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ra1l [238]
3 years ago
10

Find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution. (Enter your answ

er using interval notation.) (x − 3)y'' + 4y = x, y(0) = 0, y'(0) = 1
Mathematics
1 answer:
Ivan3 years ago
7 0

Answer:

(-\infty,3)

Step-by-step explanation:

We are given that

(x-3)y''+4y=x

y''+\frac{4}{x-3}y=\frac{x}{x-3}

y(0)=0

y'(0)=1

By comparing with

y''+p(x)y'+q(x)y=g(x)

We get

p(x)=\frac{4}{x-3}

g(x)=\frac{x}{x-3}

q(x)=0

p(x),q(x) and g(x) are continuous for all real values of x except 3.

Interval on which p(x),q(x) and g(x) are continuous

(-\infty,3)and (3,\infty)

By unique existence theorem

Largest interval which contains 0=(-\infty,3)

Hence, the larges interval on which includes x=0 for which given initial value problem has unique solution=(-\infty,3)

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1) f(x) = 2x + 4, g(x) = 4x2 + 1; Find (g ∘ f)(0).
Sholpan [36]

Answer:

<h2>(g \: \circ \: f)(0) = 17</h2>

Step-by-step explanation:

f(x) = 2x + 4

g(x) = 4x² + 1

In order to find (g ∘ f)(0) we must first find

(g ° f )(x)

To find (g ° f )(x) substitute f(x) into g(x) that's for every x in g(x) replace it with f(x)

That's

<h3>(g \: \circ \: f)(x) = 4( ({2x + 4})^{2} ) + 1 \\  = 4(4 {x}^{2}  + 16x + 16) + 1 \\  =  {16x}^{2}  + 64x + 16 + 1</h3>

We have

<h3>(g \: \circ \: f)(x) =  {16x}^{2}  + 64x + 17 \\</h3>

Now to find (g ∘ f)(0) substitute the value of x that's 0 into (g ∘ f)(0)

We have

<h3>(g \: \circ \: f)(0) = 16( {0})^{2}  + 64(0) + 17 \\</h3>

We have the final answer as

<h3>(g \: \circ \: f)(0) = 17</h3>

Hope this helps you

8 0
4 years ago
I don't know how to do anything. I basically need help with everything
lutik1710 [3]
Okay,

Radius, is half of the diameter.
Diameter, is the line that splits the circle in half.

1). R=50 D=100
2). R=10 D=20
3). R=5   D=10
4). R=29 D=58
5). R=11 D=22
6). R=31.5 D=63
7). R=45 D=90
8). R=7   D=14
9). R=49 D=98

 
5 0
4 years ago
Read 2 more answers
GEOMETRY HELPP -- WILL MARK BRAINLIEST
lukranit [14]

Answer: d = 29 miles

Step-by-step explanation:

S11°W  = 259° on a unit circle

N75°E = 15° on a unit circle

x separation after two hours

x = 2(8cos15 - 18cos259) = 21.179 miles

y separation after two hours

x = 2(8sin15 - 18sin259) = 19.7398 miles

total distance between them is

d = √(19.7398² + 21.179²) = 28.9518... ≈ 29 miles

3 0
3 years ago
_______ the problem by formulating assumptions and recognise certain variables and their relations
patriot [66]

Answer:

Research Hypothesis solves the problem by .....

Step-by-step explanation:

Research Hypothesis is a set of assumed statements, consisting certain variables & their relationships

The variables whose relationship are to be checked by hypothesis testing, are independent & dependent variables. The causal variable(s) are independent variables & the effected variable is the dependent variable.

  • Null Hypothesis : It is the hypothesis assuming no statistically significant relationship between independent & dependent variables
  • Alternate Hypothesis : It is the hypothesis assuming statistically significant relationship between independent & dependent variable

Example : To check the research question, of relationship between research variables, by formulating hypothesis assumed statement

Y = b0 + b1X ; where

Y = dependent variable, X = independent variable, b0 = autonomous, b1 = X intercept on Y  

  • H0 : b1 = 0 {No significant relationship between X & Y}
  • H1 : b1 ≠ 0 {Significant relationship between X & Y}

This way : Research hypothesis solves the problem by - formulating hypothesis assumptions, which recognise the variables & their relations. At last, acceptance of null  or alternate hypothesis gives the final research conclusion & interpretation

7 0
3 years ago
Which inequality best represents the graph? O A. 2x + y = 6 O B. x + 2y 6 O c. 2r- y&lt; 6 O D. 2x - y &gt; -6 E. 2x + y26​
Misha Larkins [42]

Answer:

It would be A

Step-by-step explanation:

5 0
3 years ago
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