The distance walked will be (12-x) km
the distance rowed will be (9+x²) km
A] The function T(x) will be given by:
Time=distance/speed
thus we shall have:
T(x)=[√(9+x²)]/2.5+(12-x)/4
B] To get the distance x=c that minimizes the time travel, we differentiate the above.
T'(x)=(1/2.5)[1/(2.5√9+x²)*2x-1/4]
this should give us 0 for x=c, thus
c/[2.5*√(9+c²)]-1/4=0
⇒c/[2.5*√(9+c²)]=1/4
c/√(9+c²)=2.5/4
squaring both sides we get:
c²/(9+c²)=5/8
8c²=5(9+c²)
8c²=45+5c²
3c²=45
c²=15
c=3.87 km
c] The least travel time is
T(c)=[√(9+c²)]/2.5+(12-c)/4
this will give us:
T(c)=[√(9+3.87²)]/2.5+(12-3.87)/4
T(c)=3.9999209~4 hours
d] The second derivative will be:
T"(x)=1/[2.5√(9+x²)]-x²/[2.5(9+x²)^(3/2)]
but
x=c=3.87
T"(x)=0.01668 hours/ mile²
Given that T(c)=0, while T(x)<0 for x<c and T(x)>0 for x>c proves that T(x) decreases for x<c and increases for x>c, so there is a minimum at x=c
Answer:
The amplitude of the sinusoidal function is 3
Step-by-step explanation:
Use PEMDAS. Parenthesis. Exponents. Multiplication. Division. Addition. Subtraction. there are no parenthesis so that doesn't matter. there are no exponents. but there is multiplication. 8×7 = 56. so now the equation is 56+4×2-11-7×4. you still have multiplication so now we do 4×2 which is 8. the equation is now 56+8-11-7×4. you still have multiplication so now do 7×4 which is 28. the equation is now 56+8-11-28. there is no multiplication. or division. next is addition. 56+8 which is 64. now the equation is 64-11-28. next you do subtraction. 64-11 which is 53. now the equation is 53-28 which is 25. 25 is the answer. I hope this helped ☺️
Answer:
-7/4
Step-by-step explanation:
- First, we find the <u>lowest common denominator</u> which is "14", we put it in the common numerator.
<h3><em><u>MissSpanish</u></em></h3>
