The answer is C 66 square inches
Let 
. The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by 
, then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or 
, 
, and 
.
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
<u>Given</u><u> </u><u>:</u><u>-</u>
<u>Solution</u><u> </u><u>:</u><u>-</u>
>> 2x + 5 < x + 1 / 4
>> 4 (2x + 5) < x + 1
>> 4 × (2x + 5) < x + 1
>> 8x + 20 < x + 1
>> 8x - x < 1 - 20
>> 7x < 1 - 20
>> 7x < -19
>> x = -19 / 7
Answer:
The answer to your question is the letter D. 19.5 u²
Step-by-step explanation:
Process
1.- Calculate the Area of the rectangle ABCD
Area of a rectangle = base x height
= (4 + 5) x 3
= 9 x 3
= 27 u²
2.- Calculate the area of the large triangle
Area of a triangle = base x height/2
-Substitution
Area of a triangle = (4 + 5) x 3/2
-Simplification
Area of a triangle = 9 x 3/2
-Result
Area of a triangle = 13.5 u²
3.- Calculate the area of the small triangle
Area of the triangle = 4 x 3/2
Area of the triangle = 6 u²
4.- Sum up the area of the triangles
Shaded area = 13.5 + 6 = 19.5 u²
