SHOW THAT THE ANGEL BETWEEN ANY 2 DIAGONALS OF A CUBE IS cos-1 (1/3)

Answers

Answer 1

Answer: $Look\ at\ the\ picture.\n\n|BD|=a\sqrt2\n\n|BD_1|=|DB_1|=a\sqrt3\n\n|BE|=|DE|=(a\sqrt3)/(2)\n\nUse\ law\ of\ cosine:\n\n(a\sqrt2)^2=\left((a\sqrt3)/(2)\right)^2+\left((a\sqrt3)/(2)\right)^2-2\cdot(a\sqrt3)/(2)\cdot(a\sqrt3)/(2)\cdot cos\theta\n\n2a^2=(3a^2)/(4)+(3a^2)/(4)-(3a^2)/(2)cos\theta$

$(3a^2)/(2)cos\theta=(6a^2)/(4)-2a^2\n\n(3a^2)/(2)cos\theta=(6a^2)/(4)-(8a^2)/(4)\n\n(3a^2)/(2)cos\theta=-(2a^2)/(4)\n\n(3a^2)/(2)cos\theta=-(a^2)/(2)\ \ \ \ \ /\cdot(2)/(3a^2)\n\ncos\theta=-(1)/(3)$

Answer 2

Answer: Vector for one diagnol (1,1,1) - (0,0,0) = (1,1,1)
Vector for another diagnol (0,1,1) - (1,0,0) = (-1,1,1)

Do cos product of two vectors , that is

sqrt(3) sqrt(3) cos(theta) = (1,1,1).(-1,1,1)
3cos(theta) = 1.(-1) + 1.(1) + 1.(1) = 1

therefore cos(theta) = 1/3
angle betwwen diagnols = cos-1 (1/3)

Related Questions

A car rents for $45 per day plus 21 cents per mile. You are on a daily budget of $66. What mileage will allow you to stay within your budget?
True or false, A function is a relation if and only if the x-values do not repeat in a given set
F(x)=x^2+1;g(x)= x-3Help me find (f•g)(x)
What does it mean when we say we say direct and inverse(indirect) proportion ???
How do I find the value of K?

The equation f(x) = 5x2 − 30x + 6 represents a parabola. What is the vertex of the parabola?(−5, 281)
(5, −19)
(−3, 141)
(3, −39) ((my answer))

Answers

you are correct
And if you plug them in they wouldn't give you the correct y except your answer

Answer:

(3, −39)

Step-by-step explanation:

How to simplify rational expressions?

Answers

Steps to simplify rational expressions. 4) If possible, look for other factors that are common to the numerator and denominator. In our example, we can use foil in reverse to factor an (x − 1) in the denominator and further cancel this binomial from both the numerator and the denominator.

Find the range of the data.

76, 72, 81, 71, 73, 89, 83, 75

Answers

Answer:

Range is 18

Step-by-step explanation:

In order: 71, 72, 73, 75, 76, 81, 83, 89

The range is the smallest number subtracted by the largest number:

89-71=18

Answer:

$18$

Step-by-step explanation:

$71, 72, 73, 75, 76, 81, 83, 89$

$\mathrm{The \: range \: is \: equal \: to:}$

$\mathrm{Biggest \: no. - Smallest \: no.}$

$89-71$

$=18$

Solve the inequality.–4s < –8

s < –4
s < 2
s > –4
s > 2

Answers

I think it's s>2

Divide -4 and -8 by -4, this flips the sign, and leaves s and 2 behind

Answer:

s > 2

Step-by-step explanation:

What is the sum of the geometric sequence 3, 15, 75, … if there are 8 terms?39,062
58,593
195,312
292,968

Answers

If you would like to know the sum of the geometric sequence, you can calculate this using the following steps:

3, 15, 75, 75 * 5 = 375, 375 * 5 = 1875, 1875 * 5 = 9375, 9375 * 5 = 46875, 46875 * 5 = 234375

3 + 15 + 75 + 375 + 1875 + 9375 + 46875 + 234375 = 292,968

The correct result would be 292,968.

Answer:

292,968

Step-by-step explanation:

Step 1: Use geometric sequence formula $s_n=(a1r^n)/(1-r)$