In each of problems, determine intervals in which solutions are sure to exist.

1. y^(4) + 4y"' + 3y = t
2. ty"' + (sin t)y" + 3y = cos t
3. t(t - 1)y^(4) + e^ty" + 4t^2y = 0
4. y"' + ty" + t^2y' + t^3y = ln t
5. (x-1)y^(4) + (x + 1)y" + (tan x)y = 0
6. (x^2 - 4)y^(6) + x^2y"' + 9y = 0

At the many chips cookie company they are serious about the number of chocolate chips in their cookies they claim that each cookie hasn't c chips. if their claim is true there will be 200 chips in 10 cookies

What is the probability of throwing several dice with sum equal to 6 (six)? show the ways of possibilities for sum 6 (as the numerator) and the ways of throwing n dices for n = 1, 2, 3, 4 or 5 as denominator for all the questions to earn full credits. (a)throw one die, (b) throw two dice, (c) throw three dice (d) throw 4 dice, (e) throw 5 dice

Arefrigeration system at your company uses temperature sensors fixed to read celsius (°c) values, but the system operators in your control room understand only the fahrenheit scale. you have been asked to make a fahrenheit (°f) label for the high temperature alarm, which is set to ring whenever the system temperature rises above –10°c. what fahrenheit value should you write on the label?