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4 years ago

Help ASAP Find the first four terms in An = 10n - 11

Mathematics

1 answer:

PolarNik [594]4 years ago

8 0

Answer:

The first four numbers would be 10, -1, -12, -23

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Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

4 0

4 years ago

5+4+2 (-3)+7+(-5) equals to?

Cerrena [4.2K]

5+4+2(-3)+7+(-5)
or
5+4+2-3+7+(-5)?

7 0

3 years ago

Read 2 more answers

Guys can u please help me out

sladkih [1.3K]

Answer:

$-0.36a^5x^6b^6$

Step-by-step explanation:

Ok first multiply the first two monomials:

$-0.6a^3x^6b^3$

Then multiply THAT with the OTHER monomial:

$-0.36a^5x^6b^6$

This should be the answer. Let me know if it's wrong.

6 0

3 years ago

If two cubes have edges of 1 and 2 , what is the sum of their volume???

Ivan

Volume of a cube: V = s^3, where s is the length of the edge.

So, the sum of them will be 1^3 + 2^3 = 9

7 0

3 years ago

AB:BD = 3:4 <br><br> AC:CD = 3:2 <br><br> Work out AB:BC:CD

Papessa [141]

Answer:

15:6:14

Step-by-step explanation:

AB:BD is split into a total of 3+4=7 parts.

AC:CD is split into a total of 3+2=5 parts.

So, if the two ratios are put on a number line together with the points A, B, C, and D, the number line would be split into a total of 35 parts (the LCM of 7 and 5).

AB would be (3/7)*35=15.

CD would be (2/5)*35=14

BC would be 35-(15+14)=6

So, the ratio is 15:6:14.

5 0

3 years ago