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marishachu [46]
4 years ago
6

The volume of a rectangle chinese box is given bthe formula v=lwh. The volume of the box shown on he right is 96 cu. Find the wi

dth and the length.
Mathematics
1 answer:
Klio2033 [76]4 years ago
6 0

the volume of a rectangular box or a rectangular prism is obtained by determining the product of length, width and height. In this case, the dimensions are height equal to 2, length equal to x + 2 and width equal to x. Hence 2*x*(x+2) = 96; x is equal to 6 units. the width is 6 units while the length is 8 units. 
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(1 point) a tank contains 1060 l of pure water. a solution that contains 0.06 kg of sugar per liter enters the tank at the rate
kirill115 [55]
(a) There is 0 kg of sugar in the tank at the beginning since it contains pure water at the start. The sugar only comes from the solution.

(b)

S' = f(t,S) = \left(0.06 \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) - \left(\dfrac{S}{1060} \dfrac{\text{kg}}{\text{L}}\right)\left(9\dfrac{\text{L}}{\text{min}}\right) \ \Rightarrow \\ \\ S' = 0.54 \text{ kg}/\text{min} - \dfrac{9S}{1060}

So yes, you enter S' = 0.54 - (9S/1060)

(c)

\displaystyle\frac{dS}{dt} = 0.54 - \frac{9S}{1060} \ \Rightarrow\ \frac{dS}{dt} = \frac{572.4 - 9S}{1060}\ \Rightarrow\ \dfrac{dS}{572.4 - 9S} = \frac{1}{1060} dt\ \Rightarrow \\ \\
\int \dfrac{dS}{572.4 - 9S} = \int \frac{1}{1060} dt\ \Rightarrow\textstyle\ -\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t + C \\ \\
S(0) = 0 \ \Rightarrow\ -\frac{1}{9}\ln|572.4 - 0| = \frac{1}{1060}(0) + C\  \Rightarrow\ C = -\frac{1}{9} \ln 572.4

-\frac{1}{9}\ln|572.4 - 9S| = \frac{1}{1060}t  -\frac{1}{9} \ln 572.4\ \Rightarrow \\ \\
\ln|572.4 - 9S| = \ln 572.4 - \frac{9}{1060}t \ \Rightarrow \\ \\
|572.4 - 9S| = e^{\ln 572.4 - 9t/1060}\ \Rightarrow \\ \\
572.4 - 9S= \pm 572.4 e^{-9t/1060}\ \Rightarrow \\ \\
S = \frac{-1}{9}\left(-572.4 \pm 572.4 e^{-9t/1060}\right)

But only (+) satisfies S(0) = 0

S= -\frac{1}{9}\left(-572.4 + 572.4 e^{-9t/1060}\right) \\ \\
S= 63.6 - 63.6 e^{-9t/1060}\text{ kg}

Enter
in S = 63.6 - 63.6 * e^(-9t/1060)

3 0
3 years ago
if the ratio of minutes spent on homework to the number of weeknights is 120 to 5 what is the unit of homework per night
sashaice [31]
To solve this problem, divide both sides by 5 and you get a ratio of 24 to 1. The answer is 24 minutes per night. I hope this helped!
8 0
4 years ago
Read 2 more answers
T/(5/12)=(-3/10)<br> what is t ???
andrew11 [14]

Answer:

t = - \frac{1}{8}

Step-by-step explanation:

Given

\frac{t}{\frac{5}{12} } = - \frac{3}{10}

Multiply both sides by \frac{5}{12}

t = \frac{5}{12} × - \frac{3}{10} ← cancel 5 and 10 by 5 and 3 and 12 by 3, leaving

t = \frac{1}{4} × - \frac{1}{2} = - \frac{1}{8}

4 0
4 years ago
I need help please :( !!!
Neporo4naja [7]
Number of cans donated the first week = 132
Number of cans donated the second week = 146
Number of cans donated the third week = c, where c is some positive number

Add up the three values (132, 146, and c) to get 132+146+c. I'm choosing not to simplify because each answer choice hasn't simplified either.

The expression of 132+146+c represents the total amount of cans donated for weeks 1 through 3. We want "at least 325 cans", so that means the expression is 325 or larger. That translates to this inequality

132+146+c \ge 325

The "greater than or equal to" sign indicates we want that sum to be 325 or larger.

Now we solve for c

132+146+c \ge 325
278+c \ge 325
278+c-278 \ge 325-278
c \ge 47

So the amount of cans donated for week three needs to be 47 or larger. If you collect exactly 47 cans for week three, then you meet the goal of 325 total cans. If you collect more than 47 cans for week three, then you exceed the goal of 325 total cans.

------------------------------------

In summary we have the inequality 
132+146+c \ge 325
which solves to
c \ge 47

Meaning that the answer is choice D


4 0
3 years ago
Jamie says the value of the expression 1.43 x -17/33 is close to -0.75 does Jamie’s estimate seem reasonable explain
yaroslaw [1]

Answer:

yes, Jamie is right

Step-by-step explanation:

-(17÷33)=- 0.515

-0.515 * 1.43 = 0.737 ~ 0.75

7 0
3 years ago
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