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2 years ago

Consider the trinomial x^2+10x+24

Mathematics

1 answer:

tino4ka555 [31]2 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

(a)

(x + 2)(x + 12) ← expand using FOIL gives

x² + 14x + 24 ≠ x² + 10x + 24

(b)

consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term (+ 10)

the factors are + 6 and + 4 , since

6 × 4 = 24 and 6 + 4 = 10 , then

x² + 10x + 24 = (x + 6)(x + 4)

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Which expression is equivalent to (4x+11)+7x?

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2 years ago

What equality is shown here on the number above?

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3 years ago

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

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2 years ago

Could someone do all the problems and/or check my work?

MArishka [77]

11. You’ve done it correctly

12. Let x^2=y
y^2+13y+40=0
(y+8)(y+5)=0
y=8, 5
Since y=x^2
x^2=8 x^2=5
x=+/-√5 x= +/-2√2

13. x^4-x^2-x^2-8=0
x^4-2x^2-8=0
let x^2=y
Y^2-2y-8=0
(y-4)(y+2)=0
y=4, -2
Since y=x^2
X^2=4 X^2=-2
X= +/- 2 This wouldn’t be a real solution

14. It’s pretty much the same process, just substitute y in for x^2. If you’re confused feel free to ask and I can do it, or you can put it through Photomath

15. You’re on the right track so I’m just going to continue from where you left off
x^2(4x+5)-4(x+5)=0
(x^2-4)(4x+5)=0
x= +/- 2 4x=5
x=5/4 or 1 1/4

Hope this helped :)

8 0

3 years ago

Read 2 more answers

the cost of an ice cream sundae is 4.75$ plus 30 cents per topping. megan spends $6.26 on her sundae how many toppings did he ge

alexgriva [62]

Answer:

Step-by-step explanation:

$4.75 + 0.3x = $6.26

0.3x = 1.51

x = 5.033

4 0

3 years ago