All categories

3 years ago

Chemical company makes two brands of antifreeze. The first brand is

1 answer:

6 0

We have 60% and 85% antifreeze
We need 140 gallons of 70% antifreeze
x + y = 140
.60x + .85y = .70 * 140

X = 84 gallons 60%
Y = 56 gallons 85%

You might be interested in

For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f

butalik [34]

$\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k$

Let

$\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k$

The curl is

$\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)$

where $\partial_\xi$ denotes the partial derivative operator with respect to $\xi$ . Recall that

$\vec\imath\times\vec\jmath=\vec k$

$\vec\jmath\times\vec k=\vec i$

$\vec k\times\vec\imath=\vec\jmath$

and that for any two vectors $\vec a$ and $\vec b$ , $\vec a\times\vec b=-\vec b\times\vec a$ , and $\vec a\times\vec a=\vec0$ .

The cross product reduces to

$\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k$

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

$\nabla\times\vec f=\vec0$

which means $\vec f$ is indeed conservative and we can find $f$ .

Integrate both sides of

$\dfrac{\partial f}{\partial y}=2xze^{2xyz}$

with respect to $y$ and

$\implies f(x,y,z)=e^{2xyz}+g(x,z)$

Differentiate both sides with respect to $x$ and

$\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}$

$2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}$

$4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}$

$\implies g(x,z)=4\sin(xz^2)+h(z)$

Now

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)$

and differentiating with respect to $z$ gives

$\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}$

$2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}$

$\dfrac{\mathrm dh}{\mathrm dz}=0$

$\implies h(z)=C$

for some constant $C$ . So

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C$

3 0

4 years ago

You purchase a $220 airline ticket. you have a discount code to recieve 10% off. There is 10.5% service charge added to the tota

gayaneshka [121]

You will pay 221.1 dollars

6 0

3 years ago

What is 1.43 as a mixed number

denpristay [2]

143 over 100 Would be an examaple of a mixed number would just fine.

8 0

3 years ago

Read 2 more answers

Which expressions are equivalent to 647 x 39

stellarik [79]

25233 is your answer for this problem

8 0

3 years ago

Read 2 more answers

A suspension bridge has two main towers of equal height. A visitor on a tour ship

Scilla [17]

Answer:

The Height of the tower is 188.67 ft

Step-by-step explanation:

Given as :

The angle of elevation to tower = 15°

The distance travel closer to tower the elevation changes to 42° = 497 ft

Now, Let the of height of tower = h ft

The distance between 42° and foot of tower = x ft

So, The distance between 15° and foot of tower = ( x + 497 ) ft

So, From figure :

Tan 42° = $\frac{perpendicular}{base}$

Or , Tan 42° = $\frac{AB}{BC}$

Or, 0.900 = $\frac{h}{x}$

∴ h = 0.900 x

Again :

Tan 15° = $\frac{perpendicular}{base}$

Or , Tan 15° = $\frac{AB}{BD}$

Or, 0.267 = $\frac{h}{( x + 497 )}$

Or, h = ( x + 497 ) × 0.267

So, from above two eq :

0.900 x = ( x + 497 ) × 0.267

Or, 0.900 x - 0.267 x = 497 × 0.267

So, 0.633 x = 132.699

∴ x = $\frac{132.699}{0.633}$

Or, x = 209.63 ft

So, The height of tower = h = 0.900 × 209.63

Or, h = 188.67 ft

Hence The Height of the tower is 188.67 ft Answer

3 0

3 years ago