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3 years ago

Help please! I need this question answered!

Mathematics

1 answer:

Pavel [41]3 years ago

5 0

Answer:

1) f(g(-2))=-3, 2) g(f(0))=5

Step-by-step explanation:

1)f(g(-2))

First, g(-2) means that x=-2. Hence, you must find the value of g(x) in the table when x=-2. You can see that, when x=-2, g(-2) = -3.

Next, you must find f(-3) in the graph, where x=-3. You can see in the graph that, when x=-3, f(-3) = -2.

Therefore, f(g(-2))=-3

2) g(f(0))

In the case, we must apply the inverse procedure. First, check in the graph that, when x=0, f(0) =1.

Next, we must look at the table and see that, when x=1, g(1)=5. Hence,

g(f(0))=5

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3 years ago

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Step-by-step explanation:

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3 years ago

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Help me please,Thanks

alisha [4.7K]

Answer: The width is: " 10 in. " .
________________________________________________
Explanation:
________________________________________________
Consider a "rectangular prism".
________________________________________________
The formula for the Volume of a rectangular prism:
________________________________________________

V = L * w * h ;
_________________________________________________
in which:

V = volume = 120 in.³ ;
L = length = 8 in.
w = width = ??
h = height = 1.5 in.
____________________________________________
We want to solve for "w" (width) ;
____________________________________________
Given the formula:
____________________________________________

V = L * w * h ;
____________________________________________
Rewrite the formula; by dividing EACH SIDE of the equation by
"(L * h)" ; to isolate "w" on one side of the equation;
and to solve for "w" ;
_____________________________________________
→ V / (L * h) = ( L * w * h) / (L * h) ;

to get:
_________________________________
→ V / (L * h) = w ;

↔ w = V / (L * h) ;
_________________________________
Plug in our given values for "V", "L"; and "h"; to solve for "w" ;
____________________________________________________
→ w = (120 in.³) / (8 in. * 1.5 in.) ;

→ w = (120 in.³) / (12 in.²) ;

→ w = (120/12) in. = 10 in.
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8 0

3 years ago

Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions

monitta

I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take $z=y'$ , so that $z'=y''$ and we're left with the ODE linear in $z$ :

$y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2$

Now suppose $y$ has a power series expansion

$y=\displaystyle\sum_{n\ge0}a_nx^n$
$\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}$
$\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}$

Then the ODE can be written as

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0$

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0$

$\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0$

All the coefficients of the series vanish, and setting $x=0$ in the power series forms for $y$ and $y'$ tell us that $y(0)=a_0$ and $y'(0)=a_1$ , so we get the recurrence

$\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}$

We can solve explicitly for $a_n$ quite easily:

$a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}$

and so on. Continuing in this way we end up with

$a_n=\dfrac{a_1}{n!}$

so that the solution to the ODE is

$y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x$

We also require the solution to satisfy $y(0)=a_0$ , which we can do easily by adding and subtracting a constant as needed:

$y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}$

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3 years ago

If 3/5 of a sum of money is 1200. what is the sum

inna [77]

Answer:

2000

Step-by-step explanation:

let the sum=x

3/5 of x=1200

x=1200×5/3=2000

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3 years ago

Read 2 more answers