Answer:
It's 63,000 milligrams
Step-by-step explanation:
Multiply the mass by 1000, and you get your answer, 63 x 1000 = 63000
Get a common denominator, in this case, we can use 40
multiply the numerator and denominator of each fraction to get the common denominator equivilent
1/2*20= 20/40
3/5*8= 24/40
1/8*5= 5/40
now add the numerators together
20+24+5= 49/40 or 1 and 9/40
add the whole numbers
24+32+44= 100
add the previous numbers
101 and 9/40
Answer:
absolute max=
(4.243,18)
absolute min =(-1,-5.916)
absolute max=(pi/6, 2.598)
absolute min = (pi/2,0)
Step-by-step explanation:
a) ![f(t) = t\sqrt{36-t^2} \\](https://tex.z-dn.net/?f=f%28t%29%20%3D%20t%5Csqrt%7B36-t%5E2%7D%20%5C%5C)
To find max and minima in the given interval let us take log and differentiate
![log f(t) = log t + 0.5 log (36-t^2)\\Y(t) = log t + 0.5 log (36-t^2)](https://tex.z-dn.net/?f=log%20f%28t%29%20%3D%20log%20t%20%2B%200.5%20log%20%2836-t%5E2%29%5C%5CY%28t%29%20%3D%20log%20t%20%2B%200.5%20log%20%2836-t%5E2%29)
It is sufficient to find max or min of Y
![y'(t) = \frac{1}{t} -\frac{t}{36-t^2} \\\\y'=0 gives\\36-t^2 -t^2 =0\\t^2 =18\\t = 4.243,-4.243](https://tex.z-dn.net/?f=y%27%28t%29%20%3D%20%5Cfrac%7B1%7D%7Bt%7D%20-%5Cfrac%7Bt%7D%7B36-t%5E2%7D%20%5C%5C%5C%5Cy%27%3D0%20gives%5C%5C36-t%5E2%20-t%5E2%20%3D0%5C%5Ct%5E2%20%3D18%5C%5Ct%20%3D%204.243%2C-4.243)
In the given interval only 4.243 lies
And we find this is maximum hence maximum at (4.243,18)
Minimum value is only when x = -1 i.e. -5.916
b) ![f(t) = 2cost +sin 2t\\f'(t) = -2sint +2cos2t\\f"(t) = -2cost-4sin2t\\](https://tex.z-dn.net/?f=f%28t%29%20%3D%202cost%20%2Bsin%202t%5C%5Cf%27%28t%29%20%3D%20-2sint%20%2B2cos2t%5C%5Cf%22%28t%29%20%3D%20-2cost-4sin2t%5C%5C)
Equate I derivative to 0
-2sint +1-2sin^2 t=0
sint = 1/2 only satisfies I quadrant.
So when t = pi/6 we have maximum
Minimum is absolute mini in the interval i.e. (pi/2,0)
Answer:
2^3 times 11 times 3
Step-by-step explanation:
264
/ /
2 132
/ /
2 66
/ /
2 33
/ / 11 and 3