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AlladinOne [14]
2 years ago
8

For what values of x and y is the equation (x2 + y2)2 = (x2 – y2)2 + (2xy)2 true?

Mathematics
1 answer:
denis-greek [22]2 years ago
6 0

Answer:

A) all values of x, and all values of y

B) (3a + 4b) (9a² − 12ab + 16b²)

Step-by-step explanation:

(x² + y²)² = (x² − y²)² + (2xy)²

x⁴ + 2x²y² + y⁴ = x⁴ − 2x²y² + y⁴ + 4x²y²

x⁴ + 2x²y² + y⁴ = x⁴ + 2x²y² + y⁴

27a³ + 64b³

(3a)³ + (4b)³

(3a + 4b) (9a² − 12ab + 16b²)

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Answer:

The value of function at x = 2 is 8.

Step-by-step explanation:

Given : Function f(x)=2x^2+5\sqrt{x-2}

We have to find the value of given function at x = 2 , that is f(2)

Consider the given function  f(x)=2x^2+5\sqrt{x-2}

To find the value f(2) put x = 2 in given function ,

We have,

f(2)=2(2)^2+5\sqrt{2-2}

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4 0
3 years ago
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(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal pla
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Answer:

following are the solution to the given points:

Step-by-step explanation:

In point a:

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    =\sqrt{1+1}\\\\=\sqrt{2}

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\frac{\vec{v}}{|\vec{v}|} = \frac{-1i+1j}{\sqrt{2}}

the point Q is at a distance h from P(6,6) Here, h=0.1  

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In point b:

Calculating the directional derivative of f (x, y) = \sqrt{x+3y} at P in the direction of \vec{v}

f_{PQ} (P) =\fracx{f(Q)-f(P)}{h}\\\\

            =\frac{f(5.92928 ,6.07071)-f(6,6)}{0.1}\\\\=\frac{\sqrt{(5.92928+ 3 \times 6.07071)}-\sqrt{(6+ 3\times 6)}}{0.1}\\\\= \frac{0.197651557}{0.1}\\\\= 1.97651557

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Computing the directional derivative using the partial derivatives of f.

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