Use Euler's formula to answer the question.A polyhedra has 36 edges and 20 faces. How many vertices does it have?
A. 18
B. 54
C. 15
D. 56
Answer: A
Mathematics
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Express the relationship between a small change in x and the corresponding change in y in the form 
.f(x) = csc(3x2 - 1)
A. dy = -6x csc(6x) cot(6x) dx B. dy = -3x2 csc(3x2 - 1) cot(3x2 - 1) dx C. dy = -6x csc(3x2 - 1) cot(3x2 - 1) dx D. dy = 6x csc(3x2 - 1) cot(3x2 - 1)dx
Mathematics
Solve the problem.The focal length f of a lens with index of refraction n is 
= (n - 1)
where R1and R2 are the radii of curvature of the front and back surfaces of the lens. Express f as a rational expression.
A. f = 
B. f = 
C. f = 
D. f = 
Mathematics
Find the consumer surplus at the equilibrium point.D(x) = 
; x = 5
A. $3.70 B. $1.20 C. $2.50 D. $4.80
Mathematics
Estimate the fraction as 0, 
, or 1.
A. 1
B. 0
C. 
Mathematics