Given the volume of a pyramid V = (1)/(3)xyh, we need to find the expression for x in terms of V, y, and h.

Here are the solutions to your questions. Problem 1: Given the volume of a pyramid V = (1)/(3)xyh, we need to find the expression for x in terms of V, y, and h. Step 1: Write the given formula. V = (1)/(3)xyh Step 2: Multiply both sides by 3 to eliminate the fraction. 3V = xyh Step 3: Divide both sides by yh to isolate x. x = (3V)/(yh) The expression for x is (3V)/(yh). Problem 2: A right cone with base diameter 18 cm and perpendicular height 8 cm is made to form a sector of a circle. Step 1: Determine the base radius of the cone. The base diameter is 18 cm, so the base radius r is half of the diameter. r = (18)/(2) = 9 cm The perpendicular height h is 8 cm. a) Calculate the Radius of the Sector Step 2: The radius of the sector is equal to the slant height (L) of the cone. Use the Pythagorean theorem to find the slant height. L = sqrt(r^2 + h^2) L = sqrt(9^2 + 8^2) L = sqrt(81 + 64) L = sqrt(145) cm L ≈ 12.04 cm The radius of the sector is 12.04 cm. b) Calculate the Angle of the Sector Step 3: The arc length of the sector is equal to the circumference of the cone's base. C = 2 r C = 2 (9) C = 18 cm Step 4: Use the arc length formula S = R, where S is the arc length (18), R is the radius of the sector (sqrt(145)), and is the angle in radians. 18 = sqrt(145) = (18)/(sqrt(145)) radians Step 5: Convert the angle from radians to degrees. _degrees = (18)/(sqrt(145)) × (180^)/() _degrees = (18 × 180^)/(sqrt(145)) _degrees = (3240^)/(sqrt(145)) _degrees ≈ (3240^)/(12.04159) _degrees ≈ 269.06^ The angle of the sector is approximately 269.06^. Send me the next one 📸