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2 years ago

If alpha beta are the roots of the equation

Mathematics

1 answer:

Vikki [24]2 years ago

8 0

Answer:

Step-by-step explanation:

Hello, I believe that we can consider a different from 0.

By definition of the roots we can write.

$ax^2+bx+c=a(x-\alpha)(x-\beta)=a(x^2-(\alpha + \beta)x+\alpha \cdot \beta)\\\\\text{So we can say that:}\\\\\alpha + \beta = \dfrac{-b}{a}\\\\\alpha \cdot \beta=\dfrac{c}{a}\\\\\text{So the expected quadratic equation is}\\\\(x+\dfrac{b}{a})(x-\dfrac{c}{a})=0\\\\ \Large \boxed{\sf \bf \ (ax+b)(ax-c)=0 \ }$

Thank you

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Which of the following is closest to the area of the shaded region below?

enot [183]

Answer:

C is the answer

Step-by-step explanation:

Find the area of the whole circle, r=12cm

=pie× radius sq

=3.14×12×12

=452.16cm sq

The are of the smaller circle, r=6cm

=same formula

=3.14×6×6

=113.04cm sq

Subtract them to find the area of the shaded region

452.16 - 113.04

=339.12

Closest is answer is 339 cm sq which is c

Hope it's helpful..... 

5 0

2 years ago

Helpppp please!!!!!!!!!!

hram777 [196]

Answer:

128.86 cm^2

Step-by-step explanation:

So to start off we need to find the area of the rectangle.

The formula for the area of a rectangle is $l$ × $w$ .

L stands for the length which is 12 and w is the width which is 11.

So 11 × 12 = 132 cm^2.

Now time for the area of a circle.

The formula for that is $\pi r^{2}$ .

So first we need to do 1 × 1 which is 1.

Then 1 × $\pi$ which is just $\pi$ .

Then we do 132 - $\pi$ which is an irrational number.

It looks like this shortened 128.858407346.

Now rounding to the nearest hundreth it would be 128.86 cm^2.

Hence, the area of the shaded region is 128.86 cm^2.

8 0

2 years ago

Use synthetic division to find the expression for the area of the base of a rectangular prism with height x 4 and volume x3 2x2

IRINA_888 [86]

The expression for the area of the base of Prism is x2 – 2x – 9

The volume of a rectangular prism is this

Volume = Area x Height

Substituting the given expressions

x3 + 2x2 - 17x - 36 = Area x (x + 4)

Area = (x3 + 2x2 - 17x - 36) / (x + 4)

Now, let's use synthetic division

-4 | 1 2 -17 -36

---- __-4___8___36

1 -2 -9 0

The expression for the area is

Area = x2 - 2x - 9

Learn more about Synthetic Division:

brainly.com/question/14645972

#SPJ4

6 0

1 year ago

Avani wrote the linear equation y = 5 x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5 x + 4 and t

Margarita [4]

Avani wrote the linear equation y = 5x + 4. Then, she wrote the equation of the line that is perpendicular to y = 5x+ 4 and that passes through (15,–2). If her new equation is in the form $y-\frac{1}{5}x+b$ , what is the value of b?

$\bf y=mx+b$

m is the slope
b is the y-intercept

The equation of a line that is perpendicular to another line always has the opposite reciprocal slope. In the original equation, the slope is 5. The opposite of 5, which refers to the sign, is -5. The reciprocal of -5 is -1/5. That means the slope of the new line is -1/5.

The perpendicular line:

Has a slope of $-\frac{1}{5}$

Passes through the point (15, -2)

To find the equation of a line that passes through a specific point, you need to use slope-intercept form.

$\bf y-y_{1} =m(x-x_{1})$

y₁ is the y-value of the point
m is the slope
x₁ is the x-value of the point

y₁ is -2, m is -1/5, and x₁ is 15.

Substitute the known values into the equation:

$y-(-2)=-\frac{1}{5}(x-15) \rightarrow y+2= -\frac{1}{5}(x-15)$

Open the parentheses and distribute:

$-\frac{1}{5}(x-15) \rightarrow -\frac{1}{5} \cdot x\ + -\frac{1}{5} \cdot -15 \rightarrow -\frac{1}{5}x +3$

The new equation will be:

$y+2=-\frac{1}{5}x+3$

Lastly, you need to move the positive 2 to the other side to keep it in y = mx + b form.

$y+2-2=-\frac{1}{5}x+3-2 \rightarrow y=-\frac{1}{5}x+1$

The equation of the perpendicular line is:

$\bf y=-\frac{1}{5}x+1$

The value of b is 1.

5 0

2 years ago

Use the divergence theorem to calculate the surface integral ??s f · ds; that is, calculate the flux of f across s. f(x,y,z = ex

Kamila [148]

$\mathbf f(x,y,z)=e^x\sin y\,\mathbf i+e^x\cos y\,\mathbf j+yz^2\,\mathbf k$

By the divergence theorem, the surface integral can be evaluated by computing the triple integral

$\displaystyle\iint_Sf(x,y,z)\,\mathrm dS=\iiint_V\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV$
$=\displaystyle\iiint_V\left(\dfrac{\mathrm d\mathbf f}{\mathrm dx}+\dfrac{\mathrm d\mathbf f}{\mathrm dy}+\dfrac{\mathrm d\mathbf f}{\mathrm dz}\right)\,\mathrm dV$
$=\displaystyle\int_{x=0}^{x=4}\int_{y=0}^{y=3}\int_{z=0}^{z=4}2yz\,\mathrm dz\,\mathrm dy\,\mathrm dx$
$=72$

7 0

2 years ago