In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.
So, in your case, we have
![\sin(Z) = \dfrac{XY}{XZ}](https://tex.z-dn.net/?f=%5Csin%28Z%29%20%3D%20%5Cdfrac%7BXY%7D%7BXZ%7D)
In order to find XY, we have
![XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24](https://tex.z-dn.net/?f=XY%20%3D%20%5Csqrt%7BXZ%5E2-YZ%5E2%7D%20%3D%20%5Csqrt%7B1600-1024%7D%3D%5Csqrt%7B576%7D%20%3D%2024)
So, the ratio for the sine is
![\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}](https://tex.z-dn.net/?f=%5Csin%28Z%29%20%3D%20%5Cdfrac%7BXY%7D%7BXZ%7D%20%3D%20%5Cdfrac%7B24%7D%7B40%7D%20%3D%20%5Cdfrac%7B3%7D%7B5%7D)
The Domain and Range of tan(x) are mathematically given as
Domain ![:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}](https://tex.z-dn.net/?f=%3A%7Bx%2Fx%20%5Cneq.....%5Cfrac%7B-3%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B-%5Cpi%7D%7B2%7D%2C....%7D)
Range: all Real numbers
<h3>What is The Domain and Range of
tan(x)?</h3>
All real numbers are in the domain of the function "y=tan (x)," with the exception of the value "
" for all integers n, which is the case when cos(x) = 0.
It follows that "
" is not in the domain of "tan (x)" among the possible values.
In conclusion,
Domain ![:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}](https://tex.z-dn.net/?f=%3A%7Bx%2Fx%20%5Cneq.....%5Cfrac%7B-3%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B-%5Cpi%7D%7B2%7D%2C....%7D)
Range: all Real numbers
Read more about a Domain
brainly.com/question/13113489
#SPJ1
Answer:
![\bar X= \frac{1.83+1.85+1.79+1.73+1.69+1.74+1.76+1.70}{8}= 1.76125](https://tex.z-dn.net/?f=%5Cbar%20X%3D%20%5Cfrac%7B1.83%2B1.85%2B1.79%2B1.73%2B1.69%2B1.74%2B1.76%2B1.70%7D%7B8%7D%3D%201.76125)
Now we can estimate the population variance with the sample variance given by:
![s^2 = \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28x_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D)
And replacing we got:
![s^2 = 0.0033839](https://tex.z-dn.net/?f=%20s%5E2%20%3D%200.0033839)
And the estimator for the population deviation
is given by :
![\hat \sigma = \sqrt{s^2}= \sqrt{0.0033839}= 0.058172](https://tex.z-dn.net/?f=%5Chat%20%5Csigma%20%3D%20%5Csqrt%7Bs%5E2%7D%3D%20%5Csqrt%7B0.0033839%7D%3D%200.058172)
Step-by-step explanation:
For this case we have the following data given:
1.83,1.85,1.79,1.73,1.69,1.74,1.76,1.70
First we need to calculate the mean with the following formula:
![\bar X= \frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%5Cbar%20X%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
And replacing we got:
![\bar X= \frac{1.83+1.85+1.79+1.73+1.69+1.74+1.76+1.70}{8}= 1.76125](https://tex.z-dn.net/?f=%5Cbar%20X%3D%20%5Cfrac%7B1.83%2B1.85%2B1.79%2B1.73%2B1.69%2B1.74%2B1.76%2B1.70%7D%7B8%7D%3D%201.76125)
Now we can estimate the population variance with the sample variance given by:
![s^2 = \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28x_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D)
And replacing we got:
![s^2 = 0.0033839](https://tex.z-dn.net/?f=%20s%5E2%20%3D%200.0033839)
And the estimator for the population deviation
is given by :
![\hat \sigma = \sqrt{s^2}= \sqrt{0.0033839}= 0.058172](https://tex.z-dn.net/?f=%5Chat%20%5Csigma%20%3D%20%5Csqrt%7Bs%5E2%7D%3D%20%5Csqrt%7B0.0033839%7D%3D%200.058172)
Area = l * w 104 =(w+5) * w w2 +5w -104 =0 (w+13)(w-8)=0w=13 and w=8so width =8length=13