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Alja [10]
2 years ago
7

What is the area of an equalateral triangle of side length x?

Mathematics
1 answer:
OLEGan [10]2 years ago
5 0
First you need to make a line that is perpendicular to one side. The diagram is shown below. then the length of the line that is perpendicular to the triangle is
\frac{ \sqrt{3}x }{2}
then the area of the equilateral triangle equals to
\frac{1}{2} height  \times base
so the area would be
\frac{ \sqrt{3} {x}^{2}  }{4}

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write in graphing form please! A parabola that opens down with no stretch factor that has a vertex of (-6,5)
wolverine [178]
If it has no stretch factor, then there will be no coefficient. Meaning this is a lot easier. So, we equation is

(x+6)^2 + 5

Hope this helps!
<span />
8 0
2 years ago
20 points and brainliest <br> I’m in quiz in need it asap <br> Number 4
iren [92.7K]

Answer and step-by-step explanation:

The polar form of a complex number a+ib is the number re^{i\theta} where r = \sqrt{a^2+b^2} is called the modulus and \theta = tan^-^1 (\frac ba) is called the argument. You can switch back and forth between the two forms by either remembering the definitions or by graphing the number on Gauss plane. The advantage of using polar form is that when you multiply, divide or raise complex numbers in polar form you just multiply modules and add arguments.

(a) let's first calculate moduli and arguments

r_1 = \sqrt{(-2\sqrt3)^2+2^2}=\sqrt{12+4} = 4\\ \theta_1 = tan^-^1(\frac{2}{-2\sqrt3}) =-\pi/6\\r_2=\sqrt{1^2+1^2}=\sqrt2\\ \theta_2 = tan^-^1(\frac 11)= \pi/4

now we can write the two numbers as

z_1=4e^{-i\frac \pi6}; z_2=e^{i\frac\pi4}

(b) As noted above, the argument of the product is the sum of the arguments of the two numbers:

Arg(z_1\cdot z_2) = Arg(z_1)+Arg(z_2) = -\frac \pi6 + \frac \pi4 = \frac\pi{12}

(c) Similarly, when raising a complex number to any power, you raise the modulus to that power, and then multiply the argument for that value.

(z_1)^1^2=[4e^{-i\frac \pi6}]^1^2=4^1^2\cdot (e^{-i\frac \pi6})^1^2=2^2^4\cdot e^{-i(12)\frac\pi6}\\=2^2^4 e^{-i\cdot2\pi}=2^2^4

Now, in the last step I've used the fact that e^{i(2k\pi+x)} = e^i^x ; k\in \mathbb Z, or in other words, the complex exponential is periodic with 2\pi as a period, same as sine and cosine. You can further compute that power of two with the help of a calculator, it is around 16 million, or leave it as is.

7 0
1 year ago
Determine the number of centimeters in 2 inches.
Paul [167]

Answer:

5

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
-3x – 10 = 32Help me I need the answer
Nesterboy [21]

Answer:

<h2><u><em>x = - 14</em></u></h2>

Step-by-step explanation:

-3x – 10 = 32 Help me I need the answer

-3x – 10 = 32

-3x = 32 + 10

-3x = 42

x = 42 :(-3)

x = - 14

-----------------

check

-3 × (-14) - 10 = 32                      (remember pemdas)

42 - 10 = 32

32 = 32

the answer is good

6 0
11 months ago
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
Savatey [412]

Answer: (2, 18)

Step-by-step explanation:

When x=2, f(2)=2(3)^{2}=18.

So, it should pass through (2, 18).

8 0
1 year ago
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