please i need someone to solve question 8 and 9 now. i need to see all the work

Question

please i need someone to solve question 8 and 9 now. i need to see all the work and step by step please

thanks

For problems 1-3 below indicate a) If the equation specifies a function or a relation (and tell why) b) If the equation is even, odd or neither and explain why c) what are the roots are for each equation 1) y=3x2-x-2 2) y= x3 +2x 3) y 3 x2 -6 4) Find the inverse for problem #3 above (find x (y). Is it a function or a relation, (and tell why)? 5) A linear equation has a slope of-10 and a vertical intercept of 4. Write the equation of this line. 6) A linear equation has a slope of 5 and a horizontal intercept of -2. Write the equation of this line. 7) A linear equation passes through the two points (-1,2) and (3,1). Write the equation of this line. 8) We have 70 radioactive particles. It is known that the number of particles at some time t> 0 is given by: N= Noe-t/t No-70: = 100 year What is the damping coefficient for these particles? About how long (via the rule of thumb) will it take for N to be about zero? 9) Given that Y= 8 sin ((/6) t + /3) Specify the period for Y. If we wanted to plot this function for one period starting at x-0, would be needed for this plot, and what is the corresponding range? what domain

Explanation / Answer

question 8

i am writing tou as y

given N= No e -t/y No= 70 y= 100 years

1/y is the damping coefficient i.e 1/100

by thumb of rule we take mean life to be 1/damping coefficient = y = 100 years

(it will take exactly infinite time to make N zero)

question 9

y= 8 sin(pi/6 t + pi/3)

w= pi/6

so T= 2*pi / w = 2x6 = 12 secs

here x=0 i think implies starting from y=0

so take t= 4 as the strting point and go till t= 16 sec for complete period(12 sec)

because at t= 4 sec

y = 8 sint(4x pi/6 + pi/3 ) = 8sin( pi) = 0

so domain of t [4,16]

we know range of sine function to be [-1,1]

hence range is [-8 , 8] because simple sine function multiplied with constant 8

Answer of ques 9

T= 12 secs

domain [4,12]

range [-8, 8]

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