The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
Find all the areas and add them together
Base Rectangle : LxW = 14 x 12 = 168
Bases Triangles (2) 2x (8x12)/2 = 96
2 Lateral rectangles 14x10 =140 (double) = 280
Surface Area = 168 +96 + 280 = 544
Answer:
X = 35.7 Y=54.3
Step-by-step explanation:
Let the 2 angles be called X and Y were X is the smaller angle
we know that both angles are complementary therefore
X+Y=90
X = Y - 18.6 ( Given )
Y - 18.6 + Y = 90 ( substitution)
2Y = 90 + 18.6
Y = 108.6/2
Y=54.3
X= Y-18.6= 54.3-18.6 = 35.7
Check : X + Y = 35.7+54.3=90
The answer is 7 R 4! hoped this helps!
