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jenyasd209 [6]
2 years ago
9

Find the value of the trigonometric ratio, cos L.

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
5 0

Answer:

b/h

Step-by-step explanation:

remember SOH CAH TOA. Sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. So in this case use CAH for cos L. Adjacent to L is b, and the hypotenuse is h. Therefore the answer is b/h.

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Which expression is equivalent to 3x – 5?
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the equation 2x-4-1+x would be the answer

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Find all unit vectors that are orthogonal to the vector u = 1, 0, −4 .
KIM [24]

Answer:

Step-by-step explanation:

Given:

u = 1, 0, -4

In unit vector notation,

u = i + 0j - 4k

Now, to get all unit vectors that are orthogonal to vector u, remember that two vectors are orthogonal if their dot product is zero.

If v = v₁ i + v₂ j + v₃ k is one of those vectors that are orthogonal to u, then

u. v = 0                    [<em>substitute for the values of u and v</em>]

=> (i + 0j - 4k) . (v₁ i + v₂ j + v₃ k)  = 0               [<em>simplify</em>]

=> v₁ + 0 - 4v₃ = 0

=> v₁ = 4v₃

Plug in the value of v₁ = 4v₃ into vector v as follows

v = 4v₃ i + v₂ j + v₃ k              -------------(i)

Equation (i) is the generalized form of all vectors that will be orthogonal to vector u

Now,

Get the generalized unit vector by dividing the equation (i) by the magnitude of the generalized vector form. i.e

\frac{v}{|v|}

Where;

|v| = \sqrt{(4v_3)^2 + (v_2)^2 + (v_3)^2}

|v| = \sqrt{17(v_3)^2 + (v_2)^2}

\frac{v}{|v|} = \frac{4v_3i + v_2j + v_3k}{\sqrt{17(v_3)^2 + (v_2)^2}}

This is the general form of all unit vectors that are orthogonal to vector u

where v₂ and v₃ are non-zero arbitrary real numbers.

3 0
3 years ago
Find the standard form of the equation of the parabola with the given characteristics. Vertex: (-6, 1); focus: (-6, 0)
GREYUIT [131]

Answer: (x+6)^2=-4(y-1)

Step-by-step explanation:

Given

Vertex of the parabola (-6,1)

Focus of the parabola (-6,0)

As the x coordinate of vertex and focus is same and focus lie below the vertex, therefore the parabola is the type of

(x+6)^2=-4a(y-1)

distance between Vertex and focus is 1 unit

\therefore a=1

Parabola becomes

\Rightarrow (x+6)^2=-4(y-1)

8 0
3 years ago
Solve the solution of the equations 10x-3y=3 and 2x+y=9
forsale [732]

Answer:

x=1.875   y=-0.875

Step-by-step explanation:

10x-3y=3                     10x-3y=3

3(2x+y)=(9)3                +<u>6x+3y=27</u>

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   10x-3y=3                  10x-3y=3

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                                    1/-8(-8y)=(7)1/-8 = y=-0.875

4 0
2 years ago
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