answer:The given expression is an infinite geometric series with first term a = -frac{50}{59} and common ratio r = frac{1}{2}. The sum of an infinite geometric series is given by the formula: S = frac{a}{1-r} Substituting the values of a and r, we get: S = frac{-frac{50}{59}}{1-frac{1}{2}} = frac{-frac{50}{59}}{frac{1}{2}} = -frac{100}{59} Therefore, the sum of the infinite geometric series is -frac{100}{59}. The answer is -frac{100}{59}

answer:Yes, John Adams was indeed committed to avoiding conflict with France. In 1797, he sent ambassadors to Paris with the aim of restoring peaceful relations. However, upon their arrival, the French officials demanded an upfront payment of 250,000 before engaging in any discussions with the Americans, which significantly hindered the prospect of a truce.

answer:Given: Board thickness, s = 0.1 m Initial velocity, u = 400 m/s Final velocity, v = 300 m/s (a) Using the equation {eq}v^2 = u^2 + 2as {/eq}, we can find the acceleration: {eq}begin{align*} (300 m/s)^2 &= (400 m/s)^2 + 2a(0.1 m) 90,000 &= 160,000 + 2a 2a &= 90,000 - 160,000 2a &= -70,000 a &= frac{-70,000}{2} a &= -35,000 m/s^2 end{align*} {/eq} The acceleration of the bullet is -35,000 m/s². (b) Using the equation {eq}v = u + at {/eq}, we can find the time: {eq}begin{align*} 300 m/s &= 400 m/s + (-35,000 m/s^2)t t &= frac{300 - 400}{-35,000} t &= frac{-100}{-35,000} t &= 0.00284 s end{align*} {/eq} The total time the bullet is in contact with the board is 0.00284 s.

answer:1. To rewrite the equation in standard form, we complete the square for both x and y terms. 2. The classification of the conic is determined by the coefficients of x^2, y^2, and the xy term. In this case, since the coefficients of x^2 and y^2 are equal and there is no xy term, the conic is a circle. 3. The center of the circle is found by identifying the values of h and k in the standard form equation. 4. The radius of the circle is calculated using the formula r = sqrt(h^2 + k^2). 5. The circumference of the circle is calculated using the formula C = 2πr. 6. The area enclosed by the circle is calculated using the formula A = πr^2. Classification: Circle Equation: 7 left(x-frac{2}{7}right)^2+7 left(y+frac{1}{7}right)^2=frac{47}{7} Center: left(frac{2}{7},-frac{1}{7}right) Radius: frac{sqrt{47}}{7} Circumference: frac{2 sqrt{47} pi }{7} Area Enclosed: frac{47 pi }{49}