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2 years ago

Solve for x.

Mathematics

2 answers:

Alex Ar [27]2 years ago

6 0

Answer:

Step-by-step explanation:

3x^2 - 4x - 2 = 0

Solution:

x = 2 + sqrt 10/3

x = 2 - sqrt 10/3

Decimal:

x = 1.72076.....

x = 0.38743.....

Solve Quadratic equation:

3x^2 - 4x - 2 = 0

Use quadratic formula:

a = 3

b = -4

c = -2

Showing Work:

x = -b +/- sqrt b^2 - 4ac/2a

x = -( -4) +/- sqrt (-4^2) - 4(3) ( -2)/ 2(3)

x = 4 +/- sqrt 40/6

Ans: x = 2/3 + 1/3 sqrt 10 or x = 2/3 + -1/3 sqrt 10

Hope that helps!!!!!! : ) -P-

Sphinxa [80]2 years ago

4 0

Answer

1.72 or -0.387

Explanation

3x²-4x-2=0

3x²-4x = 2

x² - (4/3)x = 2/3

x² - (4/3)x + (2/3)² = 2/3 + 4/9

(x - 2/3)² = 10/9

x - 2/3 = √10/3 or x - 2/3 = -√10/3

x = √10/3 + 2/3 or x = -√10/3 + 2/3

= 1.72 or = -0.387

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3 years ago

Read 2 more answers

An open metal tank of square base has a volume of 123 m^3

snow_lady [41]

Answer:

a) h = 123/x^2

b) S = x^2 +492/x

c) x ≈ 6.27

d) S'' = 6; area is a minimum (Y)

e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

123 = x^2·h

h = 123/x^2

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

$S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}$

c) The derivative of the area with respect to x is ...

$S'=2x-\dfrac{492}{x^2}$

When this is zero, area is at an extreme.

$0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583$

d) The second derivative is ...

$S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6$

This is positive, so the value of x found represents a minimum of the area function.

e) The minimum area is ...

$S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78$

The minimum area of metal used is about 117.78 m².

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2 years ago

Curve fitting is a methode of finding

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2 years ago

What does y equal in this problem 5y-3(2-y)=10

Pepsi [2]

Steps:

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Hope this helps! :)

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2 years ago

Joey and Armando live on the same st as the park. The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando'

AleksandrR [38]

Let's start by assuming Armando's house is between Joey's and the park.

Let $x$ be the distance Joey walked to Armando's house.

The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando's home. Then Joey and Armando walk 3/5 mile to the park.

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$x = \dfrac{9}{10} - \dfrac{3}{5} = \dfrac{9}{10} -\dfrac{6}{10} = \dfrac{3}{10}$

That's probably the answer they're looking for. But what if the park is between Joey and Armando's houses or Joey is between the park and Armando? (The latter isn't really possible with the given distances.)

Let $a, b, c$ be the distances between three collinear points like we have here. Our equation is really a few equations in one, something like

$\pm a \pm b = \pm c$

Let's get rid of the plus/minuses. Squaring,

$a^2 + b^2\pm 2ab = c^2$

$\pm 2ab = c^2-a^2-b^2$

$4a^2b^2 = (c^2-a^2-b^2)^2$

For us, that's a quadratic equation for $c^2$

$4(9/10)^2(3/5)^2= (c^2-(9/10)^2 - (3/5)^2)^2$

I'll skip right to the solutions,

$c^2=\dfrac{9}{100} \textrm{ or } c^2=\dfrac{9}{4}$

$c=\dfrac{3}{10} \textrm{ or } c=\dfrac{3}{2}$

We could have gotten the 3/2 just by adding 9/10+3/5 but this was more fun.

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