Answer:
C
Step-by-step explanation:
The slope is 1. Note how each time x increases by 1 unit, y also increases by 1 unit.
The y-intercept is (0, -1).
Answer C is correct.
Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
#5) 7.065 sq. ft.
#6) 36 ft
#7) 200.96 sq. ft.
#8) 176.625 sq. ft.
Explanation
#5) Converting 18 inches to feet, 18/12 = 1.5. The area of the circle would be given by A=3.14(1.5)² = 3.14(2.25) = 7.065 sq. ft.
#6) The radius is 18 inches, so the diameter is twice that: 18*2 = 36 inches. Converting this to feet, we have 36/12 = 3 feet. Each stone is 3 feet across. Laying 12 of them against each other would give us a total length of 12*3 = 36 feet.
#7) The radius of the entire mirror with frame is 20/2 = 10. The area of the entire mirror with frame is A=3.14(10²) = 3.14(100) = 314 in².
The area of the mirror without the frame is A=3.14(6²) = 3.14(36) = 113.04 in².
The difference between the two will give the area of the frame:
314-113.04 = 200.96 in²
#8) The area of the circular region is given by A=3.14(7.5²) = 176.625 ft²
Answer: No solution
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the greatest possible error is 0.5
