The temperature of a chemical reaction ranges between 40 degrees celsius and 180 degrees celsius. the temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 12-hour period. what is a cosine function that models this reaction? options: a f(t) = 70 cos (12t) + 110 b f(t) = 110 cos (12t) + 70 c f(t) = −70 cos (pi over 6t) + 110 d f(t) = −110 cos (pi over 6t) + 70

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

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step-by-step explanation:

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step-by-step explanation:

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