If the polar coordinates of a point are given by (9.77 m, θ) and the rectangular coordinates are given by (x, 3.50 m), determine values for θ and x.

the solutions are (9,12 m , 0.366 rad) and (-9,12 m ,  1.936 rad)

Step-by-step explanation:

given the polar coordinates (r=9.77 m ,  θ) and  (x, y=3.50 m) , since we know that

x²+y²=r² → x = ±√(r²-y²) = ±√(9.77 ²-3.50 ²)= ± 9,12 m

then

x = r* cos θ → for θ = cos ⁻¹ (x/r)

thus

for x= 9,12 m → θ = cos ⁻¹ (9,12 m/9.77 m) = 0.366 rad

for x= -9,12 m → θ =  0.366 rad + π/2 rad = 1.936 rad

therefore the solutions are (9,12 m , 0.366 rad) and (-9,12 m ,  1.936 rad)

X - 6%
y - 11%
We need 10 liters of 8%.
A) x + y = 10
B) .06x + .11y = (10 * .08)
Multiplying equation A by -.06
A) -.06x + -.06y = -.6   Then adding this to B)
B) .06x + .11y = (10 * .08)
.05y = .2
y = 4 liters of 6%
x = 6 liters of 11%