The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin πt + 5 cos πt, where t is measured in seconds. (Round your answers to two decimal places.)(a) Find the average velocity during each time period.

V(t) = π(4cos πt -5sinπt) cm

Step-by-step explanation:

Given the displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin πt + 5 cos πt, where t is measured in seconds, the average velocity of the body will be expressed as the change in displacement of thee particle with respect to time.

This is expressed mathematically as V = ds/dt

Differentiate the displacement function to get the velocity V

V = 4πcos πt + (-5πsin πt)

open the parenthesis

V = 4πcos πt - 5πsin πt

bring out the common factor

V = π(4cos πt -5sinπt)

Hence the average velocity of the body during each time is expressed as

V(t) = π(4cos πt -5sinπt) cm

answer: a clock

step-by-step explanation:

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2