Find the volume of the rectangular prism

SCORPION-xisa [38]

Answer:

Physical and chemical changes can occur in matter. The look of material changes as a result of a physical change. Physical changes are sometimes known as phase changes. When materials change phase, they transition from solid to liquid, liquid to gas, or some other combination. If you mix materials together and see fire, bubbles, or a change in color, you might be able to see a chemical shift.

3 0

2 years ago

Read 2 more answers

Let divf = 6(5 − x) and 0 ≤ a, b, c ≤ 12. (a) find the flux of f out of the rectangular solid 0 ≤ x ≤ a, 0 ≤ y ≤ b, and 0 ≤ z ≤

dusya [7]

Continuing from the setup in the question linked above (and using the same symbols/variables), we have

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}(\nabla\cdot f)\,\mathrm dV$
$=\displaystyle6\int_{z=0}^{z=c}\int_{y=0}^{y=b}\int_{x=0}^{x=a}(5-x)\,\mathrm dx\,\mathrm dy\,\mathrm dz$
$=\displaystyle6bc\int_0^a(5-x)\,\mathrm dx$
$=6bc\left(5a-\dfrac{a^2}2\right)=3abc(10-a)$

The next part of the question asks to maximize this result - our target function which we'll call $g(a,b,c)=3abc(10-a)$ - subject to $0\le a,b,c\le12$ .

We can see that $g$ is quadratic in $a$ , so let's complete the square.

$g(a,b,c)=-3bc(a^2-10a+25-25)=3bc(25-(a-5)^2)$

Since $b,c$ are non-negative, it stands to reason that the total product will be maximized if $a-5$ vanishes because $25-(a-5)^2$ is a parabola with its vertex (a maximum) at (5, 25). Setting $a=5$ , it's clear that the maximum of $g$ will then be attained when $b,c$ are largest, so the largest flux will be attained at $(a,b,c)=(5,12,12)$ , which gives a flux of 10,800.

7 0

3 years ago

a gas station sells regular gas for $2.10 per gallon and premium gas for $2.90 a gallon. at the end of a business day 280 gallon

insens350 [35]

200 gallons of regular gas and 80 gallons of premium gas were sold.

Let the amount of regular gas sold be x gallons. So, the amount of premium gas sold will be (280 - x).

Now, forming the equation using the given information, to find the amount of each type of gallon.

Equation -

2.10x + 2.90(280 - x) = 652

Performing multiplication with values inside bracket in Left Hand Side

2.10x + 812 - 2.90x = 652

Rewriting the equation -

812 - 652 = 2.90x - 2.10x

Performing subtraction

160 = 0.8x

Rewriting the equation according to x

x = 160÷0.8

Performing division to find the value of x

x = 200

So, 200 gallons of regular gas was sold.

Amount of premium gas sold = 280 - 200

Performing subtraction

Amount of premium gas sold = 80 gallons

Hence, 200 gallons of regular gas and 80 gallons of premium gas was sold.

Learn more about problems on gas -

brainly.com/question/14746001

#SPJ4

4 0

1 year ago

Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water. PART A: Write an equati

Lelechka [254]

Part A:
there is 60% of lemon juice in a 1 liter of water
so 60% *OF* the 1 liter
( of technically means * in mathematics)
so
60% * 1 liter
or 0.6 * 1 liter
Now to find the total number of liters of lemon juice and water in the bottle
(0.6*1)+x= 1
(x being the amount of water)

Part B: We can calculate the number of liters of lemon juice that are present in the bottle
60% * 1
0.6 * 1
that is 0.6
So there is 0.6 liters of lemon juice in the bottle

Hope this helps :)

6 0

2 years ago

What is 3.2 x 10^-8 expressed as a decimal?

aniked [119]

Answer:

3.2MULTIPLY10-8

Step-by-step explanation:BECUASE THERE IS A NEGATIVE SENSE AND WHEN YOU PRESS YOUR CALACULTAOR U WILL SEE IT TRY IT IF DONT UNDERSTAND LET ME KNOW AGAIN THANKS

4 0

3 years ago