1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mariana [72]
3 years ago
11

Find the angle between the diagonal of a cube of side length 15 and the diagonal of one of its faces, so that the two diagonals

have a common vertex. The angle should be measured in radians. (Hint: we may assume that the cube is in the first octant, the origin is one of its vertices, and both diagonals start at the origin.)
Mathematics
1 answer:
Daniel [21]3 years ago
7 0

Answer:

the angle between the diagonal is 0.6155 RADIANS

Step-by-step explanation:

Given the data in the question

as illustrated in the image below;

O is [0,0,0]

B is [15,0,15]

E is [15,15,15]

Now to find angle BOE

vector OB = [15,0,15]

vector OE = [15,15,15]

OB.OE = [15,0,15].[15,15,15] = 15 × 15 + 15 × 15 = 450 = |OB||OE|cos[angleBOE]

|OB| = √(15² + 15²) = √(225 + 225) = √450

|OE| = √(15² + 15² + 15²) = √(225 + 225 + 225) = √675

so

Angle BOE = cos⁻¹ (  450 / ( √450 × √675 )

Angle BOE = cos⁻¹ ( 0.81649 )

Angle BOE = 35.265°

Angle BOE = 0.6155 RADIANS

Therefore, the angle between the diagonal is 0.6155 RADIANS  

You might be interested in
I need some help with this question :/
Masteriza [31]
You have one of the answers correct. The fraction 4/8 is equal to 1/2

Other answers are: 5/10, 10/20, and 6/12

If you reduced each of those fractions, you'd get to 1/2. 

You can use a calculator to find that
4/8 = 0.5
1/2 = 0.5
5/10 = 0.5
10/20 = 0.5
6/12 = 0.5
All fractions mentioned lead to the same decimal value, so this confirms all of the fractions are equivalent to one another.
7 0
3 years ago
Read 2 more answers
The ratio of two numbers is 8:7. The product of these numbers is 896. What is the smaller of these two
Darina [25.2K]

Answer:

  28

Step-by-step explanation:

You want the smaller of the two factors of 896 that have the ratio 8:7.

<h3>Setup</h3>

Let x represent the smaller of the two factors (the one we want to find). Then the larger factor is (8/7)x, and their product is ...

  x(8/7)x = 896

  (8/7)x² = 896

<h3>Solution</h3>

Multiplying by the inverse of the coefficient of x², we have ...

  x² = (7/8)(896) = 784

  x = √784 = 28 . . . . . . . . take square root

The smaller of the two numbers is 28.

__

<em>Additional comment</em>

The larger is (8/7)(28) = 32.

5 0
1 year ago
Who ever gets it right first gets brainliest
sleet_krkn [62]

Answer: Playing chess with Katie cause who'd play chess by themself right?

Step-by-step explanation:

7 0
2 years ago
Can you exchange the coordinates of points ( x 1, y 1) and ( x 2, y 2) in the distance formula and still find the correct distan
notka56 [123]

Answer:

yes

Step-by-step explanation:

As an example

(x₁, y₁ ) = (1,2) and (x₂, y₂ ) = (5,3), then

d = \sqrt{(5-1)^2+(3-2)^2} = \sqrt{4^2+1^2} = \sqrt{16+1} = \sqrt{17}

Now let (x₁, y₁ ) = (5,3) and (x₂, y₂ ) = (1,2), then

d = \sqrt{(1-5)^2+(2-3)^2} = \sqrt{(-4)^2+(-1)^2} = \sqrt{16+1} = \sqrt{17}


3 0
3 years ago
if the area of a square is 144 feet and the perimeter of the triangle is 28 feet, what is the perimeter of the room's floor?
FinnZ [79.3K]

Answer:

52+12\pi

Step-by-step explanation:

The diagram for the question is attached below

perimeter of the triangle is 28 feet

area of a square is 144 feet

Area of the square is side^2

side ^2= 144

take square root on both sides

side = 12

side of the square = 12

side is the diameter of the semicircle

Diameter = 12 , so radius = 12 divide 2 = 6

circumference of semicircle = 2\pi r=2\pi (6)=12\pi

one side of the rectangle is calculated in the perimeter of triangle and other side is calculated using circumference

perimeter of other two side = 2(12)= 24

Total perimeter = 28+24+12\pi =52+12\pi

4 0
3 years ago
Other questions:
  • What is 20 plus 20.
    13·2 answers
  • I don't understand #9
    14·1 answer
  • What happened to Japanese-Americans during this time in WWII?
    8·1 answer
  • What is -0.8a-8=0.2a ?
    8·1 answer
  • Two teams of interns are wrapping donated gifts at a hospital. if the teams work alone, team a can wrap all of the gifts in 7 ho
    8·1 answer
  • Two parallel lines cut by a transversal can create all of the following types of angles EXCEPT
    7·2 answers
  • What is 0.039 as a fraction?
    15·1 answer
  • Which two tables represent data sets that could be fit to a normal distribution curve? A. value 1 2 3 4 5 6 7 8 9 10 11 percenta
    15·2 answers
  • Jessica borrows $1500 at 7% simple interest per week. If she ends up owing $2235, how may weeks did it take her to pay back the
    9·2 answers
  • There are 4 black, 4 red, and 4 white marbles in a box. How many marbles do you have to take out (without looking) to be sure yo
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!