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- Manufacturing to Specifications. A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8π ft2. What should the radius of the circular top and bottom of the container be? (Hint: The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled.)
Problem 29
Problem 29
Solve each problem. See Example 3. How many gallons of a 5% acid solution must be mixed with 5 gal of a 10% solution to obtain a 7% solution?
Problem 29a
Find each product or quotient. Simplify the answers. √-13 * √-13
- Solve each inequality. Give the solution set in interval notation. . | 3x - 4 | ≥ 2
Problem 30
- Solve each equation using the square root property. See Example 2. x^2 = -400
Problem 30
- Dimensions of a SquareWhat is the length of the side of a square if its area and perimeter are numerically equal?
Problem 31
Problem 31
Simplify each power of i. i11
- Solve each inequality. Give the solution set in interval notation. See Example 4. 10≤2x+4≤16
Problem 31
- Solve each inequality. Give the solution set in interval notation. | 1/2 - x | ≤ 2
Problem 31
Problem 31
Solve each problem. See Example 3. Aryan wishes to strengthen a mixture from 10% alcohol to 30% alcohol. How much pure alcohol should be added to 7 L of the 10% mixture?
Problem 31a
Find each product or quotient. Simplify the answers. √-3 * √-8
- Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 1/2(6x+20) = x+4 +2(x+3)
Problem 32
- Solve each inequality. Give the solution set in interval notation. | 3/5 + x | < 1
Problem 32
- Solve each equation using the square root property. See Example 2. (4x + 1)^2 = 20
Problem 32
- Radius of a CanA can of Blue Runner Red Kidney Beans has surface area 371 cm^2. Its height is 12 cm. What is the radius of the circular top? Round to the nearest hun-dredth.
Problem 33
Problem 33
Simplify each power of i. i1001
- Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 2(x-8) = 3x-16
Problem 33
Problem 33
Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?
Problem 33a
Find each product or quotient. Simplify the answers. √-30 / √-10
- Solve each inequality. Give the solution set in interval notation. See Example 4. 2>-6x+3>-3
Problem 34
- Solve each inequality. Give the solution set in interval notation. 5| x + 1 | > 10
Problem 34
Problem 34
Solve each equation. See Example 2. (x+4)/2x = (x-1)/3
- Solve each equation using the square root property. See Example 2. (x - 4)^2 = -5
Problem 34
- Solve each inequality. Give the solution set in interval notation. | 5 - 3x | > 7
Problem 35
Problem 35
Simplify each power of i. i-27
- Solve each inequality. Give the solution set in interval notation. See Example 4. -4≤(x+1)/2≤5
Problem 35
Problem 35
Solve each equation. See Example 2. 2x/(x-2) = 5 + 4x2/(x-2)
Problem 35
Solve each problem. See Example 4. Cody sells some property for $240,000. The money will be paid off in two ways: a short-term note at 2% interest and a long-term note at 2.5%. Find the amount of each note if the total annual interest paid is $5500.
Problem 35a
Find each product or quotient. Simplify the answers. √-24 / √8
Problem 36
Simplify each power of i. 1/i17