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3 years ago

What are the solutions of 3x^2-x+4=0

1 answer:

6 0

3x² -x+4=0

We can use quadratic formula
a=3, b= -1, c=4
$x= \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} 
\\ \\ x= \frac{1+/- \sqrt{1-4*3*4} }{2*3} 
\\ \\ x = \frac{1+/- \sqrt{-47} }{6} 

This equation does not have real roots, it has only 2 imaginary roots.$

$x= \frac{1+ \sqrt{47}i }{6} 
\\ \\ x= \frac{1- \sqrt{47}i }{6}$

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Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?

Veronika [31]

Answer:

Largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

Step-by-step explanation:

We are given the following information in the question:

Right triangles whose hypotenuse has a length of 12 cm.

Let x and y be the other two sides of the triangle.

Then, by Pythagoras theorem:

$x^2 + y^2 = (12)^2 = 144\\y^2 = 144-x^2\\y = \sqrt{144-x^2}$

Perimeter of Triangle = Side 1 + Side 2 + Hypotenuse.

$P(x) = x + \sqrt{144-x^2} + 12$

where P(x) is a function of the perimeter of the triangle.

First, we differentiate P(x) with respect to x, to get,

$\frac{d(P(x))}{dx} = \frac{d(x + \sqrt{144-x^2} + 12)}{dx} = 1-\displaystyle\frac{x}{\sqrt{144-x^2}}$

Equating the first derivative to zero, we get,

$\frac{dP(x))}{dx} = 0\\\\1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0$

Solving, we get,

$1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0\\\\x = \sqrt{144-x^2}}\\\\x^2 = 144-x^2\\\\x = \sqrt{72} = 6\sqrt{2}$

Again differentiation P(x), with respect to x, using the quotient rule of differentiation.

$\frac{d^2(P(x))}{dx^2} = \displaystyle\frac{-(144-x^2)^{\frac{3}{2}}-x^2}{(144-x)^{\frac{3}{2}}}$

At x = $6\sqrt{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Then, by double derivative test, the maxima occurs at x = $6\sqrt{2}$

Thus, maxima occurs at x = $6\sqrt{2}$ for P(x).

Thus, largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

7 0

3 years ago

The perimeter of a pentagon (5 sides) is 10.5 centimeters. The sides are x,x,x,x and 1.7 cm. What is the value of x

Drupady [299]

Answer:

What did she sayyyyyyyy? Um I don't know what x,x,x,x is ma'am or sir

Step-by-step explanation:

4 0

3 years ago

Find the perimeter and the area.PLEASE HELP!

alexandr1967 [171]

Answer:

4. P=32 A=64 and 3 is just complicated sorry

Step-by-step explanation:

4 0

3 years ago

What is the slope-intercept equation of the line below?

yKpoI14uk [10]

Slope is known as rise over run. Because the line is pointing "\", it is negative.

The rise, the distance from one point to another, specifically from (0,4) to (1,1) is 3, as 4-1=3. your run is 1-0=1.

So your rise over run is -3/1 or, -3.

Your y-int is where when x=0, y=?

In this case y=4 when x=0.

Your equation is

y=-3x+4

5 0

2 years ago

Evaluate -4a + 10 when a = -2

stiks02 [169]

Answer:

18

Step-by-step explanation:

replace a with -2

-4(-2) + 10

multiply the -4 and the -2, the negatives cancel out and leave you with 8

8 +10

just add

4 0

3 years ago