+3 and -18
The pair of integers are -3 and 6.
-3 + 6 = +3
-3 * 6 = -18
-14 and +24
The pair of integers are -2 and -12
-2 + -12 = -14
-2 * - 12 = +24
Answer:
36 dollars
Step-by-step explanation:
We need to think backwards to solve this question.
(8 - 2) x 2 = 12
(12 - 2) x 2 = 20
(20 - 2) x 2 = 36
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i

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:
I believe the answer is c
Step-by-step explanation:
What i got tho was... 3x-5y=-20