Answer:
Step-by-step explanation:
The depth function is:
After 3 minutes, a submarine had descended to −320 feet.
This means that 
. So
After 8 minutes, the submarine had descended to −420 feet.
This means that 
. So
From the first equation:
So
And
So
Answer:
x ≈ 46°
Step-by-step explanation:
Since the triangle is right use the sine ratio to solve for x
sinx = 
= 
, hence
x = 
( ) ≈ 46°
Answer: y = 6cm
Step-by-step explanation: Pranking, or playing a practical joke on someone, is a time honored tradition among friends, enemies, and professionals alike.[1] And king among prank-worthy days: April Fools' Day.[2] This is the perfect time for put your pranking skills to the test, though depending on your personality, you might enjoy pranking any ol' day of the week. No worry if you don't have a favorite prank to play on your friends, all you need is a straight face, some effort, and a dash of creativity, and you'll soon be watching your target stumble unwittingly into your prank.
E) 2
Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5
Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.
