Let us consider the function given. It is
![y=cos \frac{1}{2}x](https://tex.z-dn.net/?f=y%3Dcos%20%5Cfrac%7B1%7D%7B2%7Dx%20)
. The coefficient of x (here 1/2) gives the frequency of the curve. What this means is that we see 1/2 a cycle between x=0 and x=
![2 \pi](https://tex.z-dn.net/?f=2%20%5Cpi%20)
. Put another way, to see a full cycle we would need
![\frac{2 \pi }{ \frac{1}{2} }=4 \pi](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%20%5Cpi%20%7D%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%3D4%20%5Cpi%20%20)
. The period of the function given is
![4 \pi](https://tex.z-dn.net/?f=4%20%5Cpi%20)
.
Let us think about a cycle of cosine. It starts (x=0) and ends (
![x=4 \pi](https://tex.z-dn.net/?f=x%3D4%20%5Cpi%20)
) its cycle at its highest value (here f(x)=1). It is at it's lowest (here f(x)=-1) in the middle (
![x=2 \pi](https://tex.z-dn.net/?f=x%3D2%20%5Cpi%20)
) it is between the highest and the lowest that it crosses the x-axis.
That is, it has an x-intercept between 0 and
![2 \pi](https://tex.z-dn.net/?f=2%20%5Cpi%20)
That is, at
![\pi](https://tex.z-dn.net/?f=%20%5Cpi%20)
The next one comes between
![2 \pi](https://tex.z-dn.net/?f=2%20%5Cpi%20)
and
![4 \pi](https://tex.z-dn.net/?f=4%20%5Cpi%20)
. That is, at
![3 \pi](https://tex.z-dn.net/?f=3%20%5Cpi%20)
The attached shows the function and it's x-intercepts. You can see that they occur at:
![\pi ,3 \pi ,5 \pi ,7 \pi ,9 \pi ,...](https://tex.z-dn.net/?f=%20%5Cpi%20%2C3%20%5Cpi%20%2C5%20%5Cpi%20%2C7%20%5Cpi%20%2C9%20%5Cpi%20%2C...)
. This is the arithmetic sequence that contains the x-intercepts of the function.
As you can see the nth zero will occur at
Are you cheating on this test?
Answer:
t1= 1.1475 sec
t2=9.48 sec
Step-by-step explanation:
This question asking for the time when an object reach a specific height. I will explain what the formula stand for to make this easier.
h= height = 174feet
v0= initial velocity = 170 feet/s
t= time
h0= initial height= ground level = 0
The question have predetermined formula for the height, so we should use it instead of formula that involve gravity value.
h= -16
+v0t + h0t
174 feet = -16
+ 170 feet/s x t + 0 x t
-16
+ 170 feet/s x t - 174 feet = 0
8
- 85 feet/s x t + 87 feet = 0
This equation will be hard to solve since its value in fraction, so lets use the quadratic formula
![x= \frac{-b±\sqrt{ b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%20%20%5Cfrac%7B-b%C2%B1%5Csqrt%7B%20b%5E2-4ac%7D%7D%7B2a%7D)
![t= \frac{(85)±\sqrt{ -85^2-4(8)(87)}}{2(8)}](https://tex.z-dn.net/?f=t%3D%20%20%5Cfrac%7B%2885%29%C2%B1%5Csqrt%7B%20-85%5E2-4%288%29%2887%29%7D%7D%7B2%288%29%7D)
![t= \frac{85±\ 66.64}{16}](https://tex.z-dn.net/?f=t%3D%20%20%5Cfrac%7B85%C2%B1%5C%2066.64%7D%7B16%7D)
t1= ![\frac{85-\ 66.64}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B85-%5C%2066.64%7D%7B16%7D)
t1= 1.1475
t2= ![\frac{85+\ 66.64}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B85%2B%5C%2066.64%7D%7B16%7D)
t2=9.48
Answer:
d. 11
> Step-by-step explanation:
So we are trying to find the numerator of 42 in relation of 6/7.
42 divided by 7= 6 So 6 x 6 from the numerator of 6/7 = 36.
So 6/7 written as a fraction with a denominator of 42 is 36/42.