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Oliga [24]
2 years ago
11

Y – 1 = 2(x – 2), solve for y

Mathematics
1 answer:
solmaris [256]2 years ago
6 0

Answer:

y = 2x-3

Step-by-step explanation:

y – 1 = 2(x – 2)

Distribute

y-1 =2x-4

Add 1 to each side

y-1+1 = 2x-4+1

y = 2x-3

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Please help me with the below question.
Snezhnost [94]

6a. By the convolution theorem,

L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}

6b. Similarly,

L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}

7. Take the Laplace transform of both sides, noting that the integral is the convolution of e^t and f(t).

\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau

\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)

where g(t) = e^t. Then G(s) = \frac1{s-1}, and

F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}

We have the partial fraction decomposition,

\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)

Then we can easily compute the inverse transform to solve for f(t) :

F(s) = -\dfrac1s + \dfrac4{s+3}

\implies \boxed{f(t) = -1 + 4e^{-3t}}

6 0
1 year ago
In a circle a chord 10 inches long is parallel to a tangent and bisects the radius drawn to the point of tangency. How long is t
Lorico [155]
Check the picture below.

keeping in mind that the point of tangency for a radius line and a tangent is alway a right-angle, since the "red" chord is parallel to the "green" tangent line outside, then the chord is cutting the "green" radius there in two equal halves at a right-angle, as you see in the picture.

we know the chord is 10 units long, so 5 + 5, since is perpendicularity with the radius will also cut the chord in two equal halves.

anyhow, all that said, we end up with triangle you see on the right-hand-side, and then we can just use the pythagorean theorem.

\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2
\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
-------\\
c=2a\\
a=a\\
b=5
\end{cases}\implies (2a)^2=a^2+5^2

\bf (2^2a^2)=a^2+25\implies 4a^2=a^2+25\implies 3a^2=25
\\\\\\
a^2=\cfrac{25}{3}\implies a=\sqrt{\cfrac{25}{3}}\implies a=\cfrac{\sqrt{25}}{\sqrt{3}}\implies a=\cfrac{5}{\sqrt{3}}
\\\\\\
\textit{and then we can \underline{rationalize the denominator} }
\\\\\\
a=\cfrac{5}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}}\implies a=\cfrac{5\sqrt{3}}{\sqrt{3^2}}\implies a=\cfrac{5\sqrt{3}}{3}

7 0
3 years ago
Who knows the full dk rap if you get it right then you get 10 points if it takes you less than 10 minutes
Harlamova29_29 [7]
So they're finally here, performing for you
If you know the words, you can join in too
Put your hands together, if you want to clap
As we take you through this monkey rap!
Huh!


DK
Donkey Kong!


He's the leader of the bunch, you know him well
He's finally back to kick some tail
His coconut gun can fire in spurts
If he shoots ya, it's gonna hurt!
He's bigger, faster, and stronger too
He's the first member of the DK crew!
Huh!

DK
Donkey Kong!
DK
Donkey Kong is here
7 0
2 years ago
Read 2 more answers
4 and one-third divided by 5 and StartFraction 1 over 6 EndFraction
tigry1 [53]

Answer:

31/6

Step-by-step explanation:

I got it right on my quiz

3 0
2 years ago
Pabalo is training for a race. His goal is to run 8.5 miles over the next 3 days. This distances he ran each day are shown in th
goblinko [34]

Answer:

He ran a total of 8.439 miles. Over the three days he ran less than he needed to for his goal, he has to run 0.061 more miles to gain his goal

Step-by-step explanation:

simple! add all of the data numbers and you get a total of 8.439 miles. He has to run 8.5 miles but he does not reach that. he has to run 0.061 miles to gain his goal (8.5-8.439) I hope this helps! (got here as soon as possible)

6 0
3 years ago
Read 2 more answers
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