Answer:
The surface area of the prism is 108 square in.
The rate of change of the area of the triangle when t=1 is also equal to 3.
<h3>Rate of change</h3>
Given the function of height of a triangle expressed as:
The rate of change is expressed as
The rate of change of the area of the triangle when t=1 is also equal to 3.
Learn more on rate of change here: brainly.com/question/8728504
The formula for the circumference is 2πr.
The diameter d is given, which is 2 times the radius r (d = 2r)
So you have to calculate π d = 3.142×1.8 ≈ 5.7
We know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
where (h,k,l) is the center and r is the radius
we have
x²+y²+z²<span>−2x−4y+8z+17=0
</span>
Group terms that contain the same variable, and move the
constant to the opposite side of the equation
(x²+2x)+(y²-4y)+(z²+8z)=-17
<span>Complete
the square. Remember to balance the equation by adding the same constants
to each side
</span>(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=-17+1+4+16
(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=4
Rewrite as perfect squares
(x+1)²+(y-2²)+(z+4)²=4
(x+1)²+(y-2²)+(z+4)²=2²
the center is the point (-1,2,-4) and the radius is 2 units
