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.)
Answers
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
Related Questions
Find the degree of the term.
- 3x^3
The degree of – 3x^3 is
Answers
Answer:
the degree of -3x^3 is 3
Step-by-step explanation:
the exponent is 3
Use ΔDEF, shown below, to answer the question that follows:
What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.
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A bag contains 1 green, 4 red and 5 yellow balls. Two balls are selected at
random. Find the probability if there is no replacement of P(1 green and 1
yellow).
Answers
Answer:
The probability is 1/18.
Step-by-step explanation:
There are 10 balls in total. Let's start with the probability of just the green. There is 1 green ball.out of 10 balls total, so the probability of pickin just the green one would be 1/10. Since we aren't replacing the balls after we choose them, the total number of balls is now 9. now the probability of picking one yellow ball out of the nine balls left is 5/9 because there are 5 yellow balls. To get the probability of the green and yellow balls picked, we multiply the individual probabilities to get the actual probability of choosinf one green and one yellow ball without replacement. So multiply 1/10×5/9= 5/90, simplified to 1/18.
Two balls are selected at random, the probability of choosing two balls 1 green and 1 yellow without replacement is 1 / 20
Probability-based problem:What information do we have?
Number of green balls = 1
Number of red balls = 4
Number of yellow balls = 5
Total number of balls = 1 + 4 + 5 = 10
Probability of green ball = 1 / 10
Probability of yellow ball = 5 / 10
Probability if there is no replacement of P(1 green and 1 yellow) = (1/10)(5/10)
Probability if there is no replacement of P(1 green and 1 yellow) = 1 / 20
Find out more information about 'Probability'.
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How might a victory at Gettysburg have benefited the confederacy? Plz I need this fast!!!! I will mark brainist!!!
Answers
Answer:
It might have convinced European nations to align with the South.
Step-by-step explanation:
i did this one twice
If Izzy has 43 minutes to do her work and her brother has 30 because he started before her how many minutes they would have together do you have to multiply to find it out
Answers
Answer:
you dont have to multiply
Step-by-step explanation:
because the keyword "Have together" in math indicates it is an adding problem
Which expression is equivalent to
Answers
Answer:
C
Step-by-step explanation:
16 times 0.5x equals 8x.
16 times -0.75 equals -12y, so this means A and D are incorrect.
16 times 2 is 32, so this means that B is wrong, for you must multiply each number in the parentheses by 16.
Hope that helps :)
WILL GIVE BRAINIEST TO THE FIRST PERSON WHO ANSWERS THEM ALL CORRECTLY, BUT U HAVE TO BE QUICK!!!
Answers
Answer:
A) a^8
B) 16a^14
C)a^mn
D)24a^yz
E)a^3
F)5a^2
G) a^5
H)a^m-n
28 orders in 4 days = orders per day
Answers
Answer:
7 orders per day
Step-by-step explanation:
28/4=7
Answer:
7
Step-by-step explanation:
divide 28 / 4 = orders per day
Find the circumference and area of the circle to the nearest hundredth. Use 3.14 for . Round to the nearest hundredth if necessary.
The circumference of the circle is about ____ cm.
The area of the circle is about ____ cm2.
Please answer!
Answers
Answer:
The circumference of the circle is about 166.42 cm.
The area of the circle is about 2205.07 cm².
Step-by-step explanation:
Diameter = 53 cm
Radius = r = 53cm/2 = 26.5 cm
π = 3.14
Circumference = C = 2 π r
C = 2(3.14)(26.5cm) = 166.42cm
The circumference of the circle is about 166.42cm.
Area = A = π r²
A = (3.14)(26.5cm)² = 2205.07 cm²
The area of the circle is about 2205.07 cm².
Tyler poured 15 cups of water into 2 equal sized bottles and filled each bottle. How much water was in each bottle?
Answers
Answer:7.5
Step-by-step explanation:
you divided 15 into 2
Answer:
7 and a half
Step-by-step explanation:
Divide 2 and 15 toet 7 and a alf
PS
The diagram shows the dimensions of a coal bunker.
The volume of the bunker is 0.432 m^3
Calculate the length, a, shown on the diagram. Give your answer in centimetres.
Answers
Answer:
Step-by-step explanation:
80×= 8×+16
Write 6.789 in word from
Answers
Answer:
six- and seven hundred eighty nine hundredths
Step-by-step explanation:
6 is the whole number
789 is ow many hundreths there is
What shape is this cross-section?
A. Rectangle
B. Pyramid
O C. Trapezoid
D. Triangle
Answers
If you're referring to the actual 3D shape, that would be a rectangle. If you're referring to the shape in the middle, it would be a Trapezoid.
Answer:
A. Rectangle
Step-by-step explanation:
It is a rectangle, not any of the other shapes listed in the other answer choices.
Hope this helps! :)
Calcul
A train travels 60 miles in 90 minute
Calculate the train's average speed.
Answers
Answer:
Step-by-step explanation:
Speed per min = 60 ÷ 90 = 0.66 miles
Answer:
0.66 miles/1 min
Step-by-step explanation:
60/90=0.66/1
!! HELP IM IN 7TH GRADE AND M LEARNING 9TH AND 8TH GRADE MATH!!
QUESTION~
If f(x) = 2|x| is graphed on a regular
coordinate grid, does the graph
form an acute, right, or obtuse
angle at its vertex?
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Answer:
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what is the y-intercept of the line perpendicular to the line y = 4/3 x + 1 that includes the point (4, 1)
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An ecological group suspects tuna are consuming dangerous levels of copper in a region of the world. Dangerous levels of copper are classified when they reach beyond 5.7 parts per million. A random sample of 21 tunas in the region were tested and the data is shown in the stemplot.
Part A: What proportion of the tuna in the sample have dangerous levels of copper in their systems? (4 points)
Part B: Construct and interpret a 98% confidence interval for the mean copper levels of the tuna if the sample of 21 tuna has a mean copper level of 4.77 parts per million and standard deviation of 1.16 parts per million. (6 points)
Answers
Answer:
a. 5 out of 21
b. (4.1811, 5.3589)
Step-by-step explanation:
a. We can see from the stem plot that 5 out of the 21 tunas have dangerous levels of copper in their system because the copper level reached over 5.7, and the problem states "Dangerous levels of copper are classified when they reach beyond 5.7 parts per million"
b. How to find it on calculator
Step 1: [stat]
Step 2: go to [tests]
Step 3: go down to [7: zinterval]
Step 4: make sure input is on [stats]
Step 5: input the following
: 1.16
X (with the line above it): 4.77
n: 21
c-level: .98
The solution is :
A.) The required proportion is 5/21=0.2381
B.) 98% confidence the true copper level (in parts per million) lies in the interval (4.13, 5.41).
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
here, we have,
A) From the stem-leaf plot, we see that out of 21 tunas, 5 have dangerous levels of copper since the levels go beyond 5.7 parts per million. The required proportion is 5/21=0.2381
B) Given the sample mean is {x}=4.77, sample standard deviation s=1.16 and the sample size is n=21.
Since the population standard deviation is not known, we use t-distribution.
So the 98% CI for mean is
4.77 ± t{1-0.02 /2,20} x 1.16/sqrt(21) = (4.13, 5.41)}
We are sure with 98% confidence the true copper level (in parts per million) lies in the interval (4.13, 5.41)
Learn more about standard deviation here:
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Gordon read 18 pages of a book about rockets in 40 minutes. What was the unit rate per minute? Per hour?
Answers
Answer:
he can read a page in about 2 minutes and i.d.k about the hour part
Step-by-step explanation:
you do
40 divided by 18 and get 2.2
Answer:
.45 per minute and 27 per hour
Step-by-step explanation:18/40 simplified
someone help solve this! f + 1 1/2 = 4 1/4
f= ?
Answers
Because -1 and 1/4 + 11/2= 4 and 1/4
Answer:
2 1/4
Step-by-step explanation:
The figure is made up of a square and a rectangle. Find the area of the shaded region 16 by 3 by 7
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Answer:
Go on Answers.com your welcome.
Mr. Kershner is a school nurse. He uses, on average, 24 self-adhesive bandages during each spring month: March, April, and May. He also knows that in June there are several field days and he will need 4 times the number of bandages for that month.
If the bandages cost 3 cents each, what is his total cost for March through June?
Answers
If the bandages cost 3 cents each, Mr. Kershner's total cost for bandages from March through June is $5.04.
What is an arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
The number of bandages used by Mr. Kershner in March, April, and May is 24 bandages each month, for a total of 24 x 3 = 72 bandages for those three months.
In June, he will need four times as many bandages as in the other months, for a total of 4 x 24 = 96 bandages.
The total number of bandages used from March through June is 72 + 96 = 168 bandages.
The cost of each bandage is 3 cents, so the total cost for 168 bandages is 168 x 3 = 504 cents, or $5.04.
Therefore, Mr. Kershner's total cost for bandages from March through June is $5.04.
To learn more about the arithmetic operation visit,
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Help&EXPLAIN
Don’t use for points or I’ll take it back and report
Answers
Answer: 6
Step-by-step explanation:
Answer:
x = 105 degrees
Step-by-step explanation:
180 degrees total
180 - 75 = 105
x = 105 degrees
100 point question. I attached a screenshot of the problem.
Answers
Answer:
9
Step-by-step explanation:
What is the area of a rectangle whose length is 36 inches and whose width is 42 inches?
Answers
Answer:
1512
Step-by-step explanation:
L x W = Area
<A and <B are vertical
angles. if m<A =(3x+13)° and <B=(5x+9)° then find the measure of <A
Answers
Answer:
Step-by-step explanation:
3x+13 = 5x+9
2x = 4
x = 2
A = 3x+13 = 19°
The high temperatures for a week are shown.
15°, 34°, 17°, 15°, 16°, 8°
Which measure of center, mean or median, would BEST represent the data?.
The median, 15.5, is best because it represents the middle most value of the data in the set.
The mean, 17.5, is best because the center of this data set is affected by outliers.
The mean, 17.5, is best because it is the average of all the values in the data set.
.
The median, 15.5, is best because the center of this data set is affected by outliers.
Answers
Answer:
i think it is a because my teacher just went over it
Step-by-step explanation:
hello
Ron walked 8/10 mile from his grandmothers house to the store. Then he walked 9/10 mile to his house. Use benchmarks to estimate how far he walked altogether.
Answers
Answer:
1 7/10 miles
Step-by-step explanation:
Linda started taking piano lessons. She had to practice 1 3/4 hours each day. If after only 8 days Linda decided she wanted to stop, how many hours did she take lessons
Answers
Answer:
If you mean how many hours did she practice because it didn't say how long her lessons are then the answer is 14 hours
Step-by-step explanation:
1 3/4 = 1.75
8 times 1.75 = 14
If the diagonals of a shombus are 10 and 24, find the area of the rhombus
A
120 units
B
240 units
С
60 units
D
180 units
Answers
Kevin can travel 22 1/2 miles in 1/3 hours. What is his average speed in miles per hour
Answers
Answer:
67 1/2
Step-by-step explanation:
22 1/2*3