7cos(x) + 1 = 6sec(x)
7cos(x) + 1 = 6/cos(x)
7cos^(x) + cos(x) = 6
7cos^(x) + cos(x) - 6 = 0
[7cos(x) - 6][cos(x) + 1] = 0
cos(x) = 6/7 , x = arccos(6/7) and
cos(x) = -1, x = 180
Answer:
C. 12
Step-by-step explanation:
the greatest common factor between 84 and 96 is 12
Answer:
After 1 second, the ball will reach a maximum height of 16 feet
Step-by-step explanation:
The height of the ball after t seconds: h(t) = -16t^2 + 32t
The graph of this quadratic function is parabola which opens downwards. The vertex of a quadratic equation is the maximum or minimum point on the equation's parabola
t = -b/2a = -(32)/2(-16) = -32/-32 = 1 second
then
h(t) = -16(1)^2 + 32(1) = -16 + 32 = 16
After 1 second, the ball will reach a maximum height of 16 feet
The full range is

(length

), so the half range is

. The half range sine series would then be given by

where

Essentially, this is the same as finding the Fourier series for the function

Integrating by parts yields

So the half range sine series for this function is simply
Answer:
See below.
Step-by-step explanation:
First, we can see that
.
Thus, for the question, we can just plug -1 in:

Saying undefined (or unbounded) will be correct.
However, note that as x approaches 2, the values of y decrease in order to get to -1. In other words,
will always be greater or equal to -1 (you can also see this from the graph). This means that as x approaches 2, f(x) will approach -.99 then -.999 then -.9999 until it reaches -1 and then go back up. What is important is that because of this, we can determine that:

This is because for the denominator, the +1 will always be greater than the f(x). This makes this increase towards positive infinity. Note that limits want the values of the function as it approaches it, not at it.