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2 years ago

(-14+3i)-(14i) = ? Express your answer in the form (a + bi).

Mathematics

1 answer:

gayaneshka [121]2 years ago

6 0

Answer:

-14 - 11i

Step-by-step explanation:

You may be learning about the imaginary number, i. Even though i is actually the squareroot of -1, when you are doing algebra with it, it acts just like a variable does. The special thing to remember about i is that i^2 is -1. But we don't even need that right now for this problem.

(-14 + 3i) - (14i)

= -14 + 3i - 14i

Combine the i's

= -14 - 11i

That's it. The -14 is the a, and the -11 is the b in a+bi.

If necessary to fill in a computer answer that is already formatted with a plus, like:

_ + _i

then use -14 for a and -11 for b.

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OQ is a diagonal of quadrilateral NOPQ. If NO=PQ, NQO=7y-37, and POQ=2y+93, find POQ such that NOPQ is a parallelogram. A.26° B.

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This is the concept of geometry, given that NOPQ is a parallelogram, then it implies that NQO=POQ
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4 years ago

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3 years ago

A candy box is made from a piece of cardboard that measures 15 by 9 inches. Squares of equal size will be cut out of each corner

Valentin [98]

Answer:

1.82 inches

Step-by-step explanation:

Let the size of square piece cut from the corner is d.

So, the length of the box is 15 - 2y

width of the box is 9 - 2y

height of the box is d.

Volume of the box

Volume = length x width x height

V = (15 - 2y)(9 - 2y)y

V = 4y³ - 48y² + 135y

Differentiate with respect to y.

$\frac{dV}{dy}=12y^{2}-96y+135$

It is equal to zero for maxima and minima

$12y^{2}-96y+135=0$

$y=\frac{96\pm \sqrt{96^{2}-4\times 12\times 135}}{24}$

So, y = 1.82 in or 6.2 in

Now

$\frac{d^{2}{V}}{dy^{2}}=24y-96$

For y = 1.82 in, it is negative

and for y = 6.2 in, it is positive

So, the volume of the box is maximum if the height of the box is 1.82 inch.

Thus, the size of the square cut from each of the corner is 1.82 inches.

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