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harina [27]
3 years ago
10

8. Let α, β, γ be the angles made by a vector u ∈ R 3 with positive x, y, z−axis respectively. Then, the numbers l = cos α, m =

cos β, n = cos γ are called the direction cosines of u.
(a) Find the formulas for the direction cosines: l, m, n of the vector u = hu1, u2, u3i.

(b) Prove that l 2 + m2 + n 2 = 1.

(c) Find the direction cosines l, m, n of the vector u = h1, −1, 1i.

Mathematics
1 answer:
alex41 [277]3 years ago
8 0

Answer:

The answers are given in the attachment

Step-by-step explanation:

The detailed step by step calculations are shown in the attachment.

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Find the area of the shape below
maks197457 [2]

Answer:

204 ft^2

Step-by-step explanation:

<u>triangle on the left</u>:

A= l x w x 1/2

A = 12 x 5 x 1/2

A = 30 ft^2

<u>triangle on the right</u>:

Same thing

A = 30 ft^2

<u>square in the middle</u>:

A = l x w

A = 12 x 12

A = 144 ft^2

<u>Add them up</u>:

30 + 30 + 144 = 204 ft^2

3 0
3 years ago
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6 0
3 years ago
The factorization of x2 + 3x – 4 is modeled with algebra tiles. An algebra tile configuration. 2 tiles are in the Factor 1 spot:
arsen [322]

Answer:

The factors of x^2+3x-4 are (x-1)(x+4) ....

Step-by-step explanation:

We have to find the factors of x^2+3x-4

As we know that this is a quadratic equation.

So we have to find the roots first.

The roots are -1 and 4.

Now completing the quadratic formula using the roots we have :

x^2+4x-x-4

Make a pair of first two terms and last two terms:

(x^2+4x)-(x+4)

Now take out the common from each pair:

x(x+4)-1(x+4)

(x-1)(x+4)

Thus the factors of x^2+3x-4 are (x-1)(x+4) ....

5 0
3 years ago
Read 2 more answers
Find the value of f(7) for the function f(x) = -3x + 6
Vaselesa [24]

Answer:

D. -15

Step-by-step explanation:

f(x)=7

f(x) = -3x + 6

Then substitute x for 7 and solve linearly.

-3(7)+6

-21+6

=-15

The answer is D

4 0
3 years ago
What is the slope of this graph?
fredd [130]
The slope of the graph is 1/2
5 0
3 years ago
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