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2 years ago

2l6a - - 25b

" title=" {16a}^{2} - {25b}^{2} " alt=" {16a}^{2} - {25b}^{2} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Kay [80]2 years ago

6 0

Answer:

(a+5b)⋅(a−5b)

Step-by-step explanation:

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Which expression is equivalent to 4?

Alenkinab [10]

Answer:

c-10-(4+2)

Step-by-step explanation:

I don't know the answer choices because this is the correct answer

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3 years ago

Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?

Veronika [31]

Answer:

Largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

Step-by-step explanation:

We are given the following information in the question:

Right triangles whose hypotenuse has a length of 12 cm.

Let x and y be the other two sides of the triangle.

Then, by Pythagoras theorem:

$x^2 + y^2 = (12)^2 = 144\\y^2 = 144-x^2\\y = \sqrt{144-x^2}$

Perimeter of Triangle = Side 1 + Side 2 + Hypotenuse.

$P(x) = x + \sqrt{144-x^2} + 12$

where P(x) is a function of the perimeter of the triangle.

First, we differentiate P(x) with respect to x, to get,

$\frac{d(P(x))}{dx} = \frac{d(x + \sqrt{144-x^2} + 12)}{dx} = 1-\displaystyle\frac{x}{\sqrt{144-x^2}}$

Equating the first derivative to zero, we get,

$\frac{dP(x))}{dx} = 0\\\\1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0$

Solving, we get,

$1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0\\\\x = \sqrt{144-x^2}}\\\\x^2 = 144-x^2\\\\x = \sqrt{72} = 6\sqrt{2}$

Again differentiation P(x), with respect to x, using the quotient rule of differentiation.

$\frac{d^2(P(x))}{dx^2} = \displaystyle\frac{-(144-x^2)^{\frac{3}{2}}-x^2}{(144-x)^{\frac{3}{2}}}$

At x = $6\sqrt{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Then, by double derivative test, the maxima occurs at x = $6\sqrt{2}$

Thus, maxima occurs at x = $6\sqrt{2}$ for P(x).

Thus, largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

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3 years ago

Which of the following inequalities is correct?

grin007 [14]

Which of the following inequalities is correct?

-9 ≥ -7 is wrong as 9>7 but -9 < -7
-10 > |-10| is wrong as |-10|= 10
6 ≤ |-6| is right cause |-6| =6 and we have 6=6 or 6 ≤ |-6| is also right
0 < -13 is totally wrong
Have fun

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3 years ago

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IRINA_888 [86]

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Step-by-step explanation:

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3 years ago

Can someone please help me thanks :)

Dmitrij [34]

29 degrees. You can just add 12 and 17 to find this, since the 12 is negative

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3 years ago