2 years ago

Factor the perfect square trinomial 25x^2-60x+36

Mathematics

1 answer:

zaharov [31]2 years ago

4 0

Since it is a perfect square trinomial, it is of the form:

a^2x^2-2abx+b^2 which simplifies to (ax-b)^2

Therefore:

sqrt(a)=sqrt(25)=5

sqrt(b)=sqrt(36)=6

Plug in a and b:

(ax-b)^2

(5x-6)^2

Test to make sure it did fit the formula:

-2abx=-60 (where x is 1)

-2(5)(6)=-60

-2(30)=-60

-60=-60

Answer:

(5x-6)^2

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Ley y = tan x. (a) Find the differential dy.(b) Evaluate dy and Δy if x = π/4 and dx = −0.1. (Round Δy to four decimal places.)

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Answer:

Required differential (a) $dy=-0.0002\times10^{3}$ and (b) $\Delta y=-0.3370$ .

Step-by-step explanation:

Given,

$y=\tan x$

Let, $y=f(x)=\tsn x\hfill (1)$

(a) To find differential,

$dy$ differentiate (1) we get,

$dy=\sec^2 x dx$

when, $x=\frac{\pi}{4}$ and dx=-0.1, then

$dy=\sec^2(\frac{\pi}{4})\times (-0.1)=-0.2$

$dy=-0.0002\times 10^{3}$ (Correct upto four decimal places)

(b) To find,

$\Delta y=\Delta f(x)=f(x+h)-f(x)$ ( where h=dy)

when $x=\frac{\pi}{4}, dx=h=-0.1$

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$=-0.3370$

Correct upto four decimal places.

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