Dependent variables: A variable whose value depends on the value of another variable or variables
independent variable: A variable whose value determines the value of another variable or variables
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y = 7x - 4x²
<span>7x - 4x² = 0 </span>
<span>x(7 - 4x) = 0 </span>
<span>x = 0, 7/4 </span>
<span>Find the area of the bounded region... </span>
<span>A = ∫ 7x - 4x² dx |(0 to 7/4) </span>
<span>A = 7/2 x² - 4/3 x³ |(0 to 7/4) </span>
<span>A = 7/2(7/4)² - 4/3(7/4)³ - 0 = 3.573 </span>
<span>Half of this area is 1.786, now set up an integral that is equal to this area but bounded by the parabola and the line going through the origin... </span>
<span>y = mx + c </span>
<span>c = 0 since it goes through the origin </span>
<span>The point where the line intersects the parabola we shall call (a, b) </span>
<span>y = mx ===> b = m(a) </span>
<span>Slope = m = b/a </span>
<span>Now we need to integrate from 0 to a to find the area bounded by the parabola and the line... </span>
<span>1.786 = ∫ 7x - 4x² - (b/a)x dx |(0 to a) </span>
<span>1.786 = (7/2)x² - (4/3)x³ - (b/2a)x² |(0 to a) </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (b/2a)a² - 0 </span>
<span>1.786 = (7/2)a² - (4/3)a³ - b(a/2) </span>
<span>Remember that (a, b) is also a point on the parabola so y = 7x - 4x² ==> b = 7a - 4a² </span>
<span>Substitute... </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (7a - 4a²)(a/2) </span>
<span>1.786 = (7/2)a² - (4/3)a³ - (7/2)a² + 2a³ </span>
<span>(2/3)a³ = 1.786 </span>
<span>a = ∛[(3/2)(1.786)] </span>
<span>a = 1.39 </span>
<span>b = 7(1.39) - 4(1.39)² = 2.00 </span>
<span>Slope = m = b/a = 2.00 / 1.39 = 1.44</span>
Answer:
6
Step-by-step explanation:
Step 1: g(6) = 4 - 2 x 6
Step 2: g(6) = 4 - 12
Step 3: g(6) = -8
Step 4: g(9) = 4 - 2 x 9
Step 5: g(9) = 4 - 18
Step 6: g(9) = -14
(Final Step) Step 7: g(6) - g(9) = -8 - (-14) = 6
Answer:
C
Step-by-step explanation:
Per year: 12,986.64 * 1.11 = 14,415.1704 US dollars
Per month: 14,415.1704/12 = 1,201.2642 US dollars
