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3 years ago

If a+b+c=16 and a^2+b^2+c^2=90 then find the value a^3+b^3+c^3-3abc

1 answer:

3 0

$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\\(16)^2=90+2(ab+bc+ca)\\256-90=2(ab+bc+ca)\\166/2=ab+bc+ca\\83=ab+bc+ca\\a^3-b^3-c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)\\(a+b+c)(a^2+b^2+c^2-(ab+bc+ca))\\16(90-(83))\\16(7)\\=112$

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Can someone solve this

marysya [2.9K]

From the Arithmetic Information given, Pr = 0.049375 ≠ -8.050625 ≠ 0.0325 See explanation below.

<h3>

What are the step by steps solution to the questions above?</h3>

First, lets us restate the question properly. We have

Pr = 1 - ((6*12+6)/80)² = 1 - ((9*12²)/1600) - ((3*12*6)/1600) - (6²/6400) = 1 - 0.005625 * 12² - 0.001875 * 12 * 6 - 0.00015625 * 6²

Note that there are three equals signs. So lets divide the problem according and solve for the different parts.

Lets 1 - ((6*12+6)/80)² ............A

1 - ((9*12²)/1600) - ((3*12*6)/1600) - (6²/6400) .............B; and

1 - 0.005625 * 12² - 0.001875 * 12 * 6 - 0.00015625 * 6² ........C

Solving for A we have

1 - (78/80)²

= 1 - (0.975)²

= 1 - 0.950625

A = 0.049375

Solving for B we have

1 - ((9*12²)/1600) - ((3*12*6)/1600) - (6²/6400)

= 1- (14,256/1600) - (216/1600) - (36/6400)
= 1 - 8.91 - 0.135 - 0.005625

B = -8.050625

Solving for C we have

1 - 0.005625 * 12² - 0.001875 * 12 * 6 - 0.00015625 * 6²

= 1 - 0.005625 * 144 - 0.001875 * 12 * 6 - 0.00015625 * 144

= 0.0325

In summary we can state that:

A = 0.049375

B = -8.050625

C = 0.0325

Given that there were no abstract quantities, we can state that

Pr = A ≠ B ≠C or

Pr = 0.049375 ≠ -8.050625 ≠ 0.0325

Learn more about equations with equal signs at

brainly.com/question/18924248
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4 0

2 years ago

Find the side length of the equilateral triangle whose area is the square root of 3 cm2

Alla [95]

Here, Given

Area of Equilateral triangle = 3cm2

therefore, we know;

Area of Equilateral triangle =( $\sqrt{3}$ ÷4)× $a^{2}$

so,

3 =( $\sqrt{3}$ ÷4)× $a^{2}$

3÷( $\sqrt{3}$ ÷4) = $a^{2}$

2.63 cm = a .

The area of an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of the shape is the number of unit squares that fit inside.

Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.

Learn more about Area of triangle here: brainly.com/question/17335144

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2 years ago

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