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Anika [276]
3 years ago
6

Write the expression as a square of a binomial: 9/25a^6b^2-a^4b^4+25/36a^2b^6

Mathematics
2 answers:
sergiy2304 [10]3 years ago
6 0

Answer:

a^2b^2(18a^2-25b^2)^2 over 900

Step-by-step explanation:

Over 900 means that is a fraction

kolbaska11 [484]3 years ago
4 0

Answer:

  (3/5a^3b -5/6ab^3)^2

Step-by-step explanation:

Your trinomial

  9/25a^6b^2 - a^4b^4 + 25/36a^2b^6

has three terms, as it must if it is to be the square of a binomial. The terms all have degree 8, so each of the terms of its square root will have degree 8/2 = 4.

The term with the highest degree of the variable "a" is the first one ...

  9/25a^6b^2

All parts of this term are perfect squares:

  • 9/25 = (3/5)^2
  • a^6 = (a^3)^2
  • b^2 = (b)^2

so, this term can be written as the square ...

  (3/5a^3b)^2

___

The term with the highest degree of the variable "b" is the last one ...

  25/36a^2b^6

All parts of this term are perfect squares:

  • 25/36 = (5/6)^2
  • a^2 = (a)^2
  • b^6 = (b^3)^2

so, this term can be written as the square ...

  (5/6ab^3)^2

___

If the given trinomial is truly the square of a binomial, then the remaining term, the middle one, will be twice the product of the terms of the binomial. Here that means we want to make sure that ...

  a^4b^4 = 2 · (3/5a^3b) · (5/6ab^3)

  = 2 · 3/5 · 5/6 · a^4b^4

  = a^4b^4 . . . . . . as required

So, we know the two terms of the binomial, 3/5a^3b and 5/6ab^3, and we know the sign of the middle term of the given trinomial is negative. That negative sign means the sign in our binomial must be negative. Then the expression we're asked to write is ...

  9/25a^6b^2 - a^4b^4 + 25/36a^2b^6 = (3/5a^3b -5/6ab^3)^2

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Use a graphing calculator to graph f(x) = x+cos(kx). Use calculus to determine which values of k lead to a function with no loca
nataly862011 [7]

Answer:

Below, you can see the graph of the function:

f(x) = x + cos(k*x)

for different values of k, as follows:

red: k = 1

green: k = 2

orange: k = 0.

Now let's find the values of k such that our function does not have local maxima nor local minima.

First, remember that for a given function f(x), the local maxima or minima points are related to the zeros of the first derivate of f(x).

This means that if:

f'(x0) = 0.

Then x0 is a maxima, minima or an inflection point.

Then if a function is such that the f'(x) ≠ 0 , ∀x, then this function will not have local maxima nor minima.

Now we have:

f(x) = x + cos(k*x)

then:

f'(x) = 1  - k*sin(k*x)

This function will be zero when:

1 = k*sin(k*x)

1/k = sin(k*x)

now, remember that -1 ≤ sin(θ) ≤ 1

then if 1/k is smaller than -1, or larger than 1, we will not have zeros.

And this will happen if -1 < k < 1.

7 0
2 years ago
The cost (in dollars) of a custom made sweatshirt is represented by 3.5n +29.99, where n is the number of different colors in th
juin [17]

Answer:

52.5n+449.85

Step-by-step explanation:

The cost is given for <em>1 sweatshirt</em>. To find the cost of 15 sweatshirts, we need to multiply the expression by 15. Let's do this:

15(3.5n+29.99)\\=15(3.5n+29.99)\\=15(3.5n)+15(29.99)\\=52.5n+449.85

This is the expression that represents the cost of 15 sweatshirts.

8 0
3 years ago
What is the shortest Hamilton path for the vertex-edge graph?
marin [14]

Answer:

The first one is the answer

3 0
3 years ago
Find the distance between the points (-1,-7) and (8,-9). The answer must be a whole number or a fully simplified radical express
ruslelena [56]

Answer:

The answer is

<h2>\sqrt{85}  \:  \:  \: units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  }  \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-1,-7) and (8,-9)

The distance between them is

d =  \sqrt{( { - 1 - 8})^{2}  +  ({ - 7 + 9})^{2} }  \\  =  \sqrt{ ({  - 9})^{2} +  {2}^{2}  }  \\  =  \sqrt{81 + 4}

We have the final answer as

\sqrt{85}  \:  \:  \: units

Hope this helps you

3 0
3 years ago
What is |3.5| simplified?
erastovalidia [21]
|3.5| = 3.5

Any negative or positive number will always have an absolute value that is positive.

For example, | -3.5| = 3.5

3.5 can also be expressed a fraction.

3.5 * 2/2 = 7/2
8 0
3 years ago
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