The answer is 1/2 or 8/16 if it asks not to simplify
Answer:
yes
Step-by-step explanation:
the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.
the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).
so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.
but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.
there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).
but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.
The answer is 19.125 or you can round it to 19.13
Answer:
5
Step-by-step explanation:
To find B and C prime, you must multiply them by .25, or 1/4.
B' =
(-2 x .25),(1 x .25)
I did mine in fraction form, because it will prove to be more useful in future mathematics.
B' = (1/2 , 1/4)
Repeat the process with C.
C' =
(14 x .25),(17 x .25)
C' =
(7/2 , 17/4)
You only need to focus on B and C because you are finding the length of B'C'.
The formula for distance is the square root of x to the sub of 2 minus x to the sub of 1 squared minus y to the sub of 2 minus y to the sub of 1 square.
x2 - x1 = 7/2 - 1/2 = 6/2 = 3 squared = 9
y2 - y1 = 17/4 - 1/4 = 16/4 = 4 squared = 16
16 + 9 = 25
Square root of 25 is 5.
Therefore, the distance is 5.
Answer:
9.0 ft
Step-by-step explanation:
Let the distance from the bottom of the board to the edge of the wall be represented as "x"
Angle measure = θ = 53.13°
Hypotenuse = 15 ft
Adjacent side = x ft
The trigonometric ratio we would apply would be CAH:
Thus,
Cosine θ = Adjacent/Hypotenuse
Plug in the values
Cos 53.13° = x/15
Multiply both sides by 15
15 * Cos 53.13 = x
9.00002143 = x
x ≈ 9.0 ft (nearest tenth)
Therefore, distance from the bottom of the board to the edge of the wall = 9.0 ft
