Answer:
18pi units³ or 56.5 units³ (3 sf)
Step-by-step explanation:
pi×r²×h - (4/3)(pi×r³)
r = 3 h = 2r = 6
pi(3²×6 - (4/3)(3³))
18pi units³
Answer: x ≤ 3
Step-by-step explanation:
4x ≤ 12
divide each side by 4
x≤3
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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>
The cost of one adult ticket is $7.5 and one child ticket is $3.5
Julia will pay $48 for 5 adult tickets and 3 child tickets.
Step-by-step explanation:
Let,
Cost of one adult ticket = x
Cost of one child ticket = y
According to given statement;
3x+5y=40 Eqn 1
x+5y=25 Eqn 2
Subtracting Eqn 2 from Eqn 1
Dividing both sides by 2
Putting x=2.5 in Eqn 1
Dividing both sides by 5
The cost of one adult ticket is $7.5 and one child ticket is $3.5
5 adult tickets = 5*7.5 = $37.5
3 child tickets = 3*3.5 = $10.5
Total = 37.5+10.5 =$48
Julia will pay $48 for 5 adult tickets and 3 child tickets.
Keywords: linear equation, subtraction
Learn more about subtraction at:
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Answer:
$365.93
Step-by-step explanation:
Register amount minus the fee
