The region bounded by the curve y = 2/(1 + e−x), the x- and y-axes, and the line x = 10 is rotated about the x-axis. Use Simpson
1 answer:
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Answer:
a ) y = 1 and x = -1
d) y = 5 and x = -1/2
Step-by-step explanation:
<h2><u>Substitution method</u></h2><h2><u>Question a</u></h2>y = x+ 2
y = 2x + 3
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = x + 2
x = y - 2
now put y - 2 where x is in the second equation
y = 2x + 3
y = 2(y - 2) + 3
y = 2y - 4 +3
now solve
4 - 3 = 2y -y
y = 1
since y = 1 we can find what x is by putting into the first formula
y = x +2
x = y - 2
x = (1) -2
x = -1
<h3><u>hence y = 1 and x = -1 </u></h3><h3><u /></h3><h2><u>Question d</u></h2>y = 2x + 6
y = 4 - 2x
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
now place (y-6)/2 where x is in the second formula
y = 4 -2x
y = 4 - 2 ()
now solve
the multiplication by 2 and division by 2 are cancelled out
hence making the simplified equation as:
y = 4 - y + 6
2y = 4 + 6
2y = 10
y = 5
now place this into the first equation
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
x = (5-6)/2
x = -1/2
<h3><u>hence y = 5 and x = -1/2</u></h3>
Answer:
y² + bs²y - 6b²s⁴
General Formulas and Concepts:
- Expand by FOIL (First Outside Inside Last)
- Exponent Power Rule:
Step-by-step explanation:
<u>Step 1: Define expression</u>
(y - 2bs²)(y + 3bs²)
<u>Step 2: FOIL</u>
- First: y · y = y²
- Outside: y · 3bs² = 3bs²y
- Inside: -2bs² · y = -2bs²y
- Last: -2bs² · 3bs² = -6b²s⁴
<u>Step 3: Simplify</u>
- Combine: y² + 3bs²y - 2bs²y - 6b²s⁴
- Combine like terms: y² + bs²y - 6b²s⁴