2 3/4 divided by ( -1 2/3

The price of a train ticket consists of an initial fee plus a constant fee per stop.

Ivan

I believe the answer is 2.16

4 0

2 years ago

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

Which of the following demonstrates how the 20 is calculated using the<br> combination pattern?

ZanzabumX [31]

Answer:

D

Step-by-step explanation:

The diagram shows Pascal's triangle. Pascal's triangle is a triangular array of the binomial coefficients.

The entry in the $n^{th}$ row (start counting rows from 0) and $k^{th}$ column (start counting columns from 0) of Pascal's triangle is denoted by

$C^n_k=\left(\begin{array}{c}n\\ k\end{array}\right)$

Coefficient 20 stands in 6th row, then n = 6 and in 3rd column, so k = 3.

Hence,

$20=C^6_3=\left(\begin{array}{c}6\\ 3\end{array}\right)=\dfrac{6!}{3!(6-3)!}$

4 0

3 years ago

Pls tell me so quotes of not giving up

lesantik [10]

Answer:

Step-by-step explanation:

Knowledge is knowing a tomato is a fruit, wisdom is not putting it in a fruit salad

Your time is too valuable to waste on those who don't deserve it

Never give up great things take time

Failure is not an acception

As a wise fish once said "Just Keep Swimming" the more u swim the closer you get to your goal.

4 0

2 years ago

the local farm sell a 4 pound basket of apples for 5.60 each apple weighs 4 ounces. what is the price per apples

valina [46]

Because there are 16 ounces in a pound, we can multiply 16 by 4 to get 64, there are 64 ounces of apples which is also the same as 4 pounds of apples. If 64 ounces of apples equals $5.60, and each apple is 4 ounces, we have to also divide 64 by 4 to find the number of apples. 64 divided by 4 is 16, so 16 apples for $5.60. To get the price PER apple, or for one apple, we have divide $5.60 by 16, which will give us $0.35, or $.35 per apple, which is actually a good price.

4 0

3 years ago