Answer:
Check the explanation
Step-by-step explanation:
Let X denotes steel ball and Y denotes diamond
= 1/9( 50+57+......+51+53)
=530/9
=58.89
= 1/9( 52+ 56+....+ 51+ 56)
=543/9
=60.33
difference = d =(60.33- 58.89)
=1.44
s12 = 1/9( 502+572+......+512+532) -9/8 (58.89)2
=31686/8 - 9/8( 3468.03)
=3960.75 - 3901.53
=59.22
s1 = 7.69
s22 = 1/9( 522+ 562+....+ 512+ 562) -9/8 (60.33)2
=33295/8 - 9/8 (3640.11)
=4161.875 - 4095.12
=66.75
s2 =8.17
sample standard deviation for difference is
s=![\sqrt{[(n1-1)s_1^2+ (n2-1)s_2^2]/(n1+n2-2)}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B%28n1-1%29s_1%5E2%2B%20%28n2-1%29s_2%5E2%5D%2F%28n1%2Bn2-2%29%7D)
= ![\sqrt{[(9-1)*59.22+ (9-1)*66.75]/(9+9-2)}](https://tex.z-dn.net/?f=%5Csqrt%7B%5B%289-1%29%2A59.22%2B%20%289-1%29%2A66.75%5D%2F%289%2B9-2%29%7D)
= 
=7.93
sd = 
=
=7.93* 0.47
=3.74
For 95% confidence level 
=1.96
confidence interval is
=(1.44 - 1.96* 3.75 , 1.44+1.96* 3.75)
=(1.44 - 7.35 , 1.44 + 7.35)
=(-2.31, 8.79)
There is sufficient evidence to conclude that the two indenters produce different hardness readings.
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You have
y as an implicit function of
x:
sin(xy) – x = 0Use implicit differentiation. As
y is a function of
x, then you must apply the chain rule there:
d d—— [ sin(xy) – x ] = —— (0) dx dx d d d—— [ sin(xy) ] – —— (x) = —— (0) dx dx dx d—— [ sin(xy) ] – 1 = 0 dx d—— [ sin(xy) ] = 1 dx dcos(xy) · —— (xy) = 1 dxNow, apply the product rule for that last derivative:
![\mathsf{cos(xy)\cdot \left[\dfrac{d}{dx}(x)\cdot y+x\cdot \dfrac{dy}{dx}\right]=1}\\\\\\ \mathsf{cos(xy)\cdot \left[1\cdot y+x\cdot \dfrac{dy}{dx}\right]=1}\\\\\\ \mathsf{y\,cos(xy)+x\,cos(xy)\cdot \dfrac{dy}{dx}=1}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%28xy%29%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D1%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%28xy%29%5Ccdot%20%5Cleft%5B1%5Ccdot%20y%2Bx%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cright%5D%3D1%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7By%5C%2Ccos%28xy%29%2Bx%5C%2Ccos%28xy%29%5Ccdot%20%5Cdfrac%7Bdy%7D%7Bdx%7D%3D1%7D)
dyIsolate
—— :
dx dyx cos(xy) · —— = 1 – y cos(xy) dxAssuming
x cos(xy) ≠ 0,
dy 1 – y cos(xy)—— = ———————— <——— this is the answer.
dx x cos (xy)I hope this helps. =)
The expression would me m / 7 or m and 7 as a fraction. M is on the top
Answer:
c
Step-by-step explanation:
th two lines on each side of the x means absolute value. meaning the negative signs don't matter... l-4l=4
