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MrMuchimi
3 years ago
8

Solve by sunstitution y=-x+4, y=3x

Mathematics
1 answer:
enyata [817]3 years ago
4 0

Answer:

x=2

Step-by-step explanation:

y=-x+4   y=3x

3x=x+4

2x=4

x=2

(I hope this is the answer)

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\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill

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6 0
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diamong [38]

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Step-by-step explanation:

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<u>a) The x-axis </u>

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     = ( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy

     = ( 2π ) * [ 2/3 * y^3  - y^4 / 4 ] ²₀

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<u>c) The y-axis  ( using shell method )</u>

h = 2-y  = h = 2 - √x

p = x

vol = (2\pi ) \int\limits^4_0 {ph} \, dx

     = (2\pi ) \int\limits^4_0 {x(2-\sqrt{x}  ) } \, dx

     = ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀

vol = ( 2π ) ( 16/5 ) = 32/5 π

<u>d) The line x = -1    (using shell method )</u>

p = 1 + x

h = 2√x

vol = (2\pi ) \int\limits^4_0 {ph} \, dx

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attached below is the graphical representation of P and h

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