All categories

2 years ago

what is the capacity of a container that is filled in 35 minutes by a tap that supplies 240 liters per hour

Mathematics

2 answers:

AlekseyPX2 years ago

8 0

Answer:

capacity = 140 liters

Step-by-step explanation:

1 h = 60 min

60 min ................ 240 l

35 min ...................... x l

x =35×240/60 = 8400/60 = 140 liters

pshichka [43]2 years ago

4 0

Answer:

$\Huge \boxed{\mathrm{140 \ liters}}$

Step-by-step explanation:

$\displaystyle \sf 35 \ minutes = \frac{7}{12} \ hour$

$\sf \displaystyle liters \ per \ hour =\frac{liters}{hour}$

Let the liters amount be x.

$\sf \displaystyle 240 =\frac{x}{\frac{7}{12} }$

Multiplying both sides by $\sf \frac{7}{12}$

$\sf \displaystyle 240 \cdot \frac{7}{12} =\frac{x}{\frac{7}{12} } \cdot \frac{7}{12}$

$\sf 140=x$

The capacity of the container is 140 liters.

You might be interested in

What is the range of y=3sin(x)?

den301095 [7]

Answer:

The range is -3≤y≤3 - 3≤y≤3.

Step-by-step explanation:

I hope this helps! :)

6 0

2 years ago

A number has been round to 7700.what might the number

ankoles [38]

7699......................

3 0

3 years ago

Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using integration by parts:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x$

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

6x – 4y = -5 4x + 5y = -11

kipiarov [429]

Answer:

x= -1.5, y= -1

Step-by-step explanation:

6x= -5+4y

x= (-5+4y) / 6

4((-5+4y) / 6) + 5y = -11

4(-5+4y) + 5*6y = -11*6

-20+16y+30y= -66

16y + 30y = -66+20 = -46

y(16 + 30) = -46

y= -46 / (16 + 30)

y= -46 / 46

y= -1

x= (-5+4(-1)) / 6

x= (-5-4) / 6

x= -9 /6

x= -1.5

3 0

3 years ago

A refrigerator costs $580 a year to run. A family purchases a new one for $1200 that will save them 22% annually in energy costs

NeTakaya

Answer:

It will take nine years and four months for the refrigerator to pay for itself.

Step-by-step explanation:

The new refrigerator which costs $1200, saves the family 22% annually in energy cost.

Since the old refrigerator costs $580 to run, we want to determine how many years it will take for 22% of $580 per year to make $1200.

22% of $580

= 580 × 0.22

= 127.6

That is, it saved then $127.6 per year.

Now,

$1200/127.6

≈ 9.4

Which means, it will take 9 years and 4 months for the refrigerator to pay for itself.

7 0

2 years ago

what is the capacity of a container that is filled in 35 minutes by a tap that supplies 240 liters per hour​

what is the capacity of a container that is filled in 35 minutes by a tap that supplies 240 liters per hour