave her a $3,000 raise. What percent increase is that? PLZ HELP

Solnce55 [7]

The easiest way to find a percentage is to divide the two numbers. You're trying to find what percent 3,000 is of 25,000, so you divide 3,000 by 25,000 to find the decimal.
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$3,000 is a 12% raise from $25,000.

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gizmo_the_mogwai [7]

A reflection I think is true

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2 years ago