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3 years ago

If there are 50 trees per acre in an orchard and the orchard is 1.7 x 2.2 km, how many trees are in the entire orchard?

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

6 0

Answer:

187 trees

Step-by-step explanation:

50 trees per acre in an orchard and

the orchard is 1.7 x 2.2 km,

we calculate the orchard dimension = 1.7 x 2.2km = 3.74

to calculate how many trees are in the entire orchard = 3.74 x 50 = 187 trees

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If you're just integrating a vector-valued function, you just integrate each component:

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$=\displaystyle\left(\int\sec^2t\,\mathrm dt\right)\hat\imath+\left(\int t(t^2-1)^8\,\mathrm dt\right)\hat\jmath+\left(\int t^7\ln t\,\mathrm dt\right)\hat k$

The first integral is trivial since $(\tan t)'=\sec^2t$ .

The second can be done by substituting $u=t^2-1$ :

$u=t^2-1\implies\mathrm du=2t\,\mathrm dt\implies\displaystyle\frac12\int u^8\,\mathrm du=\frac1{18}(t^2-1)^9+C$

The third can be found by integrating by parts:

$u=\ln t\implies\mathrm du=\dfrac{\mathrm dt}t$

$\mathrm dv=t^7\,\mathrm dt\implies v=\dfrac18t^8$

$\displaystyle\int t^7\ln t\,\mathrm dt=\frac18t^8\ln t-\frac18\int t^7\,\mathrm dt=\frac18t^8\ln t-\frac1{64}t^8+C$

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