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3 years ago

What is the length of the figure?

Mathematics

1 answer:

nadezda [96]3 years ago

4 0

There are two ways to do this. One is by adding up the squares, which takes a while. The other way is if you notice that the length along the bottom is the same as that long the top, and the same is true for the sides. While it does not appear this way at first, imagine that that was the floor plan of a house. If you looked at it from the side, you wouldn't see the dent in the corner, only one side. Since the length of the top is 13 units, from -7 to 6, and the side is also 13 units, from -6 to 7, the answer is $13*2 + 13* 2 = 26 + 26 = 52$

52 units long.

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Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}

miskamm [114]

Answer:

$-3+i\sqrt{3} , 1+\sqrt{3}$

Step-by-step explanation:

Given that alpha and beta be conjugate complex numbers

such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}.

Let

$\alpha = x+iy\\\beta = x-iy$

since they are conjugates

$\alpha-\beta = x+iy-(x-iy)\\= 2iy= 2i\sqrt{3} \\y =\sqrt{3}$

$\frac{\alpha}{\beta^2} }\\=\frac{x+i\sqrt{3} }{(x-i\sqrt{3})^2} \\=\frac{x+i\sqrt{3}}{x^2-3-2i\sqrt{3}} \\=\frac{x+i\sqrt{3}((x^2-3+2i\sqrt{3}) }{(x^2-3-2i\sqrt{3)}(x^2-3-2i\sqrt{3})}$

Imaginary part of the above =0

i.e. $\sqrt{3} (x^2-3)+2x\sqrt{3} =0\\x^2+2x-3=0\\(x+3)(x-1) =0\\x=-3,1$

So the value of alpha = $-3+i\sqrt{3} , 1+\sqrt{3}$

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3 years ago

Avery and Carmen both have summer jobs. Avery gets paid 360 bucks every 4 weeks, how much money does she make in one week.

artcher [175]

Avery gets paid 90 bucks per week

Step-by-step explanation:

The per month payment is obtained by dividing the whole amount by time.

Given

Avery gets paid 360 for 4 weeks

In order to find her payment for one week, we have to divide the total amount by 4 to get the payment for one week

So,

$One\ week's\ payment = \frac{Total\ payment}{number\ of\ weeks}\\=\frac{360}{4}\\= 90$

Avery gets paid 90 bucks per week

Keywords: Unit price, payment

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