(3) use the Convolution theorom to obtain a Formula For the solution to the initia Value problem, where g(+) is Function on 9 piecewise Continious [o] and of exponential order y" = 2y + y = g(+), y(0) ==

Prove that for integers y=1 the equation 3 h-n (2 x ₁ + x₂ + .. + x₂) +3²(1)(2x₁+x₂+.+xn-₁) +...+ 3^-1 (2²₁) Y = 2x₁+x₂+...+% -3" cannot be solved with positive integers X₁₁X₂... Xny no

It is estimated that between the hours of noon and 7:00pm, the speed of highway traffic past a certain exist is s(t)=t^3-9t^2+15t+45 miles per hour, where t is time in hours after noon. At what time between noon and 7:00pm is the traffic speed decreasing most rapidly?

Suppose that the number of bacteria in a culture at time t is given byN = 5000(25+te(-t)/(20)) (a)Find the largest and smallest number of bacteria in the culture duringthe time interval 0 ≤ t ≤ 100.(b) At what time during the time interval in part (a) is the number of bacteriadecreasing most rapidly?

If /@) = 2x + 1and g(x) - x', Find Ag(3)

Show directly that the given functions are linearly dependent on the real line. That​ is, find a nontrivial linear combination of the following functions that vanishes identically. f(x)=29, g(x)=3sin^2, h(x)=4cos^2x   enter the non-trivial linear combination (12)(29)+ (     ) (3sin^2x) + (    ) (4cos^2x)=0

Rewrite y = 3 * (8) ^ (t / 15) in the form y^ prime =a(1+r)^ t or y = a(1 - r)

y^(5)−4y^(4)+4y^(3)=0Use lower case c1,c2,c3,c4, and c5 for the arbitrary constants.y(t)=

1. f(t) = at^2+b 2. g(t)=ae^bt 3. h(t) =a +bcos(22/7/40(t)) 4.j(t) = a/a+be^-t/10 for each of the above for t=0 the function is =3000 and at t= 30 the function is 45000. solve for a and b for each one above.

Suppose a company's earnings are given by E(x) = P(x) + I(x), where x is the number of years since 2000, P(x) is the total profit from 2000 to year x, and I(x) is the intangible growth (the growth in value of the company's intangible assets such as its good name). If P(x) = 1.2x + 2 and I(x) = 0.35x + 1 for a certain company, determine the average earnings formula (earnings per year since 2000). Answer Кеурad Keyboard Shortcuts A(x) =