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3 years ago

How to find the area of a circle with the circumference?

1 answer:

5 0

You can abuse the fact that PI is Circumference/diameter.

This means that, to find the diameter, you would have to do the following:

PI = circumference/diameter
(You can choose the number of decimals of PI, based on how accurate you want the diameter. 3.14 tends to work for most cases.)

After youve done this, you would be able to find the diameter like this:
PI*diameter = circumference
diameter = Circumference/pi

Then, you can use the diameter/2 to find the radius, like this:
radius = diameter/2

After this, you can simply use the formula for the surface area of a circle, like this:

SA = PI*Radius^2

I might be able to add an example, if really needed.

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X^{2} - 8x + 7 = 0<br> Solve by completing the square. Also can you include steps?

iren [92.7K]

Answer:

{1, 7}

Step-by-step explanation:

Start with x^2 - 8x + 7 = 0.

We want to modify the first two terms to resemble x^2 - ax + b - b, where a is the coefficient (here -8) of the x term and b is the square of half of a.

Here, a = -8. Half of that is -4. The square of -4 is 16, and this is the value of b.

Write out x^2 - 8x as x^2 - 8x + 16 - 16. This is the perfect square of -4, added to x^2 - 8x and then subtracted from the result

Then the original equation, x^2 - 8x + 7 = 0, can be rewritten as:

x^2 - 8x + 16 - 16 + 7 = 0, and then as (x - 4)^2 - 9, or (x - 4)^2 = 9.

We want to solve this result for x. To do this, take the square root of both sides:

x - 4 = ±√9, or x - 4 = ±3.

Adding 4 to both sides, we get:

x = 4 ± 3. Thus, the solutions are x = 4 + 3 = 7 and x = 4 - 3 = 1.

6 0

3 years ago

Read 2 more answers

2d=a-b/b-c - solve for a

Readme [11.4K]

$2d=\frac{a-b}{b-c}\\\\\frac{a-b}{b-c}=2d\ \ \ \ \ |multiply\ both\ sides\ by\ (b-c)\\\\a-b=2d(b-c)\ \ \ \ |add\ "b"\ to\ both\ sides\\\\\boxed{a=2bd-2cd+b}$

7 0

3 years ago

Unit rate for $56 and 25 gal

Anna35 [415]

You would have to divide $56 divided by 25 gallons which would equal $2.24 that the answer I hope it helped

8 0

3 years ago

Al factorizar el trinomio cuadrado perfecto, obtenemos el siguiente resultado: (que no se como resolver) xd algun pro que sepa r

PolarNik [594]

Answer:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

Step-by-step explanation:

<u>Trinomio Cuadrado Perfecto</u>

El producto notable llamado cuadrado de un binomio se expresa como:

$(a-b)^2=a^2-2ab+b^2$

Si se tiene un trinomio, es posible convertirlo en un cuadrado perfecto si cumple con las condiciones impuestas en la fórmula:

* El primer término es un cuadrado perfecto

* El último término es un cuadrado perfecto

* El segundo término es el doble del proudcto de los dos términos del binomio.

Tenemos la expresión:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}$

$\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8$

$\displaystyle b=\frac{1}{7}mpz^4$

Nos cercioramos de que el término central es 2ab:

$\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4$

Operando:

$\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5$

Una vez verificado, ahora podemos decir que:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

5 0

2 years ago

What is the value of x?

adelina 88 [10]

This is an equilateral triangle, which is a triangle that has 3 congruent/equal sides and 3 congruent angles.

To find "x", you can set the sides equal to each other because they are suppose to be the same length (you can just do two sides because all of the sides are the same)

[Side AB = Side BC]

4x - 10 = 3x + 2 Subtract 3x on both sides

x - 10 = 2 Add 10 on both sides

x = 12

[proof]

Side AB:

4x - 10 Plug in 12 for x

4(12) - 10 = 48 - 10 = 38

Side BC:

3x + 2 Plug in 12 for x

3(12) + 2 = 36 + 2 = 38

Side AC:

5x - 22 Plug in 12 for x

5(12) - 22 = 60 - 22 = 38

This is also an equilateral triangle (the tick marks show that the sides are the same)

A triangle is 180°. So the three angles add up to 180°.

Since this is an equilateral triangle, all the angles should be the same.

Each angle is 60°

[60° + 60° + 60° = 180° or you could have divided 180 by 3 = 60]

Now that you know each angle is 60°, you can do:

(2x - 4)° = 60°

2x - 4 = 60 Add 4 on both sides

2x = 64 Divide 2 on both sides

x = 32

4 0

2 years ago