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morpeh [17]
3 years ago
15

Question down below down below

Mathematics
1 answer:
ser-zykov [4K]3 years ago
3 0

Answer:

C

Step-by-step explanation:

y = 2.5 x - 57

y = Profit: 143

143 = 2.5 x - 57                     Add 57 to both sides

143 + 57 = 2x - 57 + 57    Combine like terms

200 = 2.5 x                          Divide by 2.5

200/2.5 = 2.5x/2.5

x = 80 plants

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Step-by-step explanation:

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\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}

◉ \large\bm{ -4}

\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}

Before performing any calculation it's good to recall a few properties of integrals:

\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx +  \int_{a}^bmdx}

\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a  f(x)dx= \int^c _a f(x)dx+  \int^{b} _c  f(x)dx }

So we apply the first property in the first expression given by the question:

\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}

And we solve the second integral:

\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }

\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx  = 2 \int ^3_{-2} f(x)dx +   2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }

Then we take the last equation and we subtract 10 from both sides:

\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}

\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx  = 8}

And we divide both sides by 2:

\small\longrightarrow \sf{\dfrac{2  {  \int}^{3} _{2}  }{2}  =  \dfrac{8}{2} }

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Then we apply the second property to this integral:

\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}

Then we use the other equality in the question and we get:

\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx  =  2 \int ^3_{-2} f(x)dx  = 8 +  2 \int ^3_{-2} f(x)dx  = 4}

\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}

We substract 8 from both sides:

\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}

• \small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}

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Answer:

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