Ask question

Ask question

All categories

adelina 88 [10]

3 years ago

8

Consider the initial value problem ????t(t−1)x′′′ −3tx′′ +6t2x′ −(cost)x=√t+5 x(t0) = 1, x′(t0) = 0, x′′(t0) = 7. Determine the

values of t0 and the intervals (a,b) containing t0 for which Theorem 1 guarantees the existence of a unique solution on (a, b).

1 answer:

Butoxors [25]3 years ago

6 0

The squared root to all your problems show here and now when needed

You might be interested in

What is f(x) + f(x) + f(x)?

Masteriza [31]

Answer:

3fx

Step-by-step explanation:

f(x)+f(x)+f(x)

remove parenthesis: (a)=a

add similar elements: fx+fx+fx

=3fx

3 0

3 years ago

What is the factored form of x2 – x – 2? (x – 2)(x 1) (x 2)(x 1) (x – 2)(x – 1) (x 2)(x – 1)

Alexxx [7]

A quadratic equation is an equation whose leading coefficient is of the second degree. The factored form of the quadratic equation x²-x-2 is (x+1)(x-2).

<h3>What is a quadratic equation?</h3>

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

The factored form of the quadratic equation can be done in the following manner,

$x^2-x-2\\\\= x^2-2x+x-2\\\\=x(x-2)+(x-2)\\\\=(x+1)(x-2)$

Thus, the factored form of the quadratic equation x²-x-2 is (x+1)(x-2).

Learn more about Quadratic Equations:

brainly.com/question/2263981

8 0

2 years ago

4.678<br> written to one decimal point would be

Troyanec [42]

Answer:

hello

4.678 = 4 678 / 1000

Step-by-step explanation:

7 0

2 years ago

Round these numbers to the nearesth hundredth~

hoa [83]

Answer:

1. 0.29

2. 0.12

3. 0.71

4. 0.56

5 0

4 years ago

Read 2 more answers

Suppose that the population P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its pop

jeka94

Answer:

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

$\frac{dP}{dt}=kP(600 - P)\\\frac{dP}{P(600 - P)} =kdt$

Integrate the differential equation to determine the equation of P in terms of <em>t</em> as follows:

$\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}$

At <em>t</em> = 0 the value of <em>P</em> is 300 million.

Determine the value of constant C as follows:

$\frac{P}{600-P} = Ce^{600kt}\\\frac{300}{600-300}=Ce^{600\times0\times k}\\\frac{1}{300} =C\times1\\C=\frac{1}{300}$

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then $\frac{dP}{dt}=1$ .

Determine <em>k</em> as follows:

$\frac{dP}{dt}=kP(600 - P)\\1=k\times300(600-300)\\k=\frac{1}{90000}$

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

$\frac{P(70)}{600-P(70)} = \frac{1}{300} e^{\frac{600\times 70}{90000}}\\\frac{P(70)}{600-P(70)} =1.595\\P(70)=957-1.595P(70)\\2.595P(70)=957\\P(70)=368.786$

Thus, the country's population for the year 2030 is 368.8 million.

3 0

4 years ago