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3 years ago

What factor is missing? 24 + 12= ____(8+4)

Mathematics

2 answers:

Murrr4er [49]3 years ago

7 0

Answer:

Step-by-step explanation:

24 + 12 = ___(8+4)

36 = ___(12)

36/12 = 3

Svetach [21]3 years ago

3 0

3
Aoggianaiqos Ajaxzjka

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Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the

sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let $y(t)$ be the depth of water in the barrel at time $t$ , where $y$ is measured in inches and $t$ in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

$\frac{dy}{dt}=-k\sqrt{y}$

where $k$ is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by $\frac{1}{\sqrt{y}}$

$\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k$

Multiply by $dt$

$\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt$

Take integral

$\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt$

Integrate

$2\sqrt{y}=-kt+C$

Isolate $y$

$y(t)=(\frac{C}{2} -\frac{k}{2}t)^2$

We know that the water level starts at 36, this means $y(0)=36$ . We use this information to find the value of $C$ .

$36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12$

$y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2$

At t = 1, y = 34

$34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}$

So our formula for the depth of water in the barrel is

$y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\$

To find the time, $t$ , at which all the water leaks out of the barrel, we solve the equation

$\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49$

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

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3 years ago

Match the base to the corresponding height. Base (b) Height (h) b b h b

antiseptic1488 [7]

Answer: See the diagram below

=================================================

Explanation:

The base is always perpendicular to the height, meaning the two form a 90 degree angle (aka right angle).

In column 1, refer to the figures as 1, 2 and 3 (working top to bottom).

In column 2, refer to the figures as A, B, C

Figure 1 matches with figure B

Figure 2 matches with figure C

Figure 3 matches with figure A.

These matches are of course the base with the proper height.

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3 years ago

Solve 7x+3y=8 and 4x-y=-9 simultaneously

Jobisdone [24]

Answer: x = -1 and y = 5

Step-by-step explanation:

7x + 3y = 8 ........................... equation 1

4x - y = - 9 ............................ equation 2

Solving the simultaneous linear equation by substitution method , make y the subject of the formula from equation 2 , we have

y = 4x + 9 ............................. equation 3

substitute y = 4x + 9 into equation 1 , we have;

7x + 3 ( 4x + 9 ) = 8

7x + 12x + 27 = 8

19x + 27 = 8

subtract 27 from both sides

19x = -19

divide through by 19

x = -1

substitute x = -1 into equation 3 , we have

y = 4 ( -1) + 9

y = -4 + 9

y = 5

Therefore :

x = -1 and y = 5

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