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kvasek [131]
2 years ago
6

For this Discussion, follow these three steps:

Mathematics
1 answer:
katen-ka-za [31]2 years ago
7 0

Part 1: "If it rains, then there are clouds"

a) "it rains"

b) "there are clouds"

c) true.

d) "if there are clouds, then it rains"

e) false.

Part 2: "If a number is larger than 5, then the number is larger than 3"

a)  "a number is larger than 5"

b)  "a number is larger than 3"

c) true

d) "If a number is larger than 3, then it is larger than 5"

e) False

Part 3: ""A number is even if and only if it is a multiple of 2""

a) true.

<h3>What is a conditional statement?</h3>

For two propositions P and Q, a conditional statement is:

If P then Q.

Part 1:

A conditional statement is:

"If it rains, then there are clouds"

a) The hypothesis is the first proposition, which is "it rains"

b) The conclusion is the second proposition "there are clouds"

c) The statement seems to be true, as the rain comes from the clouds, so it seems to be true.

d) The converse statement is:

"If Q then P"

In this case, it would be:

"If there are clouds, then it rains"

e) That statement is clearly false, because not always that there are clouds in the sky there is rain.

Part 2.

Another conditional statement could be:

"If a number is larger than 5, then the number is larger than 3"

a) The hypothesis is "a number is larger than 5"

b) The conclusion is "a number is larger than 3"

c) The statement is true because 5 is larger than 3, then if a number is larger than 5 it must be larger than 3.

d) The converse statement is:

"If a number is larger than 3, then it is larger than 5"

e) Which is clearly false, a counterexample is 4, which is larger than 3 but not larger than 5.

Part 3.

A biconditional statement is:

P if and only if Q.

One example is:

"A number is even if and only if it is a multiple of 2"

a) That statement is clearly true, as that is the definition of an even number.

If you want to learn more about conditional statements:

brainly.com/question/18152035

#SPJ1

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Quiz 1-2: Distance &amp; Midpoint; Partitioning a Segment
nadya68 [22]

The distances between the given pairs of points are:

  • (-8, -2) and (6, -1);  d = 14.04
  • (-4, 5) and (4,0); d = 9.85
<h3>How to find the distance between two points?</h3>

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √( (x₁ - x₂)^2 - (y₁ - y₂)^2)

1) The first pair of points is (-8, -2) and (6, -1), using the above formula we can see that the distance is:

d = √( (-8 - 6)^2 - (-2 +1)^2) = 14.04

2) The second pair is (-4, 5) and (4,0), and using the distance formula, we get:

d = √( (-4 - 5)^2 - (4 - 0)^2) = 9.85

If you want to learn more about the distance between points:

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3 0
1 year ago
Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma
Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}

The total surface area is,

\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}

Volume is,

\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}

Now, differentiate with respect to x,

\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}

Now,

\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}

Now, differentiate (1) with respect to x again,

\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}

Since, the double derivative is negative.

So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}

So, the volume becomes,

\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}

Answer: maximum volume of the cylinder is,

6 0
1 year ago
Order these numbers from least to greatest. 2.508 , 2.58 , 3.64 , 2.9
Kobotan [32]
2.508, 2.58, 2.9, 3.64
3 0
3 years ago
Read 2 more answers
A girl is 21 years old and her brother is a third her age. When the girl is 36, what will be the age of her brother?
AVprozaik [17]
21 divided by 3 = 7

That means the brother is 14 years younger.

36 - 14 = 22

The brother will be 22 years old.
7 0
3 years ago
Read 2 more answers
Which is the slope of the line passing through the points (-3,4) and (2,-1)
Alecsey [184]

Answer:

slope = -1

Step-by-step explanation:

to find the slope it is y1-y2 / x1-x2

4 - (-1) = 5

-3 - 2 = -5

m= -1

8 0
3 years ago
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