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
Debora [2.8K]
2 years ago
6

(NEED HELP! WILL RATE 5 STARS!)

Mathematics
1 answer:
vitfil [10]2 years ago
3 0

Answer:I think it's 1/61

Step-by-step explanation:If I am correct plz don't forget to thank me...

You might be interested in
PLEASE HURRY
tangare [24]
B can make a triangle
4 0
3 years ago
Read 2 more answers
Find the direction cosines and direction angles of the vector. (Give the direction angles correct to the nearest degree.) 5, 1,
Dahasolnce [82]

Answer:

The direction cosines are:

\frac{5}{\sqrt{42} }, \frac{1}{\sqrt{42} }  and  \frac{4}{\sqrt{42} }  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

Step-by-step explanation:

For a given vector a = ai + aj + ak, its direction cosines are the cosines of the angles which it makes with the x, y and z axes.

If a makes angles α, β, and γ (which are the direction angles) with the x, y and z axes respectively, then its direction cosines are: cos α, cos β and cos γ in the x, y and z axes respectively.

Where;

cos α = \frac{a . i}{|a| . |i|}               ---------------------(i)

cos β = \frac{a.j}{|a||j|}               ---------------------(ii)

cos γ = \frac{a.k}{|a|.|k|}             ----------------------(iii)

<em>And from these we can get the direction angles as follows;</em>

α =  cos⁻¹ ( \frac{a . i}{|a| . |i|} )

β = cos⁻¹ ( \frac{a.j}{|a||j|} )

γ = cos⁻¹ ( \frac{a.k}{|a|.|k|} )

Now to the question:

Let the given vector be

a = 5i + j + 4k

a . i =  (5i + j + 4k) . (i)

a . i = 5         [a.i <em>is just the x component of the vector</em>]

a . j = 1            [<em>the y component of the vector</em>]

a . k = 4          [<em>the z component of the vector</em>]

<em>Also</em>

|a|. |i| = |a|. |j| = |a|. |k| = |a|           [since |i| = |j| = |k| = 1]

|a| = \sqrt{5^2 + 1^2 + 4^2}

|a| = \sqrt{25 + 1 + 16}

|a| = \sqrt{42}

Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e

cos α = \frac{5}{\sqrt{42} }

cos β =  \frac{1}{\sqrt{42} }              

cos γ =  \frac{4}{\sqrt{42} }

From the value, now find the direction angles as follows;

α =  cos⁻¹ ( \frac{a . i}{|a| . |i|} )

α =  cos⁻¹ ( \frac{5}{\sqrt{42} } )

α =  cos⁻¹ (\frac{5}{6.481} )

α =  cos⁻¹ (0.7715)

α = 39.51

α = 40°

β = cos⁻¹ ( \frac{a.j}{|a||j|} )

β = cos⁻¹ ( \frac{1}{\sqrt{42} } )

β = cos⁻¹ ( \frac{1}{6.481 } )

β = cos⁻¹ ( 0.1543 )

β = 81.12

β = 81°

γ = cos⁻¹ ( \frac{a.k}{|a|.|k|} )

γ = cos⁻¹ (\frac{4}{\sqrt{42} })

γ = cos⁻¹ (\frac{4}{6.481})

γ = cos⁻¹ (0.6172)

γ = 51.89

γ = 52°

<u>Conclusion:</u>

The direction cosines are:

\frac{5}{\sqrt{42} }, \frac{1}{\sqrt{42} }  and  \frac{4}{\sqrt{42} }  with respect to the x, y and z axes respectively.

The direction angles are:

40°,  81° and  52° with respect to the x, y and z axes respectively.

3 0
3 years ago
Simplify (3x2 – 4x – 1) + (8x2 – x + 6)
abruzzese [7]

Answer:

11x^{2} -5x+5

Step-by-step explanation:

3x^{2}-4x-1+8x^{2} -x+6

3x^{2}+8x^{2}-4x-x-1+6

Combine like terms

11x^{2}-5x +5

6 0
2 years ago
The theorems in this lesson relate to all of the following except for:
Katarina [22]
<span>The theorems in this lesson relate to all of the following (tangents, arcs, and chords) except for <u>radii.</u></span>
7 0
3 years ago
Read 2 more answers
Identify the domain and range of each graph
vova2212 [387]

Answer:

Step-by-step explanation:

You didn't mark your graph but I'm assuming the point is (1,2)

You notice how the function stops at the point? x and y can not be above that point because there is no line above it.

The domain of the function means what can x possibly be.

The maximum value of x in this function is 1 because that's the x value of the point where the function ended. This means x can at most be one or x≤1. So the domain is x≤1.

The range of the function means what can y possibly be.

The maximum value of y in this function is 2 because that's the y value of the point where the function ended. This means y can at most be two or y≤2. So the range is y≤2.

3 0
3 years ago
Other questions:
  • In 2 pieces of cake there are 16
    13·2 answers
  • Two numbers with the sum of -19 and product of 48
    13·1 answer
  • Veronica gave 20% of her money to Bill. She used 50% of the remaining money to buy books.
    13·2 answers
  • Please help, 30 points, brainliest, and thanks!
    9·1 answer
  • Plz I don’t get this question your suppose to find the area
    13·1 answer
  • Firat cheese yeur beunda and intervals by completing the
    13·1 answer
  • Please answer please
    6·1 answer
  • The perimeter of the triangle below is 10x - 3<br><br> Show how to solve
    13·1 answer
  • Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the
    7·1 answer
  • The probability of winning on an arcade game is 0. 659. if you play the arcade game 30 times, what is the probability of winning
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!