Find the angle between the diagonal of a cube of side length 9 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.)
Answers
Firstly, we can sketch points as
O as (0,0,0)
B as (9,0,9)
E as (9,9,9)
now, we can find vectors
OB=(9,0,9)-(0,0,0)
OB=(9,0,9)
OE=(9,9,9,)-(0,0,0)
OE=(9,9,9)
we can use dot product formula to find angle
now, we can find values
now, we can plug these values
now, we can solve for theta
............Answer
The angle between the diagonal of the cube and the diagonal of one of its faces, with a common vertex, is approximately 1.23096 radians.
How did we get this value?
To find the angle between the diagonal of a cube of side length 9 and the diagonal of one of its faces, we can use trigonometry. Let's call the diagonal of the cube Dc and the diagonal of one of its faces Df.
The diagonal of a cube can be calculated using the Pythagorean theorem in 3D:
Dc =
= √(81 + 81 + 81)
= √(243) = 9√3
The diagonal of one of the cube's faces is simply the side length, which is 9.
Now, to find the angle between them, you can use the dot product formula and the formula for the angle between two vectors:
cos(θ) = (Dc ⋅ Df) / (|Dc| ⋅ |Df|)
Where:
- θ is the angle between the diagonals.
- Dc is the diagonal of the cube (9√3).
- Df is the diagonal of one of the faces (9).
- |Dc| and |Df| are the magnitudes of Dc and Df.
Now, plug in the values:
cos(θ) = (9√3 * 9) / (9√3 * 9)
cos(θ) = 27√3 / (81√3)
cos(θ) = 1/3
Now, you can find the angle θ in radians using the inverse cosine function (cos⁻¹):
θ = cos⁻¹(1/3)
θ ≈ 1.23096 radians
So, the angle between the diagonal of the cube and the diagonal of one of its faces, with a common vertex, is approximately 1.23096 radians.
learn more about vertex: brainly.com/question/21191648
#SPJ4
Related Questions
Helen is building a rectangular garden in her backyard and she wants to have a fence around it.The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per foot. How many feet of fence panels does she need
Correct reason why (x+y)^2 is not equal to x^2+y^2
This pattern repeats every 5 terms. The pattern is rectangle, pentagon, square, hexagon, pentagon. What is the 19th term of this pattern? Answers Square Pentagon Hexagon Rectangle
jay simplified the expression 3 x (3 +12 / 3) -4. for his first step ,he added 3 + 12 to get 15. what was jay's error? find the correct answer
Answers
The attached drawing is the apartment using the scale 20 ft to 1 unit from the apartment to the drawing.
As the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter,
this means that each square is
160 / 16 = 10 ft on a side.
so 10 ft in real life plots to 1 unit on the drawing
If the scale is changed to 20 :1 ,
then the drawing would be exactly the same shape, only each side would have half the original drawing units.
In stead of a 40 ft side being represented by 40 ft / 10 ft/unit = 4 units,
That side would be 40 ft / 20 ft/unit = 2 units
Hence, The attached drawing is the apartment using the scale 20 ft to 1 unit from the apartment to the drawing.
Learn more about perimeter here:
#SPJ3
Answer:
Step-by-step explanation:
As the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter, this means that each square is
160 / 16 = 10 ft on a side.
so 10 ft in real life plots to 1 unit on the drawing
If the scale is changed to 20 :1 , then the drawing would be exactly the same shape, only each side would have half the original drawing units.
In stead of a 40 ft side being represented by 40 ft / 10 ft/unit = 4 units, That side would be 40 ft / 20 ft/unit = 2 units
Answers
Answer:
5 g
Step-by-step explanation:
Answer:
16,191,000,000
Step-by-step explanation:
1 kg= 2.57 millions grains of sand
2.57 million*6300= 16,191,000,000
Answers
Answer:
0.6
Step-by-step explanation:
12/20 = 6/10 = 0.6
7 km = m
18 g = kg
43 kg = g
234 L = mL
1 346 mL = L
0.81 km = cm
0.05 dm = dam
1.32 cg = kg
3.7 mcg = mg
Answers
Answer..
Q 1, 80 mm
2, 7000
3,
Tom would like to take out a secured loan to help pay for a vacation this summer. He has offered his car as collateral.
His car is worth $3,500. His bank can offer loans for 80% of collateral value. The vacation he has planned will cost
$4,750. Approximately how much additional collateral will Tom need to offer in order to borrow enough to go on his
vacation as planned?
$1,000.00
b. $1,362.50
c. $2,437.50
d. $2,800.00
a.
Please select the best answer from the choices provided
A
B.
ОООО
D
Answers
Tom will need to offer additional collateral of C. $2,437.50 to borrow enough for his planned vacation.
What is collateral?
Collateral refers to a valued property or financial security offered by the borrower to the lender to guarantee repayment of a loan.
Lenders sell collaterals when the borrowers fail to comply with their loan terms.
How is the additional collateral determined?
Car's value = $3,500
Collateral value in percentage = 80%
Car's collateral value = $2,800 ($3,500 x 80%)
Planned cost of vacation = $4,750
Additional cost to meet vacation cost = $1,950 ($4,750 - $2,800)
Additional collateral value to meet target = $2,437.50 ($1,950/80%)
Total collateral that Tom needs to offer = $5,937.50 ($3,500 + $2,437.50)
80% of $5,937.50 = $4,750
Another way is to work with the planned cost and the collateral percentage offered by Tom's bank:
Planned cost of vacation = $4,750
Collateral value in percentage = 80%
Total collateral to be offered by Tom = $5,937.50 ($4,750/80%)
Car's collateral value = $3,500
Additional collateral value = $2,437.50 ($5,937.50 - $3,500)
Thus, Tom needs additional collateral of C. $2,437.50.
Learn more about collateral at brainly.com/question/11665626
#SPJ1
Answers
Answer:
17/100
Step-by-step explanation:
Step 1:
0.17 = 17/100
Answer:
17/100
Hope This Helps :)