The balance is $145 but after one makes he minimum payment of $20, there is $125 left to pay. However interest is added before the next month’s bill is generated.

Remember that percent means out of 100. 1.5% means 1.5/100 = .015

To find 1.5% of 125 we multiply (.015)(125) = 1.875 But as this is money the interest is rounded to two decimal places and so is $1.88

We add this to 125 to get next month’s balance which is 125 + 1.88 = $126.88

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4 years ago

The line integral of xydx×x^2y^3dy where c is the triangle with points (0,0) (1,0) (1,2) using green's theorem

lyudmila [28]

If $\mathcal C$ is the boundary of the triangle $D$ , then by Green's theorem

$\displaystyle\int_{\mathcal C}xy\,\mathrm dx+x^2y^3\,\mathrm dy=\iint_D\left(\frac{\partial(x^2y^3)}{\partial x}-\frac{\partial(xy)}{\partial y}\right)\,\mathrm dA$
$=\displaystyle\int_{x=0}^{x=1}\int_{y=0}^{y=2x}(2xy^3-x)\,\mathrm dy\,\mathrm dx$
$=\displaystyle\int_{x=0}^{x=1}x\int_{y=0}^{y=2x}(2y^3-1)\,\mathrm dy\,\mathrm dx$
$=\displaystyle\int_{x=0}^{x=1}x(8x^4-2x)\,\mathrm dx=\frac23$