Please answer them, it’s not graded, thanks -0.002.x8. The proportion of light bulbs which last longer than t hours is given by| 0.002 edx.Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, roundedto 4 decimal places. Show all reasoning in detail for full credit.9 Your hot cocoa (initially at a temperature of 190 °F) will cool at a rate which is proportional to thedifference between your cocoa's current temperature ("y") and ambient room temperature (65 °F ). Supposethat the temperature (y) of your hot cocoa satisfies the differential equationdy2.5(y – 65) °F/hour, where t is the number of hours since your cocoa was brought intodtthe 65 °F room. Solve this separable differential equation and initial condition (y(0) = 190 °F) to find aformula for the temperature of your cocoa as a function of time. Your final answer should be in the form, y = afunction of t.Show all work in detail for full credit.

The given problems are of differential in the word form, to solve the questions we just need to find…

8. The proportion of light bulbs which last longer than t hours is given by 0.002e0.002x Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, rounded to 4 decimal places. Show all reasoning in detail for full credit.

8. The proportion of light bulbs which last longer than t hours is given by 0.002e0.002x Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, rounded to 4 decimal places. Show all reasoning in detail for full credit.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter8: Graphing Quadratic Functions

Section: Chapter Questions

Problem 30CR

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Question

Please answer them, it’s not graded, thanks

-0.002.x
8. The proportion of light bulbs which last longer than t hours is given by| 0.002 e
dx.
Find the proportion of light bulbs lasting more than t = 1200 hours. Express your answer in decimal, rounded
to 4 decimal places. Show all reasoning in detail for full credit.
9 Your hot cocoa (initially at a temperature of 190 °F) will cool at a rate which is proportional to the
difference between your cocoa's current temperature ("y") and ambient room temperature (65 °F ). Suppose
that the temperature (y) of your hot cocoa satisfies the differential equation
dy
2.5(y – 65) °F/hour, where t is the number of hours since your cocoa was brought into
dt
the 65 °F room. Solve this separable differential equation and initial condition (y(0) = 190 °F) to find a
formula for the temperature of your cocoa as a function of time. Your final answer should be in the form, y = a
function of t.
Show all work in detail for full credit.

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