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2 years ago

Question 5 of 10

Mathematics

1 answer:

Dominik [7]2 years ago

8 0

Answer: Option A, B, E are correct.

A. 8^x •8^x = 64^x

B. 8^2x = 64^x

C. 8•8^2x = 8^{1 + 2x}

D.8^2•8^x = 8^{2 + x}

E. (8•8)^x = 64^x

F. 8•8^x = 8^{1 + x}

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4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

harina [27]

Answer:

$y=3e^{-4t}$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=\frac{3s+3}{s^2+5s+4}$

$L=\frac{3(s+1)}{(s+1)(s+4)}$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}$

$y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}$

7 0

3 years ago

Now write the number is standard form ?

chubhunter [2.5K]

Step-by-step explanation:

$(2 \times 10) + (6 \times 1) + (9 \times \frac{1}{1000} ) \\ \\ =20 +6+ (9 \times 0.001 ) \\ \\ = 26 + 0.009 \\ \\ = 26.009$

4 0

3 years ago

Read 2 more answers

Geoff paddles his canoe at an average speed of 3.5 miles per hour. After 5 hours of canoeing, Geoff has traveled 18 miles. Write

andriy [413]

Answer:

d(x) = 3.5x + 0.5

Step-by-step explanation:

3.5 x 5 = 17.5 which means the canoe began from a starting point of 0.5

7 0

3 years ago

How do I find the area. Please explain

olganol [36]

All you have to do is multiply it then you get the answer

7 0

3 years ago

If y is directly proportional to x and when y = 35, x = 140, what is the value of x when y = 70?

levacccp [35]

Answer: 280 = x

Step-by-step explanation: Okay you are using this equation! y = kx But you must rearrange it!

When rearranged you get y/x = k

Plug in x and y!

y/x = k

35/140 = k

0.25 = k

Now find the value of x.

You use this formula now, y/k = x

Plug in k from the last problem and y = 70

y/k = x

70/0.25 = x

280 = x

6 0

3 years ago