Answer:
4
Step-by-step explanation:
Since the question is asking how long will it take him if he has to drive 240 miles and he drives 60 mph, this can be interpreted as division.
Now that we have converted the words into math, we are really solving 240 ÷ 60 or .
240 divided by 60 is the same as 24 divided by 6 because we can cancel the 0's.
Solving:
24 ÷ 6 = 4.
Thus, our answer is that it will take Charlie 4 hours to get to Dallas.
Answer:
The direction cosines are:
,
and
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 = ---------------------(i)
cos β = ---------------------(ii)
cos γ = ----------------------(iii)
<em>And from these we can get the direction angles as follows;</em>
α = cos⁻¹ ( )
β = cos⁻¹ ( )
γ = cos⁻¹ ( )
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| =
|a| =
|a| =
Now substitute these values into equations (i) - (iii) to get the direction cosines. i.e
cos α =
cos β =
cos γ =
From the value, now find the direction angles as follows;
α = cos⁻¹ ( )
α = cos⁻¹ ( )
α = cos⁻¹ ( )
α = cos⁻¹ (0.7715)
α = 39.51
α = 40°
β = cos⁻¹ ( )
β = cos⁻¹ ( )
β = cos⁻¹ ( )
β = cos⁻¹ ( 0.1543 )
β = 81.12
β = 81°
γ = cos⁻¹ ( )
γ = cos⁻¹ ()
γ = cos⁻¹ ()
γ = cos⁻¹ (0.6172)
γ = 51.89
γ = 52°
<u>Conclusion:</u>
The direction cosines are:
,
and
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.