maple syrup = x
corn syrup = 50-x
6x + 0.8(50-x)=2.36*50
6x+40-0.8x=118
5,2x=78
x= 15 gallons of maple syrup
50-15 = 35 gallons of corn syrup
Answer:
12.0 tablet computers/month
Step-by-step explanation:
The average price of the tablet 25 months from now will be:
Next, we determine the rate at which the quantity demanded changes with respect to time.
Using Chain Rule (and a calculator)
![\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%7D%7Bdp%7D%3D%20%5Cdfrac%7Bd%7D%7Bdp%7D%5Cleft%5B%7B%20%5Cdfrac%20%7B%20100%20%7D%20%7B%209%20%7D%20%5Csqrt%20%7B%20810%2C000%20-%20p%20%5E%20%7B%202%20%7D%20%7D%20%7D%5Cright%5D%20%3D-%5Cdfrac%7B100%7D%7B9%7Dp%28810%2C000-p%5E2%29%5E%7B-1%2F2%7D)
![\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdp%7D%7Bdt%7D%3D%5Cdfrac%7Bd%7D%7Bdt%7D%5Cleft%5B%5Cdfrac%20%7B%20400%20%7D%20%7B%201%20%2B%20%5Cdfrac%20%7B%201%20%7D%20%7B%208%20%7D%20%5Csqrt%20%7B%20t%20%7D%20%7D%20%2B%20200%20%5Cright%5D%3D-25%5Cleft%5B1%20%2B%20%5Cdfrac%20%7B%201%20%7D%20%7B%208%20%7D%20%5Csqrt%20%7B%20t%20%7D%20%5Cright%5D%5E%7B-2%7Dt%5E%7B-1%2F2%7D)
Therefore:
![\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%7D%7Bdt%7D%3D%20%5Cleft%5B-%5Cdfrac%7B100%7D%7B9%7Dp%28810%2C000-p%5E2%29%5E%7B-1%2F2%7D%5Cright%5D%5Cleft%5B-25%5Cleft%5B1%20%2B%20%5Cdfrac%20%7B%201%20%7D%20%7B%208%20%7D%20%5Csqrt%20%7B%20t%20%7D%20%5Cright%5D%5E%7B-2%7Dt%5E%7B-1%2F2%7D%5Cright%5D)
Recall that at t=25, 
Therefore:
![\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009](https://tex.z-dn.net/?f=%5Cdfrac%7Bdx%7D%7Bdt%7D%2825%29%3D%20%5Cleft%5B-%5Cdfrac%7B100%7D%7B9%7D%5Ctimes%20446.15%28810%2C000-446.15%5E2%29%5E%7B-1%2F2%7D%5Cright%5D%5Cleft%5B-25%5Cleft%5B1%20%2B%20%5Cdfrac%20%7B%201%20%7D%20%7B%208%20%7D%20%5Csqrt%20%7B25%7D%20%5Cright%5D%5E%7B-2%7D25%5E%7B-1%2F2%7D%5Cright%5D%5C%5C%3D12.009)
The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.
Answer:
3: 97
10: 97
9: 83
5: 97
7: 83
16: 97
Im 100% on these answers bc Ive already taken this class :)
Answer:
(7,2)
Step-by-step explanation:
x + y = 9 + 2x - 3y = 8 is really two equations, and you should show this by separating x + y = 9 from 2x - 3y = 8 through the use of a comma, or the word "and," or through writing only one equation per line.
Here you have the system of linear equations
x + y = 9
2x - 3y = 8.
Let's solve this system by elimination. Mult. the 1st eqn by 3, obtaining the system
3x + 3y = 27
2x - 3y = 8
-------------------
5x = 35, so that x = 7. Subbing 7 for x in x + y = 9, we get 7 + y = 9, indicating that y = 2.
Thus, the solution to this system of equations is (7,2).
Answer:
Since an equilateral triangle has all three side equal then one of its side is 38mm
