CPhill

Assuming that the base angles are the equal ones meauring 75° each, we can use the Law of Sines to find the height. We have....

  .75 m / sin (15 ) = h / sin (75)    multiply each side by sin(75)

(.75 m)(sin(75)/sin(15) = height = about 2.8 m

Here's a picture if the situation....

So...we know an angle and an adjacent side....and we're looking for the opposite side...so we have....

tan (32°) = opp (height) / 25

height = 25tan(32°) = about 15.6 ft.

That's OK, Alan......I still gave you some points !!!

Let the sides of the cut squares  = x....and when we fold these up, the dimensions of the floor area of the box are just (10 - 2x) (10-2x)...and this area = 36 sq in

So we have

(10 - 2x)^2 = 36    take the square root of both sides

10 - 2x = ±√36.......so we have

2x = 10 ±√36

x = (10 ±√36) / 2

So x = (10 + 6) / 2    or   x = (10 - 6) / 2

So, x = 8 or x  = 2

But, we must reject 8 because that would mean the sides of the floor area would be (10 - 2(8)) = (10 -16) = -6 inches  ...and this is impossible.....

So the sides of the floor area are (10 - 2(2)) = (10 - 4) = 6 in.   And the height is just x = 2 in. .....I'm assuming that, since I can't see a picture, that "depth" equates to "height."

I assume this might be:

Cot x = cot 118°16’ + 450sin27°30’/(220sin50°56’sin118°16’)

$$$$cot x = cot(118.2666666666666667°) + (450sin(27.5°)/(220sin(50..9333333333333333°)*sin(118.2666666666666667°)) =

cot x = about .843

So x =

cot^-1 (.843) = about 49.85°

Thanks, Melody......I'm sorry I didn't read the question  closely enough.....I'll go back and provide an edit!!!

Thanks, again....(it's still too early for me, I guess)

We need to find two things here, the dot product of the two vectors and the magnitude of each.

The dot product is <4, 0, 1 > (dot) < 1, 1, 3 > = (4 + 0 + 3) = 7

The magnitude of a = √(4² + 0² + 1²) =√(16 + 1) = √17

And the magnitude of c  = √(1² + 1² + 3²) =√(1 + 1 + 9) = √11

And the angle is given by

cos^-1 (a(dot)c / (llall * llcll)  = cos^-1 ((7) / (√17 * √11) = cos^-1 ((7) / (√187) = cos^-1 (0.5118906968889915) = about  59.2°

In reverse order, we have......

3)    (x - (5 + i)) (x  - (5 - i)) = ((x - 5) - i)) ((x -5) + i)) = (x-5)^2 - i^2 = x^2 -10x + 25 - (-1) = x^2 - 10x +26

2) (x - (3 + 7i))(x -  (3 - 7i)) = (((x-3) - 7i)((x-3) + 7i) = (x-3)^2 - 49i^2 = x^2 - 6x + 9  -49i^2 = x^2 - 6x + 9 + 49 = x^2 - 6x + 58

1) ( x  - (2 + √5)) ( x - (2 - √5)) = ((x - 2) - √5) ((x-2) + √5) = (x-2)^2 - 5 = x^2 - 4x + 4 - 5 = x^2 - 4x - 1

There is nothing to "solve"  .....just  to "expand"

(Thanks to Melody for pointing out my earlier error......)

15/3+2-1+1

[15 / (3+2)] - [ 1 + 1 ] =

[15/5] - 2 =

3 - 2 =

1

We need to first find the slope of the given line, 2x+4y=7.......rearranging, we have

4y = -2x + 7     divide both sides by 4

y = - 2/4x = 7/4   So, since the lines will be parallel, their slopes will be -2/4 = -1/2

And using our given point and the slope, we have

y - (-1) = -1/2(x - 3)

y + 1 =  -(1/2)x + 3/2      subtract 1 from both sides

y =  -(1/2)x + 1/2