After a long day of surfing Winnie decides she needs a taco from the taco truck parked on the road. When she enters the beach from the water she is 150 feet away if she was to run straight to it. But she learned in her math class that a straight line to the Taco Truck may not be the fastest. She knows she can run at 2 ft/sec in the sand and 5 ft/sec on the asphalt. If the distance from the water across the sand directly straight ahead if she ran to the asphalt first is 80 feet. Question: How should Winnie run to the Taco Truck to minimize her time and what is the minimum time?

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer: 8d

step-by-step explanation:

45+5= 50+5=55+5=60

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92