Solve {l}{y=p^{10}+p^{9}*q^{1}*10+p^8*q^2*45+p^7*q^3*12}{p=0.01517}{q=0.98483}

$$\left. \begin{array} { l } { y = p ^ { 10 } + p ^ { 9 } \times q ^ { 1 } \times 10 + p ^ { 8 } \times q ^ { 2 } \times 45 + p ^ { 7 } \times q ^ { 3 } \times 12 } \\ { p = 0.01517 } \\ { q = 0.98483 } \end{array} \right.$$

Solve for y, p, q

$$y=0.00000000000224199227015488429507433340999035730776$$

$$p=0.01517$$

$$q=0.98483$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$y=0.01517^{10}+0.01517^{9}\times 0.98483^{1}\times 10+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Calculate 0.01517 to the power of 10 and get 0.00000000000000000064543989795087781156965042605449.

$$y=0.00000000000000000064543989795087781156965042605449+0.01517^{9}\times 0.98483^{1}\times 10+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Calculate 0.01517 to the power of 9 and get 0.000000000000000042547125771316928910326329997.

$$y=0.00000000000000000064543989795087781156965042605449+0.000000000000000042547125771316928910326329997\times 0.98483^{1}\times 10+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Calculate 0.98483 to the power of 1 and get 0.98483.

$$y=0.00000000000000000064543989795087781156965042605449+0.000000000000000042547125771316928910326329997\times 0.98483\times 10+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Multiply 0.000000000000000042547125771316928910326329997 and 0.98483 to get 0.00000000000000004190168587336605109875667957094551.

$$y=0.00000000000000000064543989795087781156965042605449+0.00000000000000004190168587336605109875667957094551\times 10+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Multiply 0.00000000000000004190168587336605109875667957094551 and 10 to get 0.0000000000000004190168587336605109875667957094551.

$$y=0.00000000000000000064543989795087781156965042605449+0.0000000000000004190168587336605109875667957094551+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Add 0.00000000000000000064543989795087781156965042605449 and 0.0000000000000004190168587336605109875667957094551 to get 0.00000000000000041966229863161138879913644613550959.

$$y=0.00000000000000041966229863161138879913644613550959+0.01517^{8}\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Calculate 0.01517 to the power of 8 and get 0.0000000000000028046885808382945886833441.

$$y=0.00000000000000041966229863161138879913644613550959+0.0000000000000028046885808382945886833441\times 0.98483^{2}\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Calculate 0.98483 to the power of 2 and get 0.9698901289.

$$y=0.00000000000000041966229863161138879913644613550959+0.0000000000000028046885808382945886833441\times 0.9698901289\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Multiply 0.0000000000000028046885808382945886833441 and 0.9698901289 to get 0.00000000000000272023976919361160867426109043205449.

$$y=0.00000000000000041966229863161138879913644613550959+0.00000000000000272023976919361160867426109043205449\times 45+0.01517^{7}\times 0.98483^{3}\times 12$$

Multiply 0.00000000000000272023976919361160867426109043205449 and 45 to get 0.00000000000012241078961371252239034174906944245205.

$$y=0.00000000000000041966229863161138879913644613550959+0.00000000000012241078961371252239034174906944245205+0.01517^{7}\times 0.98483^{3}\times 12$$

Add 0.00000000000000041966229863161138879913644613550959 and 0.00000000000012241078961371252239034174906944245205 to get 0.00000000000012283045191234413377914088551557796164.

$$y=0.00000000000012283045191234413377914088551557796164+0.01517^{7}\times 0.98483^{3}\times 12$$

Calculate 0.01517 to the power of 7 and get 0.00000000000018488388799197723063173.

$$y=0.00000000000012283045191234413377914088551557796164+0.00000000000018488388799197723063173\times 0.98483^{3}\times 12$$

Calculate 0.98483 to the power of 3 and get 0.955176895644587.

$$y=0.00000000000012283045191234413377914088551557796164+0.00000000000018488388799197723063173\times 0.955176895644587\times 12$$

Multiply 0.00000000000018488388799197723063173 and 0.955176895644587 to get 0.00000000000017659681818687834677459937703956494551.

$$y=0.00000000000012283045191234413377914088551557796164+0.00000000000017659681818687834677459937703956494551\times 12$$

Multiply 0.00000000000017659681818687834677459937703956494551 and 12 to get 0.00000000000211916181824254016129519252447477934612.

$$y=0.00000000000012283045191234413377914088551557796164+0.00000000000211916181824254016129519252447477934612$$

Add 0.00000000000012283045191234413377914088551557796164 and 0.00000000000211916181824254016129519252447477934612 to get 0.00000000000224199227015488429507433340999035730776.

$$y=0.00000000000224199227015488429507433340999035730776$$

The system is now solved.

$$y=0.00000000000224199227015488429507433340999035730776 p=0.01517 q=0.98483$$