Answer:
x = 18 cm
y = 9 cm
Step-by-step explanation:
An open-top box will have minimum surface area when it is in the shape of half a cube. The whole cube would have volume 2×2916 = 5832 cm³, so its side length would be ∛5832 cm = 18 cm.
The dimensions of the box are x = 18 cm; y = 9 cm.
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The surface area is x^2 +4xy, where y = 2916/x^2. That is, the surface area is ...
S = x^2 +11664/x
Setting the derivative to zero, we find ...
dS/dx = 0 = 2x -11664/x^2
x^3 = 5832 . . . . . . . . may look familiar
x = ∛5832 = 18
y = 2916/18^2 = 9
Answer:
False
Step-by-step explanation:
A y-intercept is a point on the y-axis that a line passes.
The line passes through the origin.
The y-intercept is (0,0).
Hope this helps.
Answer:
Step-by-step explanation:
Given
Required
Graph the solution
Multiply both sides by 3
<em>See attachment for graph (Assume T is on the x-axis)</em>
<span>
1. Find the exact value by using a half-angle identity. sin 22.5°
</span>
Using the half angle formula you get:
<span><span><span><span>sin2(</span>θ)=12<span>[1−<span>cos(2</span>θ)]</span></span>
</span>if </span><span><span>θ=22.5°</span> then </span><span><span><span>2θ=45°</span>
</span>so you get:
</span><span><span><span>sin2(22.5°)</span>=12<span>[1−<span>cos(45°)</span>]</span></span>
</span><span><span><span><span><span>sin2(22.5°)</span>=12[</span><span>1−<span>√2/2]</span><span>=<span><span>2−√2</span>4</span>
</span></span></span>and square root both sides:
</span><span><span><span><span><span>sin(22.5°)</span>=±</span><span>√<span><span>2−√2</span>4</span>=±0.382</span></span>
</span>so </span></span>
<span>
sin(22.5°)=0.382
the answer is the letter D) one half times the square root of quantity two minus square root of two
</span>
<span>2. Verify the identity.
cot x minus pi divided by two. </span>=
-tan x
Cot(x-pi/2)=-tan(x)
sin(A − B) = sin A cos B −
cos A sin B
sin(x – pi/2) = sin x cos (pi/2)
− cos x sin (pi/2)=-cosx
cos(A − B) = cos A cos B − sin
A sin B
cos(x− pi/2) = cos x cos pi/2
− sin x sin pi/2=-sinx
Cot(x-pi/2)=cos(x-pi/2)/sin(x-pi/2)
<span>=
(-sinx)/(-cosx)=-tanx--------------ok</span>
