Let N = 3/(0.00521).

Step 1: Let N = 3/(0.00521). To evaluate using logarithms, we take the logarithm of both sides: N = ( ( (75.4 × 4.83^2)/(0.00521) )^(1)/(3) ) N = (1)/(3) [ (75.4) + (4.83^2) - (0.00521) ] N = (1)/(3) [ (75.4) + 2(4.83) - (0.00521) ] Step 2: Find the logarithms of the numbers using a logarithm table (or calculator for precision): (75.4) = 1.8774 (4.83) = 0.6839 2(4.83) = 2 × 0.6839 = 1.3678 (0.00521) = 3.7168 (which is -3 + 0.7168) Step 3: Substitute these values into the equation for N: N = (1)/(3) [1.8774 + 1.3678 - (3.7168)] N = (1)/(3) [1.8774 + 1.3678 - (-3 + 0.7168)] N = (1)/(3) [1.8774 + 1.3678 + 3 - 0.7168] N = (1)/(3) [3.2452 + 3 - 0.7168] N = (1)/(3) [6.2452 - 0.7168] N = (1)/(3) [5.5284] N = 1.8428 Step 4: Find the antilogarithm of 1.8428: N = antilog(1.8428) From antilog tables, the antilog of 0.8428 is approximately 6.963. Since the characteristic is 1, the number has 1+1=2 digits before the decimal point. N = 69.63 The final answer is 69.63. --- Step 1: Start with the given formula: a = (bd)/(Nb^2 - d) Step 2: Multiply both sides by (Nb^2 - d) to eliminate the denominator: a(Nb^2 - d) = bd Step 3: Distribute a on the left side: aNb^2 - ad = bd Step 4: Collect all terms containing d on one side of the equation. Add ad to both sides: aNb^2 = bd + ad Step 5: Factor out d from the terms on the right side: aNb^2 = d(b + a) Step 6: Isolate d by dividing both sides by (b + a): d = (aNb^2)/(b + a) The final answer is d = (aNb^2)/(b + a). --- Step 1: Find the center of the circle. The center is the midpoint of the diameter PQ. Given points P(-2, 2) and Q(-2, -6). Let the center be (h, k). h = (x_1 + x_2)/(2) = (-2 + (-2))/(2) = (-4)/(2) = -2 k = (y_1 + y_2)/(2) = (2 + (-6))/(2) = (-4)/(2) = -2 The center of the circle is (-2, -2). Step 2: Find the radius of the circle. The radius is half the length of the diameter PQ. Length of diameter PQ = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) PQ = sqrt((-2 - (-2))^2 + (-6 - 2)^2) PQ = sqrt((0)^2 + (-8)^2) PQ = sqrt(0 + 64) PQ = sqrt(64) = 8 The radius r = (PQ)/(2) = (8)/(2) = 4. Step 3: Write the equation of the circle in standard form (x-h)^2 + (y-k)^2 = r^2. Substitute the center (-2, -2) and radius r=4: (x - (-2))^2 + (y - (-2))^2 = 4^2 (x + 2)^2 + (y + 2)^2 = 16 Step 4: Expand the equation to the general form $ax