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2 years ago

Find the present balance.

Mathematics

1 answer:

Triss [41]2 years ago

8 0

<h3>Credited balance:-</h3>

$\\ \rm\longmapsto 115.90+115.90+345.85$

$\\ \rm\longmapsto 231.80+345.85$

$\\ \rm\longmapsto 577.65$

<h3>Debited amount:-</h3>

$\\ \rm\longmapsto 25.85+2.00$

$\\ \rm\longmapsto 27.85$

<h3>Checked amount:-</h3>

$\\ \rm\longmapsto 19.45+21.02+95.98$

$\\ \rm\longmapsto 117+19.45$

$\\ \rm\longmapsto 136.45$

<h3>Total change in balance</h3>

$\\ \rm\longmapsto 577.65-(27.85+136.45)$

$\\ \rm\longmapsto 577.65-191.3$

$\\ \rm\longmapsto 386.35$

Now

<h3>Current balance</h3>

$\\ \rm\longmapsto 386.35+271.31$

$\\ \rm\longmapsto\$ 657.66$

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2 years ago

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Evaluate c (y + 7 sin(x)) dx + (z2 + 9 cos(y)) dy + x3 dz where c is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (hin

saw5 [17]

Treat $\mathcal C$ as the boundary of the region $\mathcal S$ , where $\mathcal S$ is the part of the surface $z=2xy$ bounded by $\mathcal C$ . We write

$\displaystyle\int_{\mathcal C}(y+7\sin x)\,\mathrm dx+(z^2+9\cos y)\,\mathrm dy+x^3\,\mathrm dz=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r$

with $\mathbf f=(y+7\sin x,z^2+9\cos y,x^3)$ .

By Stoke's theorem, the line integral is equivalent to the surface integral over $\mathcal S$ of the curl of $\mathbf f$ . We have

$\nabla\times\mathbf f=(-2z,-3x^2,-1)$

so the line integral is equivalent to

$\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\mathrm d\mathbf S$
$=\displaystyle\iint_{\mathcal S}\nabla\times\mathbf f\cdot\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv$

where $\mathbf s(u,v)$ is a vector-valued function that parameterizes $\mathcal S$ . In this case, we can take

$\mathbf s(u,v)=(u\cos v,u\sin v,2u^2\cos v\sin v)=(u\cos v,u\sin v,u^2\sin2v)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Then

$\mathrm d\mathbf S=\left(\dfrac{\partial\mathbf s}{\partial u}\times\dfrac{\partial\mathbf s}{\partial v}\right)\,\mathrm du\,\mathrm dv=(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$

and the integral becomes

$\displaystyle\iint_{\mathcal S}(-2u^2\sin2v,-3u^2\cos^2v,-1)\cdot(2u^2\cos v,2u^2\sin v,-u)\,\mathrm du\,\mathrm dv$
$=\displaystyle\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}u-6u^4\sin^3v-4u^4\cos v\sin2v\,\mathrm du\,\mathrm dv=\pi$ <span />

4 0

2 years ago

john ran at a pace of 3.5 miles per hour for a distance of 10.5 miles. how many minutes did it take him to run 10.5 miles? use t

Rainbow [258]

The minutes it takes him to run 10.5 miles is 180 minutes

<h3>How many minutes did it take him to run 10.5 miles?</h3>

The given parameters are

Speed = 3.5 miles per hour

Distance = 10.5 miles

The time is calculated as:

Time = Distance/Speed

So, we have

Time = 10.5 miles/3.5 miles per hour

Evaluate the quotient

Time = 3 hours

Convert to minutes

Time = 180 minutes

Hence, the minutes it takes him to run 10.5 miles is 180 minutes