Answer:
D
Step-by-step explanation:
Factor
this is how is should be
x + 2 = 0
=> x = -2
x - 3 = 0
=> x = + 3
Let the speed of river be x km/hr down stream.
Time = Distance / speed
Since river flows downstream, speed of boat down stream = Speed of boat + speed of river = (15 + x).
Since river flows downstream, speed of boat upstream = Speed of boat - speed of river = (15 - x).
Time Upstream - Time Downstream = 75 minutes
Time Upstream = 45 / (15 - x)
Time Downstream = 45 / (15 + x)
75 minutes = 75/60 = 5/4 hours
Time Upstream - Time Downstream = 75 minutes = 5/4 hours
45 / (15 - x) - 45 / (15 + x) = 5/4 Divide both sides by 45
1 / (15 - x) - 1 / (15 + x) = (5/4)*(1/45)
1 / (15 - x) - 1 / (15 + x) = 1/36
((15 + x) - (15 -x)) / (15-x)(15+x) = 1/36
(15 +x - 15 +x) / (15-x)(15+x) = 1/36
2x / (15-x)(15+x) = 1/36
(15-x)(15+x) = 2x*36
(15-x)(15+x) = 72x
225 - x² = 72x
0 = x² + 72x -225
x² + 72x -225 = 0 This is a
quadratic function, use a calculator that can solve the function, by
inputting the function.
x = 3, or -75. Since we are solving for speed, we can not have negative values.
x = 3 is the only valid solution.
Speed of the river = 3 km/hr downstream.
Copyright.
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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:
92
Step-by-step explanation:
85(4) = 75 + 90 + 83 + x
340 = 248 + x
x = 340 - 248
x = 92
