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Anna71 [15]
2 years ago
12

Solve the initial value problem. 7y′−4y=e−πt2, y(0)=a Let a0 be the value of a for which the transition from one type of long-ru

n behavior to another occurs. Find the critical value a0 exactly.

Mathematics
1 answer:
densk [106]2 years ago
8 0

Answer:

as shown in the attached file

Step-by-step explanation:

The detailed steps and application of differential equation, the use of integrating factor to generate the solution and to solve for the initial value problem is as shown in the attached file.

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The dimensions of the tank are 50 cm by 32 cm by 20 cm. The tank is full of water and sand. The ratio of the volume of water to
Sauron [17]

Given:

Dimensions of a tank are 50 cm by 32 cm by 20 cm

The tank is full of water and sand

Ratio of volume of water to the volume of sand is 5:1

To find:

Volume of water in the tank in liters

Solution:

Without loss of generality, let,

Length of tank = 50 cm

Breadth of tank = 32 cm

Height of tank = 20 cm

Then, we have,

Total Volume of the tank = Length * Breadth * Height

\Rightarrow Total Volume = 50*32*20 cc

\Rightarrow Total Volume = 32000 cc

It is given that,

Volume of water : Volume of sand = 5:1

\Rightarrow (Volume of water)/(Volume of sand) = 5/1

Cross multiplying, we have,

Volume of sand = (Volume of water)/5

It is also given that the tank is full of water and sand. This implies that,

Volume of water + Volume of sand = Total Volume

Using the value, we obtained, we get,

Volume of water + (Volume of water)/5 = Total Volume

\Rightarrow (6 * Volume of water)/5 = Total Volume

Plugging in the value of total volume, we get,

\Rightarrow (6 * Volume of water)/5 = 32000 cc

\Rightarrow Volume of water = \frac{32000*5}{6} cc

\Rightarrow Volume of water \approx 26,666.6667 cc

We know that,

1 cc = 0.001 liters

\Rightarrow 26,666.6667 cc = (26666.6667 * 0.001) liters

\Rightarrow 26,666.6667 cc \approx 26.667 liters

Thus, Volume of water in the tank is approximately 26.667 liters

Final Answer:

Volume of water in the tank (in liters) is approximately 26.667 liters

4 0
2 years ago
Fourteen more than a number is eighteen.
AVprozaik [17]

Answer: 4

Step-by-step explanation:

18-14=4

3 0
3 years ago
HELP MEEE OMGGGG JESSUS AMENNN
irina1246 [14]

Answer:

Answers in the pics

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

8 0
2 years ago
Steps to solve 3 raised tobthe power of 6
SVETLANKA909090 [29]
Times 3 6 times but not 3 times 6
7 0
3 years ago
Read 2 more answers
How to solve this question? Please help me
Maurinko [17]

Answer:

≈ 82 feet

Step-by-step explanation:

Since the triangle is right use Pythagoras' identity to calculate distance (d)

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

Here the hypotenuse is the distance (d) between the 2 poles, hence

d² = 80² + 45² = 6400 + 2025 = 8425 ( take the square root of both sides )

d = \sqrt{8425} ≈ 82 feet ( to the nearest foot )

8 0
3 years ago
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