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andreyandreev [35.5K]

3 years ago

13

Two sides of a triangle have the same length. The third side measures 6 m less than twice the common length. The perimeter of th

e triangle is 14 m. What are the lengths of the three sides?

1 answer:

Zepler [3.9K]3 years ago

8 0

The answer is <span>The two equal sides have a length of 4,</span>
<span>the third side has a length of 6.</span>

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The local humane society currently has 60 cats if 300 animals are in the shelter what percent are the cats

Kaylis [27]

20% are cats.

20 cats/300 total animals=0.2

0.2 is the same thing as 20%.

7 0

3 years ago

The endpoints of line segment RS are R(-2,-1), and S (2,3). Find the coordinates of the midpoint of line segment RS.

madam [21]

Midpoint coordinates are ( - 2 + 2) / 2 , (-1+3) / 2

= (0,1) Answer

6 0

3 years ago

Solve and graph the following inequality: 3(7x+17) > -19 + 14x

love history [14]

Answer:

Solving the inequality we get: $\mathbf{x>-7}$

Step-by-step explanation:

We need to solve and graph the inequality $3(7x+17) > -19 + 14x$

Solving:

$3(7x+17) > -19 + 14x$

Step 1: Multiply 3 with terms inside the bracket

$21x+51 > -19 + 14x$

Step 2:Subtracting 51 on both sides

$21x+51-51 > -19 + 14x-51\\21x>14x-70\\$

Step 3: Subtract 14x on both sides

$21x-14x>+14x-70-14x\\7x>-70$

Step 4: Divide both sides by 7

$\frac{7x}{7}>\frac{-70}{7}\\x>-10$

Solving the inequality we get: $\mathbf{x>-7}$

The graph is attached in the figure below.

5 0

3 years ago

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

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

3 0

3 years ago

Rewrite using a single positive exponent.<br> 6^5<br> 6

Fiesta28 [93]

Answer:

$6^{4}$

Step-by-step explanation:

using the rule of exponents

$\frac{a^{m} }{a^{n} }$ = $a^{(m-n)}$

note that 6 = $6^{1}$ , then

$\frac{6^{5} }{6}$ = $6^{(5-1)}$ = $6^{4}$

7 0

2 years ago