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3 years ago

If the perimeter of the following triangle is 7x-2, what is the length of the unknown side?

Mathematics

2 answers:

alisha [4.7K]3 years ago

5 0

unknown side = <span>7x-2 - (3x - 9 + x + 7)
</span> unknown side = 7x - 2 -3x + 9 -x - 7
unknown side = = 3x

answer

unknown side = 3x

AnnZ [28]3 years ago

4 0

perimeter = s+s+s

so 7x-2 = (3x-9) + (x+7) + ?

3x-9 + x+7 = 4x-2

7x-2 - 4x-2 = 3x

remaining side is 3x

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Jamie makes a road through his wooded lot. What is the area of the part of the lot that has trees?

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3 years ago

the population of a town is 9000, and it grows at a rate of 7% per year what will the population be in 6 years

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Answer:

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Step-by-step explanation:

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3 years ago

Consider the surface defined by the equation x3 + y3 + z3 = 3xyz. Use implicit differ- ∂z entiation to find ∂x. (Note z is not a

Aloiza [94]

Answer:

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

Step-by-step explanation:

Given equation is $x^{3}+y^{3}+z^{3}=3xyz$ ………………(1)

we use derivative formula $\frac{d}{dx}(x^{n}) = n x^{n-1}$

$\frac{d}{dx}(x^{3)} = 3 x^{2}$

$\frac{d}{dx}(z^{3)} = 3 z^{2}$

And also apply 'u v' formula

$\frac{d}{dx}(uv}) = u\frac{d}{dx}(v)+v\frac{d}{dx}(u)$

Differentiating equation (1) partially with respective to 'x' , we treated 'y' as constant.

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =3y(x\frac{∂z}{∂x}+z(1))$ ( here y treated as constant so the derivative of constant function is zero in addition but in multiplication the constant is keep as like 'y').

on simplification , we get

$(3x^{2} +0+3z^{2}\frac{∂z}{∂x}) =(3yx\frac{∂z}{∂x}+3yz)$

again simplification, we get

$3z^{2}\frac{∂z}{∂x}- 3yx\frac{∂z}{∂x}=3yz-3x^{2}$

taking common ' $\frac{∂z}{∂x}$ on left on side , we get

$(3z^{2}- 3yx)\frac{∂z}{∂x}=3yz-3x^{2}$

dividing ' $(3z^{2}- 3yx)$ on both sides, we get

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

<u>Final answer</u>:-

$\frac{∂z}{∂x}=\frac{(3yz-3x^{2})}{3z^{2} -3xy}$

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