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3 years ago

Write the expression as a sum of a difference of cubes and factor it: 1/64m^3+1000

Mathematics

1 answer:

yarga [219]3 years ago

3 0

Answer:

(1\64m + 20) (1\4096m^2 - 5\322m + 100)

Step-by-step explanation:

use a^3 + b^3 = (a+b)(a^2 - ab + b^2) to factor the expression = (1\64m+10)(1\4096m^2 - 10\64m + 100)

reduce the fractions with 2 = (1\64m + 10)(1\4096m^2 - 5\32m + 100)

= (1\64m + 20) (1\4096m^2 - 5\322m + 100)

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Use Laplace transform methods to solve the differential equation: The initial conditions are f(0) = 0 and <img src="https://tex.

Llana [10]

Answer:

Step-by-step explanation:

$\frac{d^2 y}{dt^2} +12\frac{dy}{dt} +32y = 10e^{-2t}$ where f(x) is replaced by y

Take Laplace on both sides

$s^2 Y -s(0)-0 +12s Y-0+32Y = \frac{10}{s+2} \\Y(s^2+12s+32) = \frac{10}{s+2}\\Y = \frac{10}{(s+2)(s+4)(s+8)}$

We can resolve into partial fraction to get Y = L(y)

Let this equals

$\frac{A}{s+2} +\frac{B}{s+4} +\frac{C}{s+8} \\10 = A(s+4)(s+8) + B(s+2)(s+8) +Cs+4)(s+2) \\$

Solving we get

s=-9

24C = 10 or C =5/12

s=-2: A=10/12=5/6

s=-4: B = -5/4

Taking inverse Laplace

$y(t) = \frac{-5e^{-4t} }{4} + \frac{5e^{-8t} }{12} +\frac{-5e^{-2t} }{6}$

6 0

3 years ago

18. Solve the equation.<br> m- 10/3 - 5m-9/7 = 1

JulijaS [17]

The answer is m = -59/42

Step by step explanation is in the image below.

4 0

3 years ago

What is six less than seven times a number is equal to -20

Naya [18.7K]

Answer:

7n-6=-20

Step-by-step explanation:

six less than seven times a number

we'll use n as "the number"

six less meaning -6

7 times a number n = 7n

7n-6=-20

7 0

3 years ago

In a police chase on the interstate, the suspect’s car reached a speed of 88 miles per hour for a total 15 minutes. In that time

Klio2033 [76]

Answer:

22 miles

Step-by-step explanation:

time must be in hours, hence

15 minutes = $\frac{15}{60}$ = $\frac{1}{4}$ hour

distance = 88 × $\frac{1}{4}$ = $\frac{88}{4}$ = 22 miles

8 0

4 years ago

Read 2 more answers

A survey of 100 high school students provided this

HACTEHA [7]

Answer:

35/100

Step-by-step explanation:

You have to find how many juniors there are, so if you add 13, 20, and 2 you get 35. For the denominator you have to find the total number of students, so just add all of the numbers together to get 100. So there is a 35/100 chance that a randomly selected student is a junior.

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2 years ago