Answer: 12 miles
Step-by-step explanation:
From the question, we are informed that Marie walk 680 miles to the south pole and that the trip took 58 days and they travel the same distance each day.
The number of miles that they travel each day to the nearest whole number will be gotten by dividing 680 miles by 58. This will be:
= 680 miles / 58
= 11.72
= 12 miles to nearest whole number.
Answer:
If 
is divisible by 3, the n is also divisible by 3.
Step-by-step explanation:
We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, is not divisible by 3.
Let n not be divisible by 3. Then 
can be written in the form of fraction 
, where x and y are co-prime to each other or in other words the fraction is in lowest form.
Now, squaring
Thus,
It can be clearly seen that the fraction 
is in lowest form.
Hence, is not divisible by 3.
Thus, by contrapositivity if is divisible by 3, the n is also divisible by 3.
Answer:
-37
Step-by-step explanation:
First, you need to find the derivative of this function. This is done by multiplying the exponent of the variable by the coefficient, and then reducing the exponent by 1.
f'(x)=3x^2-3
Now, set this function equal to 0 to find x-values of the relative max and min.
0=3x^2-3
0=3(x^2-1)
0=3(x+1)(x-1)
x=-1, 1
To determine which is the max and which is the min, plug in values to f'(x) that are greater than and less than each. We will use -2, 0, 2.
f'(-2)=3(-2)^2-3=3(4)-3=12-3=9
f'(0)=3(0)^2-3=3(0)-3=0-3=-3
f'(2)=3(2)^2=3(4)-3=12-3=9
We examine the sign changes to determine whether it is a max or a min. If the sign goes from + to -, then it is a maximum. If it goes from - to +, it is a minimum. Therefore, x=-1 is a relative maximum and x=1 is a relative miminum.
To determine the values of the relative max and min, plug in the x-values to f(x).
f(-1)=(-1)^3-3(-1)+1=-1+3+1=3
f(1)=(1)^3-3(1)+1=1-3+1=-1
Hope this helps!!
