||r'(t) x r"(t)|| Use the formula k(t) : to find k(t). 3 r(t) = ei+etj K(t)

What is t′(x) if t(x)=80x5ex?

The windchill index announced during the winter by the weather bureau measures how cold it "feels" for a given temperature t (in degrees Fahrenheit) and wind speed w (in miles per hour). It is calculated by the formula C(t, w) = 35.74 + 0.6215t - 35.75w 0.16 + 0.4275tw0.16 + '.+ If the temperature is 31 degrees and the wind speed is 10 miles per hour, estimate the change in the windchill temperature if the wind speed increases by 4 miles per hour and the temperature drops by 5 degrees. (Round your answer to two decimal places.)

Letf(x) = 6 + 5x². Findƒ (1) and: f(1) ƒ(6) Round your answers to three decimal places. (+) = i 6.138 ƒ(1) *ƒ(6)* equal to ƒ(1) ƒ(6)* Are they equal?

The traffic flow rate (cars per hour) across an intersection is r(t) = 200 + 1000t - 150t², where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 8 am? cars

Differentiate the function. r(t) = (3t². + 8)i + r'(t) = (6t)i + +(12²) ₁ r'(t) = = (1²2); - 15 i + (6t)j r'(t) = (6t)i - r'(t) = (6)i + 15 25

let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

Evaluate:

y=x2x(x>0,x≠1)