The supplement of <span><span>135°</span><span>135°</span></span> is the angle that when added together form a straight angle (<span><span>180°</span><span>180°</span></span>).<span><span><span>180°</span><span><span>−135</span>°</span></span><span><span>180°</span><span><span>-135</span>°</span></span></span>Subtract <span>135135</span> from <span>180180</span> to get <span>4545</span>.<span>45<span>°</span></span>
Step-by-step explanation:
The volume of the box is 3072 cm^3.
Getting the dimensions given the ratio 1:2:3, we can formulate the equation deriving it from the formula of the volume of the box:
Volume = l * w * h
Volume = 1x * 2x * 3x
<span>3072 = 1x * 2x * 3x
</span>3072 = 6x^3
x^3 = 512
x = cube root (512)
x = 8 cm
2x = 16 cm
3x = 24 cm
So the shortest side is 8cm.
Let point C be (x, 0), then
AC = sqrt((x - 0)^2 + (0 - 2)^2) = sqrt(x^2 + 4) and
BC = sqrt((x - 9)^2 + (0 - 4)^2) = sqrt(x^2 - 18x + 81 + 16) = sqrt(x^2 - 18x + 97)
AC + BC = sqrt(x^2 + 4) + sqrt(x^2 - 18x + 97)
For minimum AC + BC, d(AC + BC)/dx = 0
d(AC + BC)/dx = x/sqrt(x^2 + 4) + (2x - 18)/sqrt(x^2 - 18x + 97) = 0
x(x^2 - 18x + 97) = -(2x - 18)(x^2 + 4)
x^3 - 18x^2 + 97x = -(2x^3 + 8x - 18x^2 - 72) = -2x^3 + 18x^2 - 8x + 72
3x^3 - 36x^2 + 105x - 72 = 0
x^3 - 12x^2 + 35x - 24 = 0
x = 8, 3, 1
Therefore, point C = (8, 0) or (3, 0) or (1, 0)
Hi there!
Simplify th' Eqⁿ :-
5 (x - 10) = 30 - 15x
⇒ 5x - 50 = 30 - 15x
⇒ 5x + 15x = 30 + 50
⇒ 20x = 80
⇒ x =
= 4
Hence,
The required answer is. x = 4
~ Hope it helps!