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bogdanovich [222]
3 years ago
14

Compute F(s), the Laplace transform of f(t) = e^(5t) (t^2 +4t +7)

Mathematics
1 answer:
MakcuM [25]3 years ago
3 0

Recall that

\mathcal L_s\{t^ne^{ct}\}=\dfrac{n!}{(s-c)^{n+1}}

Then

F(s)=\dfrac2{(s-5)^3}+\dfrac4{(s-5)^2}+\dfrac7{s-5}

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The explicit rule for the arithmetic sequence shown in the graph is a↓n=9.5+2(n-1)
Virty [35]

Answer:

True.

Step-by-step explanation:

The explicit form for an arithmetic sequence is:

a_n=a_1+d(n-1)

where a_1 is the first term and d is the common difference.

The common difference here is 2 because the y's are going up by 2 while the x's are going up by 1.

Yes, the common difference is the slope.

So we have d=2.

The first term is 9.5 because that is what happens when x=1.

x is n.

y is a_n.

So the answer is true.

----

You can also verify by plugging in numbers for n and see if you get the outputs mentioned in the pairs given:

Let n=1:

a_1=9.5+2(1-1)

a_1=9.5+2(0)

a_1=9.5+0

a_1=9.5

Let n=2:

a_2=9.5+2(2-1)

a_2=9.5+2(1)

a_2=9.5+2

a_2=11.5

Let n=3:

a_3=9.5+2(3-1)

a_3=9.5+2(2)

a_3=9.5+4

a_3=13.5

Let n=4:

a_4=9.5+2(4-1)

a_4=9.5+2(3)

a_4=9.5+6

a_4=15.5

Let n=5:

a_5=9.5+2(5-1)

a_5=9.5+2(4)

a_5=9.5+8

a_5=17.5

Let n=6:

a_6=9.5+2(6-1)

a_6=9.5+2(5)

a_6=9.5+10

a_6=19.5

We have confirmed that we get all 6 of the mentioned points using the equation they gave.

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3 years ago
Write the situation for the relationship "y = 2x - 5."
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3 years ago
Plz I need some help with 11-12 . My teacher didn’t even explain it correctly so now I’m confused.
rusak2 [61]

Answer:

Step 1: Transpose everything to one side

12. x²+16x+15-10x+4=0

Step 2: Add the like terms

x² + (16x - 10x) + 15 + 4=0

x² + 6x + 19=0

Step 3: Use the quadratic formula to get the value(s) of x.

a=1 b=6 c=19

x =  \frac{ - b +  -  \sqrt{b {}^{2} - 4ac }  {}^{} }{2a}

therefore, x=... or x

6 0
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16. Solve 7n=42<br> 06<br> O n = 6<br> n = 7<br> O 7
Masteriza [31]

Answer:

6

Step-by-step explanation:

7n=42

n=42/7

n=6

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PLEASE HELP IM CRYING RN PLEASE ANSWER CORRECTLY AND YOU WILL GET BRAINLIEST AND 100 POINTS
Vlad [161]

Answer: B (x,y) --> (x + 4, y - 2)

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