Simplify the expression.
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What will be an ideal response?
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Find the principal unit normal vector N for the curve r(t).r(t) = (4t sin t + 4 cos t)i + (4t cos t - 4 sin t))k
A. N = (-sin t)i - (cos t)k
B. N = (cos t)i - (sin t)k
C. N = - 
(cos t)i - 
(sin t)k
D. N = (sin t)i + (cos t)k
Evaluate the function for the given values of a and b. Then use the intermediate value theorem to determine which of the statements below is true.a = 2, b = 3f(x) = x3 + 5x2 + 12x + 8
A. f(2) and f(3) have the same sign, therefore f does not have a real zero between 2 and 3. B. f(2) and f(3) have the same sign, therefore the intermediate value theorem cannot be used to determine whether f has a real zero between 2 and 3. C. f(2) and f(3) have opposite signs, therefore f has a real zero between 2 and 3. D. f(2) and f(3) have opposite signs, therefore f does not have a real zero between 2 and 3.
Solve the problem.A culture of bacteria obeys the law of uninhibited growth. If 140,000 bacteria are present initially and there are 609,000 after 6 hours, how long will it take for the population to reach one million?
Fill in the blank(s) with the appropriate word(s).
Graph the solution set of the system of inequalities or indicate that the system has no solution.-x + 2y < 10x ? 1
A. 
B. 
C. 
D. 