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natali 33 [55]
3 years ago
12

What is 64x6+27 written as a sum of cubes?​

Mathematics
1 answer:
MakcuM [25]3 years ago
6 0

Answer:

To transform the given expression to the sum of cubes, calculate first the cube root of the terms. The cube root of the first term, 64x^6 is 4x^2 and that of the second term, 27 is 3.

Thus, the answer to this is (4x^2)^3 + 3^3

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The square of the sum of two numbers is 144 and the sum of of their square is 180, find the number... Please I really need the a
mr Goodwill [35]

Answer:

The numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

Step-by-step explanation:

Let the two numbers be 'x' and 'y'.

Given:

The squares of the sum of two numbers = 144

The sum of their squares = 180

The sum of the numbers = x+y

The square of the sum of numbers = (x+y)^2

Square of first number = x^2

Square of second number = y^2

The sum of their squares = x^2+y^2

Now, as per question:

(x+y)^2=144---(1)\\\\x^2+y^2=180---(2)

Expanding equation (1) using the formula (a+b)^2=a^2+b^2+2ab

This gives,

(x+y)^2=144\\\\x^2+y^2+2xy=144\\\\\textrm{Plug in the value of }x^2+y^2\textrm{ from equation (2)}\\\\180+2xy=144\\\\2xy=144-180\\\\2xy=-36\\\\xy=-\frac{36}{2}\\\\xy=-18\\\\y=-\frac{18}{x}---(3)

Plug in the value of 'y' from equation (3) in equation (1). This gives,

x^2+(-\frac{18}{x})^2=180\\\\x^2+\frac{324}{x^2}=180\\\\x^4+324=180x^2\\\\x^4-180x^2+324=0\\\\\textrm{On solving, we get:}\\\\x^2=178.2\ or\ x^2=1.8\\\\\textrm{Square root both sides, we get:}\\\\x=\pm13.35\ or\ x=\pm1.35

Therefore,

y=-\frac{18}{x}=-\frac{18}{\pm13.35} = \pm1.35\ or\\\\y=-\frac{18}{x}=-\frac{18}{\pm1.35}=\pm13.3

Therefore, the numbers are either ±13.35 and ±1.35 or ±1.35 and ±13.3

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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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4 0
3 years ago
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Rotate the point (1,2) 90°<br> (-4,4)<br> (0,2)<br> (2,0)<br> (-2,1)
saw5 [17]

Answer: (-2,1)

Step-by-step explanation:

The point (1,2) is in quadrant 1.

When rotated 90 degrees counter clockwise, it moves to quadrant 2.

The new point becomes (-2,1)

5 0
3 years ago
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the
stellarik [79]

9514 1404 393

Answer:

  A. 0 ≤ n ≤ 7

  B. the height after 0 days (the initial height in cm)

Step-by-step explanation:

<h3>A.</h3>

The plant cannot be expected to continue its exponential growth curve, so a reasonable domain is the domain of the observations already made. The plant reached its height of about 11.26 cm after about 7 days. The reasonable domain for the growth function is ...

  0 ≤ n ≤ 7

__

<h3>B.</h3>

The y-intercept corresponds to the n=0 value, the height of the plant at the start of the study.

_____

<em>Additional comment</em>

The value of n that gives f(n) = 11.26 can be found using logarithms.

  11.26 = 8(1.05^n)

  log(11.26/8) = n·log(1.05) . . . . . . divide by 8, take logs

  n = log(11.26/8)/log(1.05) ≈ 7.00582

3 0
3 years ago
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