First, choose variables to represent the length and width of this rectangle. Why not use L and W? Then the area is L*W=84 sq. in., and this equation could be solved for either L or W. If for L, then L=84/W.
The Perimeter of the rectangle is P = 2L + 2W. Substitute the above expression for L into this expression for P. Doing so eliminates L from your equation. Now consider graphing your equation for P(W). Does your graph show a minimum value? If so, at which W value?
Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
Answer:
60 seconds
Step-by-step explanation:
When Ying reaches his lowest altitude, his velocity is 0.
The velocity, v(x) is the tiome-derivative of D(x).
(This was done by using chain rule)
Equating v(x) to 0,
Answer:
D. 2,280 cm²
Step-by-step explanation:
Surface area of triangular prism = bh + (S1 + S2 + S3)*L
Where,
b = 24 cm
h = 10 cm
S1 = 26 cm
S2 = 24 cm
S3 = 10 cm
L = 34 cm
Plug in the values
Surface area = 24*10 + (26 + 24 + 10)*34
= 240 + 2,040
= 2,280 cm²
