All categories

2 years ago

Which of the following illustrates the truth value of the following statements?

Mathematics

1 answer:

valentinak56 [21]2 years ago

4 0

Answer:

T F → T illustrates the truth value of the given statements.

Step-by-step explanation:

According to Point and Line contained in Plane Theorem: "If a point lies outside a line, then exactly one plane contains both the line and the point".

So, the statement "A line, and a point outside the line are in exactly one plane" holds true.

According to Plane Intersection Postulate: "If two planes intersect, then their intersection is a line".

So, according to this postulate, two planes intersect in a plane is false.

Although two Planes in three-dimensional space are able to intersect in one of three ways:

Two planes would only intersect in a plane if they are coincident.
Two planes would never intersect if they are parallel.
If the option 1 and 2 do not hold true, then the two planes would intersect in a line.

But, as it is not specified in the question that the planes were coincident, so we assume that two planes would intersect in a line. Hence, the statement "two planes intersect in a plane" is false.

Let p be the statement: "A line, and a point outside the line are in exactly one plane". So, the statement p is true (T).

Let q be the statement: "two planes intersect in a plane". So, the statement q is false (F).

Hence, the statement p or q is written as p ∨ q.

As p is true (T) and q is false (F), hence p ∨ q will be true (T).

i.e.

T F T

So, T F → T illustrates the truth value of the given statements.

Keywords: truth value, plane, line, intersection

learn more about truth values from brainly.com/question/9051197

#learnwithBrainly

You might be interested in

Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.

FromTheMoon [43]

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

$\rho = \sqrt{x^{2}+y^{2}+z^{2}}$

$\phi = cos^{-1}\frac{z}{\rho}$

For angle θ:

If x > 0 and y > 0: $\theta = tan^{-1}\frac{y}{x}$ ;

If x < 0: $\theta = \pi + tan^{-1}\frac{y}{x}$ ;
If x > 0 and y < 0: $\theta = 2\pi + tan^{-1}\frac{y}{x}$ ;

Calculating:

a) (4,2,-4)

$\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}$ = 6

$\phi = cos^{-1}(\frac{-4}{6})$

$\phi = cos^{-1}(\frac{-2}{3})$

For θ, choose 1st option:

$\theta = tan^{-1}(\frac{2}{4})$

$\theta = tan^{-1}(\frac{1}{2})$

b) (0,8,15)

$\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}$ = 17

$\phi = cos^{-1}(\frac{15}{17})$

$\theta = tan^{-1}\frac{y}{x}$

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = $\frac{\pi}{2}$

c) (√2,1,1)

$\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}$ = 2

$\phi = cos^{-1}(\frac{1}{2})$

$\phi$ = $\frac{\pi}{3}$

$\theta = tan^{-1}\frac{1}{\sqrt{2} }$

d) (−2√3,−2,3)

$\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}$ = 5

$\phi = cos^{-1}(\frac{3}{5})$

Since x < 0, use 2nd option:

$\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }$

$\theta = \pi + \frac{\pi}{6}$

$\theta = \frac{7\pi}{6}$

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

$r=\sqrt{x^{2}+y^{2}}$

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

$r=\sqrt{4^{2}+2^{2}}$ = $\sqrt{20}$

$\theta = tan^{-1}\frac{1}{2}$

z = -4

b) (0, 8, 15)

$r=\sqrt{0^{2}+8^{2}}$ = 8

$\theta = \frac{\pi}{2}$

z = 15

c) (√2,1,1)

$r=\sqrt{(\sqrt{2} )^{2}+1^{2}}$ = $\sqrt{3}$

$\theta = \frac{\pi}{3}$

z = 1

d) (−2√3,−2,3)

$r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}$ = 4

$\theta = \frac{7\pi}{6}$

z = 3

5 0

3 years ago

ASAP!! ILL GIVE BRAINLEST

densk [106]

Answer:

A^-1:B^-1

Step-by-step explanation:

im not 100% sure but i think this is the right answer :)

8 0

2 years ago

Simplify 3(2f+6)+7 thanks

Naya [18.7K]

{Expand} 3(2f+6): 6f+18

6f+18+7

18+7=25

= 6f+25

4 0

2 years ago

Two cards are chosen at random without replacement from a well-shuffled pack. what is the probability that the second card drawn

frosja888 [35]

Having drawn one king, there are 3 kings remaining and a total of 51 cards. Therefore the probability of drawing another king is 3/51 = 1/17.

4 0

2 years ago

What are the end points of the triangle called? How are they labeled?

horrorfan [7]

For this case we have that by definition:

A triangle is defined by three lines that are called sides, or by three points called vertices.

We know that:

The vertices of a triangle are labeled with capital letters.
The sides of a triangle are written with lowercase letters.
The angles of a triangle are written similarly to the vertices.

Answer:

The end points of the triangle are called vertices.

They are labeled in capital letters.

6 0

2 years ago