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2 years ago

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Find all explicit solutions y = ϕ(x) of the DE in part (a) defined by this relation. Give the interval I of definition of each e

xplicit solution. (Enter your answers for I using interval notation.)

1 answer:

Evgen [1.6K]2 years ago

7 0

Answer and Step-by-step explanation:

Firstly, by definition, an interval of definition of any solution is the open interval on which it is defined.

Consider the problem p′=p², p(0)=1, has solution p(t) = 1/(1−t).

The definition of this solution is on the interval (−1/2,1/3), making it an interval of definition of solution.

However, it isn't the largest. The largest interval of definition is (−∞,1).

Consider another problem: p(t)=t√ satisfies the ODE p′=1/(2p).

Meanwhile, when considered as the solution of the ODE above, the domain of square root is [0,∞), and the interval of definition is (0,∞).

But at t=0 the ODE makes no sense, so it would be wrong to assume that y satisfies the ODE in this case. Meanwhile, ODEs are generally considered only on open intervals.

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Eli needs pieces of ribbon cut into strips that are 2 1\2 feet long. The roll of ribbon is 7 1\2 feet long. Which expression cou

julsineya [31]

Answer: There are 3 strips that can be cut from the roll of ribbon.

Step-by-step explanation:

since we have given that

Length of a ribbon is given by

$7\frac{1}{2}\ ft\\\\=\frac{15}{2}\ ft$

Length of pieces of ribbon cut into strips is given by

$2\frac{1}{2}\ ft\\\\=\frac{5}{2}\ ft$

So, we need to find the number of strips that can be cut is given by

$\text{ Number of strips }=\frac{\text{Length of roll}}{\text{ Length of strip}}\\\\=\frac{\frac{15}{2}}{\frac{5}{2}}\\\\=\frac{15\times 2}{2\times 5}\\\\=\frac{15}{5}\\\\=3$

Hence, there are 3 strips that can be cut from the roll of ribbon.

6 0

2 years ago

Read 2 more answers

Suppose you roll a pair of honest dice. If you roll a total of 7 you win $22, if you roll a total of 11 you win $66, if you roll

JulijaS [17]

Answer:

The expected payoff for this game is -$1.22.

Step-by-step explanation:

It is given that a pair of honest dice is rolled.

Possible outcomes for a dice = 1,2,3,4,5,6

Two dices are rolled then the total number of outcomes = 6 × 6 = 36.

$\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

Formula for probability:

$Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

So, the possibility of getting a total of 7 = $\frac{6}{36}=\frac{1}{6}$

The possible ways of getting a total of 11,

{(5,6), (6,5)}

So, the probability of getting a total of 11 = $\frac{2}{36}$ = $\frac{1}{18}$

Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,

So, the probability of getting the sum of numbers other than 7 or 11 = $\frac{28}{36}$ = $\frac{7}{9}$

Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,

Hence, the expected value for this game is

$\frac{1}{6}\times 22+\frac{1}{18}\times 66-\frac{7}{9}\times 11$

$\frac{11}{3}+\frac{11}{3}-\frac{77}{9}$

$\frac{22}{3}-\frac{77}{9}$

$\frac{66-77}{9}$

$-\frac{11}{9}$

$-1.22$

Therefore the expected payoff for this game is -$1.22.

4 0

2 years ago

the diagonal of a tv is 26 inches long assuming that this diagonal forms a tv pair 30-60-90 right triangles what are the exact l

Alexxandr [17]

It is an application of Pythagorean Theorem

And it is clear that the lower angle is 30 and the apex angle is 60 (this is how always normal TVs look like) ... refer to the image I attached

So, to calculate the width and the length:

$\frac{length}{26} =cos(30)\\~\\length=26*cos(30)=13 \sqrt{3} ~~in$

$\frac{width}{26} =sin(30)\\~\\width=26*sin(60)=13~~in$

You can after that round the length to be 22.517 in

Hope you got the idea

3 0

2 years ago

At middle Avenue school, 1/30 of the students are on track team. The track coach offered to buy pizza or subs for everyone on th

atroni [7]

3/5 of the students ate pizza

4 0

2 years ago

The perimeter of a rectangle is 13cm and its width is 11/4. find its length.

enyata [817]

Perimeter = 2 length + 2 width

P = 2(l) + 2(11/4)

$13 = 2l +2* \frac{11}{4}$

$13 = 2l + \frac{2}{1} * \frac{11}{4}$

$13 = 2l + \frac{22}{4}$ (subtract 22/4 from each side)

$13 -\frac{22}{4} = 2l$

$13 -\frac{11}{2} = 2l$

$\frac{26}{2} -\frac{11}{2} = 2l$

$\frac{15}{2}} = 2l$

$7.5 = 2l$ (divide each side by 2)

7.5 ÷ 2 = l

3.75 = l

The answer is 3.75 or $3 \frac{3}{4}$

6 0

2 years ago