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3 years ago

In STU, M\S = (6x – 15)°, m\T = (2x − 2)°, and m\U = (4x – 7). What is the value of x? [( pic added above])

Mathematics

1 answer:

Arturiano [62]3 years ago

4 0

Answer:

Hey there!

I see you have to right idea, the first step is to write the equation: 6x-15+2x-2+4x-7=180. We can simplify this to 12x-24=180

Solving for x, we get that x=17.

Let me know if this helps :)

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Has two or more independent clauses without any punctuation between

n200080 [17]

Answer:

the answer is fused sentence i believe if thats what your asking

Step-by-step explanation:

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3 years ago

Read 2 more answers

Consider the following. (A computer algebra system is recommended.) y'' + 3y' = 2t4 + t2e−3t + sin 3t (a) Determine a suitable f

drek231 [11]

First look for the fundamental solutions by solving the homogeneous version of the ODE:

$y''+3y'=0$

The characteristic equation is

$r^2+3r=r(r+3)=0$

with roots $r=0$ and $r=-3$ , giving the two solutions $C_1$ and $C_2e^{-3t}$ .

For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.

$y''+3y'=2t^4$

Assume the ansatz solution,

${y_p}=at^5+bt^4+ct^3+dt^2+et$

$\implies {y_p}'=5at^4+4bt^3+3ct^2+2dt+e$

$\implies {y_p}''=20at^3+12bt^2+6ct+2d$

(You could include a constant term <em>f</em> here, but it would get absorbed by the first solution $C_1$ anyway.)

Substitute these into the ODE:

$(20at^3+12bt^2+6ct+2d)+3(5at^4+4bt^3+3ct^2+2dt+e)=2t^4$

$15at^4+(20a+12b)t^3+(12b+9c)t^2+(6c+6d)t+(2d+e)=2t^4$

$\implies\begin{cases}15a=2\\20a+12b=0\\12b+9c=0\\6c+6d=0\\2d+e=0\end{cases}\implies a=\dfrac2{15},b=-\dfrac29,c=\dfrac8{27},d=-\dfrac8{27},e=\dfrac{16}{81}$

$y''+3y'=t^2e^{-3t}$

$e^{-3t}$ is already accounted for, so assume an ansatz of the form

$y_p=(at^3+bt^2+ct)e^{-3t}$

$\implies {y_p}'=(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}$

$\implies {y_p}''=(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}$

Substitute into the ODE:

$(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}+3(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}=t^2e^{-3t}$

$9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c-9at^3+(9a-9b)t^2+(6b-9c)t+3c=t^2$

$-9at^2+(6a-6b)t+2b-3c=t^2$

$\implies\begin{cases}-9a=1\\6a-6b=0\\2b-3c=0\end{cases}\implies a=-\dfrac19,b=-\dfrac19,c=-\dfrac2{27}$

$y''+3y'=\sin(3t)$

Assume an ansatz solution

$y_p=a\sin(3t)+b\cos(3t)$

$\implies {y_p}'=3a\cos(3t)-3b\sin(3t)$

$\implies {y_p}''=-9a\sin(3t)-9b\cos(3t)$

Substitute into the ODE:

$(-9a\sin(3t)-9b\cos(3t))+3(3a\cos(3t)-3b\sin(3t))=\sin(3t)$

$(-9a-9b)\sin(3t)+(9a-9b)\cos(3t)=\sin(3t)$

$\implies\begin{cases}-9a-9b=1\\9a-9b=0\end{cases}\implies a=-\dfrac1{18},b=-\dfrac1{18}$

So, the general solution of the original ODE is

$y(t)=\dfrac{54t^5 - 90t^4 + 120t^3 - 120t^2 + 80t}{405}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\dfrac{3t^3+3t^2+2t}{27}e^{-3t}-\dfrac{\sin(3t)+\cos(3t)}{18}$

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3 years ago

Conner earns 24$ working every 1.5 12 blank

RoseWind [281]

Answer: That makes no sense. Maybe did your copy and paste corrupt? Or mistyped the question? Get back to me and I’ll help!!

Step-by-step explanation:

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2 years ago

Is 28/81 less than 7/9.Is 28/81 less than 4/9?

lesantik [10]

28/81 is less than 7/9

28/81 is less than 4/9

The common denominator is 81, so you say 9 can go into 81 nine times, so you multiply 9 by the numerator, so 7/9 is now 63/81 an 4/9 is now 36/81

8 0

3 years ago

A poll shows that 41% of voters in a city favor of a $0.0.1 tax increase. If 25 voters are selected at random, what is that exac

juin [17]

Answer:

The probability is 0.026 to 3 d.p

Step-by-step explanation:

To calculate this , we shall be using the Bernoulli approximation.

let P = percentage of voters supporting the increase = 41% = 41/100 = 0.41

q = percentage of voters not supporting = 100-41% = 59% = 59/100 = 0.59

Now we want to calculate that exactly 15 out of 25 will vote in favor

Mathematically that would be ;

25C15 p^15 q^10

= 25C15 0.41^15 0.59^10

= 0.025981307443 or simply 0.026 to 3 decimal places

5 0

3 years ago