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3 years ago

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What is f(−3) for the function f(a)=−2a2−5a+4?

1 answer:

andriy [413]3 years ago

4 0

Answer:

i believe the answer is 1

Step-by-step explanation:

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Consider the initial value problemy' + 3 y = 36 t, y(0) = 6.Take the Laplace transform of both sides of the given differential e

wolverine [178]

Answer:

The solution of the differential equation is $y(t) = -4 + 12t + 10e^{-3t}$ .

Step-by-step explanation:

The first step is to take Laplace transform in both sides of the differential equation. As usual, we denote the Laplace transform of $y$ as $Y=L[y]$ . Then,

$L[y'+3y](s) = L[36t](s)$

$L[y'](s)+3L[y](s) = 36L[t](s)$

$sY(s)-y(0)+3Y(s) = \frac{36}{s^2}$

In the last step we use that $L[y'](s) = sL[y](s)-y(0)$ and $L[t](s) = \frac{1}{s^2}$ .

Notice that our differential equations becomes an algebraic equation for $Y(s)$ , which is more simple to solve.

In the expression we have obtained, we can write $Y(s)$ in terms of $s$ :

$(s+3)Y(s)-6=\frac{36}{s^2}$ which is equivalent to

$Y(s) = \frac{36}{s^2(s+3)} +\frac{6}{s+3}$ .

Now, we make a partial fraction decomposition for the term $\frac{36}{s^2(s+3)}$ . Thus,

$\frac{36}{s^2(s+3)} = -\frac{4}{s} + \frac{12}{s^2} + \frac{4}{s+3}$ .

Substituting the above value into the expression for $Y(s)$ we get

$Y(s) = -\frac{4}{s} + \frac{12}{s^2} + \frac{4}{s+3} + \frac{6}{s+3} = -\frac{4}{s} + \frac{12}{s^2} + \frac{10}{s+3}.Finally, we take the inverse Laplace transform (denoted by [tex]L^{-1}$ ) in both hands of the above expression. Recall that $y(t) = L^{-1}[Y](t)$ . So,

$y(t) = L^{-1}\left[-\frac{4}{s} + \frac{12}{s^2} + \frac{10}{s+3}\right](t)$

$y(t) = -4L^{-1}\left[\frac{1}{s}\right](t) + 12L^{-1}\left[\frac{1}{s^2}\right](t) + 10L^{-1}\left[\frac{1}{s+3}\right](t)$

$y(t) = -4 + 12t + 10e^{-3t}$ .

To obtain this we have used the following identities that can be found in any table of Laplace transforms

$L^{-1}\left[\frac{1}{s}\right](t) = 1$

$L^{-1}\left[\frac{1}{s^2}\right](t) = t$

$L^{-1}\left[\frac{1}{s+3}\right](t) = e^{-3t}$

4 0

3 years ago

What characteristics can be seen in the graphs for a system that have one solution, no solution or infinitely many solutions?

Novosadov [1.4K]

<em><u>vhyfxr6xtc5fubic4zkbkft</u></em><em><u> </u></em><em><u>d4fnh</u></em>

5 0

3 years ago

At Freddy's, three steak burgers and two orders of fries cost $18. Two steak burgers and three orders of fries cost $15.75. What

Fudgin [204]

The cost for one steak burger is $4.5. The price/ The cost of one order of fries is $2.25

<h3>Solution</h3>

Let one steak burger cost $x

and one fries order cost $y

Hence, we have

3x+2y = 18-----------1

2x+3y = 15.75-------2

<h3>Let us solve the equation simultaneously</h3>

multiply equation 1 by 2 and equation 2 by 3

6x + 4y = 36 ---------3

6x + 9y = 47.25 ----4

subtraction 4 from 3 we have

0x -5y = -11.25

Divide both sides by -5

y = 11.25/5

y = $2.25

Put y = 2.25 in equation 1 to find x

3x+2(2.25) = 18-----------1

3x + 4.5 = 18

3x = 18 -4.5

3x = 13.5

x = 13.5/3

x = $4.5

Learn more about Algebra here:

brainly.com/question/12602543

6 0

2 years ago

For the function N(y) = 4|3y – 8– 4, evaluate N(y) + N(1).

Reil [10]

Answer:

4|3y-8|+12

Step-by-step explanation:

N(1)=4|3(1)-8|-4

N(1)=16

Now we have:

N(y)+N(1)=4|3y-8|-4+16

N(y)+N(1)=4|3y-8|+12

7 0

3 years ago

Which expression is equivalent to this expression?<br> 4a + (–6b) – 3a + 2b

Arlecino [84]

Answer:

a−4b

Step-by-step explanation:

=4a+−6b+−3a+2b

Combine Like Terms:

=4a+−6b+−3a+2b

=(4a+−3a)+(−6b+2b)

=a+−4b

I like your cut g ;)

5 0

3 years ago