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sweet [91]
2 years ago
14

Whats the y intercept and the rate of change please help me

Mathematics
1 answer:
GenaCL600 [577]2 years ago
6 0
Y-intercept= 5
Rate of change= 3
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Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con
monitta

Let f(x)=e^{-1/x}. Then f'(x)=\frac1{x^2}e^{-1/x}>0 for all x\ge2, so f is strictly increasing. As x\to\infty, e^{-1/x}\to e^0=1, so f is bounded above by 1. This is to say,

e^{-1/x}

and the integral of \frac1{x^2} converges over the same domain, so this integral must also converge by comparison.

We have, by setting y=-\frac1x,

\displaystyle\int_2^\infty\frac{e^{-1/x}}{x^2}\,\mathrm dx=\int_{-1/2}^0e^y\,\mathrm dy=e^0-e^{-1/2}=1-\frac1{\sqrt e}

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2 years ago
the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width
dolphi86 [110]

Answer:

  • Length = 17 inches

  • Width = 12 inches

⠀

Step-by-step explanation:

⠀

As it is given that, the length of a rectangle is 5 in longer than its width and the perimeter of the rectangle is 58 in and we are to find the length and width of the rectangle. So,

⠀

Let us assume the width of the rectangle as x inches and therefore, the length will be (x + 5) inches .

⠀

Now, <u>According to the Question :</u>

⠀

{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}

⠀

{\longrightarrow \qquad { {\sf{2 ( x + 5 + x )= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{2 ( 2x + 5  )= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x + 10= 58 }}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x = 58  - 10}}}}

⠀

{\longrightarrow \qquad { {\sf{ 4x = 48}}}}

⠀

{\longrightarrow \qquad { {\sf{ x =  \dfrac{48}{4} }}}}

⠀

{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 12}} }}} }\:  \:  \bigstar

⠀

Therefore,

  • The width of the rectangle is 12 inches .

⠀

Now, We are to find the length of the rectangle:

{\longrightarrow \qquad{ { \frak{\pmb{Length = x + 5 }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 12 + 5 }}}}}

⠀

{\longrightarrow \qquad{ { \frak{\pmb{Length = 17}}}}}

⠀

Therefore,

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⠀

8 0
1 year ago
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Andreas93 [3]

Answer:

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Step-by-step explanation:

<u>Given function:</u>

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Minimum cost is obtained at vertex.

Vertex is determined by formula x = -b/2a, in standard form of

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b.

<u>Cost at vertex is:</u>

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irinina [24]

Answer:6

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