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Problem 33
Solve each problem. Hooke's Law for a SpringHooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 lb stretches a certain spring 8 in., how much will a force of 30 lb stretch the spring?
Problem 33
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. (x + 3)3(2x - 1)(x + 4) ≥ 0
- Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=(x^2-16)/(x+4)
Problem 33
Problem 33a
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5 no zero greater than 1
Problem 33b
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5 no zero less than -3
- For each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=x^3+4x^2-5; 1
Problem 34
- Solve each problem. Use Descartes' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of ƒ(x)=x^3+3x^2-4x-2.
Problem 34
- Graph each quadratic function. Give the (a) vertex, (b) axis, (c) domain, and (d) range. See Examples 1–4. ƒ(x) = -3x^2 + 24x - 46
Problem 34
- For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x^2 - 3x-3; k = 2
Problem 35
Problem 35
Solve each problem. The speed of a pulley varies inversely as its diameter. One kind of pulley, with diameter 3 in., turns at 150 revolutions per minute. Find the speed of a similar pulley with diameter 5 in.
- Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=(3x-1)(x+2)^2
Problem 35
- Solve each problem. Is x+1 a factor of ƒ(x)=x^3+2x^2+3x+2?
Problem 35
- For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = - x^3 + 8x^2 + 63; k=4
Problem 36
- Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=(4x+3)(x+2)^2
Problem 36
- For each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=4x^3+6x^2-2x-1; 1/2
Problem 36
- For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^3 - 4x^2 + 2x+1; k = -1
Problem 37
Problem 37
Solve each problem. Current FlowIn electric current flow, it is found that the resistance offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. If a wire 0.01 in. in diameter has a resistance of 0.4 ohm, what is the resistance of a wire of the same length and material with diameter 0.03 in., to the nearest ten-thousandth of an ohm?
- Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = (x + 3)^2
Problem 37
- Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=x^3+5x^2-x-5
Problem 37
- For each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=-x^4-5x^2-4; -i
Problem 37
- Solve each problem. Find a polynomial function ƒ of degree 3 with -2, 1, and 4 as zeros, and ƒ(2)=16.
Problem 37
Problem 38
Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.
- For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^2 - 5x+1; k = 2+i
Problem 39
Problem 39
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. 2x3 - 7x2 ≥ 3 - 8x
- Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. See Example 2. ƒ(x) = -(x - 2)^2 - 5
Problem 39
- Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4. ƒ(x)=-x^3+x^2+2x
Problem 39
Problem 39
Solve each problem. Simple InterestSimple interest varies jointly as principal and time. If $1000 invested for 2 yr earned $70, find the amount of interest earned by $5000 invested for 5 yr.
Problem 40
Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.
- For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = x^2 + 4; k = 2i
Problem 41
Problem 41
Solve each polynomial inequality. Give the solution set in interval notation. See Examples 2 and 3. x^4 - x^3 - 10x^2 - 8x < 0