When at height>0, that is when it is below the water
find zeroes
0=-16x^2+18x
0=x(-16x+18)
solve
0=x
0=-16x+18
16x=18
x=18/16
x=9/8
from x=0 to x=9/8
9/8 seconds or1.125 seconds
Answer with Step-by-step explanation:
We are given that ![\lim_{x\rightarrow 0 }(csc(x)-cot(x))](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%200%20%7D%28csc%28x%29-cot%28x%29%29)
We have to prove that why the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form and prove that the limit equals to 0.
![\lim_{x\rightarrow 0 }(\frac{1}{sinx}-\frac{cosx}{sinx})](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%200%20%7D%28%5Cfrac%7B1%7D%7Bsinx%7D-%5Cfrac%7Bcosx%7D%7Bsinx%7D%29)
Because
and![cot(x)=\frac{cosx}{sinx}](https://tex.z-dn.net/?f=cot%28x%29%3D%5Cfrac%7Bcosx%7D%7Bsinx%7D)
![\lim_{x\rightarrow 0 }(\frac{1-cosx}{sinx})](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%200%20%7D%28%5Cfrac%7B1-cosx%7D%7Bsinx%7D%29)
![\frac{1-cos0}{sin0}](https://tex.z-dn.net/?f=%5Cfrac%7B1-cos0%7D%7Bsin0%7D)
We know that cos 0=1 and sin 0=0
Substitute the values then we get
![\frac{1-1}{0}=\frac{0}{0}](https://tex.z-dn.net/?f=%5Cfrac%7B1-1%7D%7B0%7D%3D%5Cfrac%7B0%7D%7B0%7D)
We know that
is indeterminate form
Hence, the limit x approaches 0(csc(x)-cot(x)) involves an indeterminate form.
L'hospital rule:Apply this rule and differentiate numerator and denominator separately when after applying
we get indeterminate form![\frac{0}{0}](https://tex.z-dn.net/?f=%5Cfrac%7B0%7D%7B0%7D)
Now,using L' hospital rule
![\lim_{x\rightarrow 0 }\frac{0+sinx}{cosx}](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%200%20%7D%5Cfrac%7B0%2Bsinx%7D%7Bcosx%7D)
because ![\frac{dsinx}{dx}=cosx,\frac{dcosx}{dx}=-sinx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdsinx%7D%7Bdx%7D%3Dcosx%2C%5Cfrac%7Bdcosx%7D%7Bdx%7D%3D-sinx%7D)
Now, we get
![\lim_{x\rightarrow 0 }\frac{sinx}{cos x}](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%200%20%7D%5Cfrac%7Bsinx%7D%7Bcos%20x%7D)
![\frac{sin0}{cos0}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin0%7D%7Bcos0%7D)
![\frac{0}{1}=0](https://tex.z-dn.net/?f=%5Cfrac%7B0%7D%7B1%7D%3D0)
Hence,![\lim_{x\rightarrow 0 }(csc(x)-cot(x))=0](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Crightarrow%200%20%7D%28csc%28x%29-cot%28x%29%29%3D0)
Answer:
This is a __simple____ hypothesis and will result in a(n) _______one-tailed test.
Step-by-step explanation:
The Simple Hypothesis predicts the relationship between two variables, in this case, height and leadership. The one-tailed test will be performed to determine whether to reject the null hypothesis. This is why the null and alternative hypotheses must be established before the statistic test is carried out. If the null hypothesis is rejected, this simply results in the acceptance of the alternative hypothesis.
Plug in for x.
7(2y - 4) + 5y = -66
14y - 28 + 5y = -66
19y - 28 = -66
19y = -38
y = -2
Put it back into the equation.
2(-2) - 4 = -8
x = -8
The x-value is x = -8
Answer:
I didn't study it I can't answer it