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2 years ago

What is 14 divided by 7/8

Mathematics

2 answers:

Dovator [93]2 years ago

7 0

Answer:

Step-by-step explanation:

Sliva [168]2 years ago

4 0

Answer:

Step-by-step explanation:

You have: 14 / (7/8)

To divide by fractions, all you have to do is take the reciprocal of the second number, aka flip it

so, if you do that, you get 14 * 8/7

14*8=112, and 112/7 is 16

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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

Colin & Brian share a lottery win of £2100 in the ratio 4 : 1. Colin then shares his part between himself, his wife & th

Paraphin [41]

Answer:

His wife gets $336 more than his son.

Step-by-step explanation:

Colin and Brian:

Ratio of 4:1.

So Colin gets $\frac{4}{4+1} = \frac{4}{5}$ of the prize.

$\frac{4*2100}{5} = 1680$

Colin got $1680. Dividing between himself, his wife and their son:

Ratio of 2:5:3.

So Colin gets $\frac{2}{2+3+5} = \frac{2}{10}$ , his wife gets $\frac{5}{2+3+5} = \frac{5}{10}$ and his son gets $\frac{3}{2+3+5} = \frac{3}{10}$

Wife:

$\frac{5*1680}{10} = 840$

His wife got $840.

Son:

$\frac{3*1680}{10} = 504$

His son got $504.

How much more does his wife get over their son?

840 - 504 = 336

His wife gets $336 more than his son.

8 0

2 years ago

You deposit $400 into an account that pays 2% annual interest compounded quarterly.

Ad libitum [116K]

Part A
The exponential model that describes the situation
The formula is
Y (x)=400 (1+0.02/4)^4x
Y (x)=400 (1+0.005)^4x
Y (x)=400 (1.005)^4x
Where x is the number of years

Part B
The value of the account after 5 years
Y (5)=400×(1.005)^(4×5)
Y (5)=441.96

3 0

2 years ago

Read 2 more answers

10(3 + 10u) what is the answer?

photoshop1234 [79]

The correct answer is 30+100u. Hope this helps!!

3 0

2 years ago

Read 2 more answers

Evaluate each expression 3 1/2 - 4 2/3

Kruka [31]

Answer:

-7/6

Step-by-step explanation:

To evaluate this, start by turning each into improper fractions.

3 1/2 - 4 2/3

7/2 - 14/3

Now give both common denominators and complete the operation.

7/2 - 14/3

21/6 - 28/6

-7/6

5 0

3 years ago