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kvv77 [185]
3 years ago
15

Who won the race between the two balls of string

Mathematics
1 answer:
motikmotik3 years ago
7 0
The higher one I think
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(with steps please) Find the inverse Laplace transform, f(t), of the function: 16/(s-4)^3
Stells [14]

Answer:  The required inverse transform of the given function is

f(t)=8t^2e^{4t}.

Step-by-step explanation:  We are given to find the inverse Laplace transform, f(t), of the following function :

F(s)=\dfrac{16}{(s-4)^3}.

We have the following Laplace formula :

L\{t^ne^{at}\}=\dfrac{n!}{(s-a)^{n+1}}\\\\\\\Rightarrow L^{-1}\{\dfrac{1}{(s-a)^{n+1}}\}=\dfrac{t^ne^{at}}{n!}.

Therefore, we get

f(t)\\\\=L^{-1}\{\dfrac{16}{(s-4)^3}\}\\\\\\=16\times\dfrac{t^{3-1e^{4t}}}{(3-1)!}\\\\\\=\dfrac{16}{2}t^2e^{4t}\\\\\\=8t^2e^{4t}.

Thus, the required inverse transform of the given function is

f(t)=8t^2e^{4t}.

6 0
3 years ago
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s
inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0
3 years ago
Miles brought the Russian novel Anna Kerenina. His paperback edition contains 992 page. Miles takes 3 days to read the first 50
Nesterboy [21]

Answer:

59.52 days

Step-by-step explanation:

So this is a simple problem we can solve easily

If it takes 3 days to read 50 pages then obviously his rate of reading is 50 pages per day

If we divide 992 by 50, then we can find how many 3 day increments it will take him

(992/50 is 19.84)

Now is we multiply 19.84 by 3, we get the total amount of days which is 59.52

I hope I helped and have a wonderful day!

7 0
2 years ago
Find the missing sides from the right-angled triangled given below
umka21 [38]

Answer:

8 cm

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
What is the value of √144
Marysya12 [62]

Answer:

12!

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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