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malfutka [58]
3 years ago
9

PLEASE!! For 22 points!!

Mathematics
1 answer:
daser333 [38]3 years ago
5 0

Answer:

y = 3/5x + 3/5.

Step-by-step explanation:

the /'s are division symbols.              3            3

                                                  y =     _   +       _

                                                           5            5

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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
At the bulk food store, Jerry bought 200 g of mixed nuts that cost $2.50. What is the cost of 1 g of nuts? show ur work
Alex Ar [27]

Step-by-step explanation:

200g=$2.50

1g=?

2.50*1=?*200

2.50/200=?

$0.0125

7 0
3 years ago
There was a 6 square foot piece of wrapping paper for a birthday present. It takes 3 3/8 feet of square feet of the paper to wra
Citrus2011 [14]

Answer: However, in real life it depends on the shape of the actual presents. If two sheets are used for the 2 presents. There should be enough left from those sheets to use for the third present. (They should be taped together.)


Step-by-step explanation:  6/3 then 3 over 8 ––> 3/8

6/ 27/8

= 6/1 / divide 27/8

= 6^2 /1 x 8/27 ^9              (^) –––>  this mean square root of 2 or 9

6 cancels and 27 cancel

= 16/9

=1  7/9

However  you will still need to buy 2 sheets




3 0
3 years ago
Can you write the equation for a circle if the given point does not lie on the circle? Explain .
Pachacha [2.7K]

Answer:

No

Step-by-step explanation:

The equation of a circle with center (a,b) and radius r is given as:

{(x - a)}^{2}  +  {(y - b)}^{2}  =  {r}^{2}

If a given point (x,y) does not lie on this circle, it will not satisfy its equation.

This means the distance from the point to the center is not equal to the radius.

It is either less or greater than the radius.

Hence you cannot write the equation of the circle.

3 0
3 years ago
Please someone help What is the volume
Kazeer [188]

Answer:

7 because 24-10=4+3=7

Step-by-step explanation:

3 0
3 years ago
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