Mathematics, 15.01.2020 03:31, yolomcswaggin20

Find the angle between a diagonal of a cube and one of its edges.

Answers: 1

Show answers

Answers

answered: AutumnGarringer

54.74°

Step-by-step explanation:

Draw a well labelled cube to have a better representation of the question.

A cube is 3-dimensional, therefore it will have coordinates in x,y and z axis. The diagonal of a cube is from one corner to another corner.

Assuming that cube is unit cube, we need to find n angle at one of its edges will make with the diagonal.

I choose the the diagonal and one edge with the unit vector (1,0,0) and (1,1,1).

a = (1,1,1)

b = (1,0,0)

To calculate the angle between two vectors,

a.b = |a||b|cosθ

For simplicity, calculate the dot product, and the magnitudes. Then we will substitute the values of the dot product, and the magnitudes of the vectors to solve for the angle.

Calculating the dot product

a.b = (1,1,1) . (1,0,0)

= (1 × 1) + (1 × 0) (1 × 0)

= 1

Calculating the magnitudes

1. Magnitude of (1,1,1)

$|a| = \sqrt{1^{2} + 1^{2} + 1^{2}}$

$|a| = \sqrt{3}$

2. Magnitude of (1,0,0)

$|b| = \sqrt{1^{2} + 0^{2} + 0^{2}}$

|b| = 1

Calculating the angle between the two vectors

cosθ $= \frac{a.b}{|a||b|}$

cosθ $= \frac{1}{\sqrt{3}* 1}$

cosθ $= \frac{1}{\sqrt{3}}$

θ $= cos^{_-1} \frac{1}{\sqrt{3}}$

θ = 54.7356°

θ ≈ 54.74°

answered: Guest

4/6 = 2/3

so it should take 3/3 hours per man. so 9 hours is the answer 3*3 =9

step-by-step explanation:

answered: Guest

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number $c\in[0.5,0.75]$ that satisfies the conclusion of the mean value theorem, that is, a number $c\in[0.5,0.75]$ such that

$f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},$

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 17:30, liamgreene90

Student price tickets to a movie are $1 and non student tickets are $2. 350 tickets are sold and the total amount made is $450. how many non student tickets were sold ? a) 100 b) 150 c) 200 d)250

Answers: 2

continue

Mathematics, 21.06.2019 17:40, shell3181

Aperpendicular bisector, cd is drawn through point con ab if the coordinates of point a are (-3, 2) and the coordinates of point b are (7,6), the x-intercept of cd is point lies on cd.

Answers: 2

continue

Mathematics, 21.06.2019 18:30, nickname0097

Barbara deposited $300 in the bank. if the bank pays her simple interest at the rate of 4 percent per year, how much money will she have in her account at the end of 9 months?

Answers: 1

continue

Mathematics, 21.06.2019 19:00, mbalderp5bxjo

Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 is he correct? explain why or why not?

Answers: 3

continue

Do you know the correct answer?

Find the angle between a diagonal of a cube and one of its edges....