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3 years ago

9

Sheila has a balance of $1190 on her credit card, which she plans to pay off by making a payment of the same amount each month.

Which of these monthly amounts will allow Sheila to pay off her balance the fastest?

2 answers:

Natasha_Volkova [10]3 years ago

6 0

The fastest payoff would occur when the monthly payment is largest.

o-na [289]3 years ago

5 0

What are the monthly amounts?

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Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

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3 years ago

A number multiplied by 3 is 33

Ber [7]

The number is 11 X 3 =33

7 0

4 years ago

(-1,1) ,(-1,4) and (1,4) are the vertices of which traingle

allochka39001 [22]

Answer:

(-1, 1), (-1, 4), and (1, 4) are the vertices of a right triangle.

Step-by-step explanation:

If you were to graph these three points on a coordinate plane, you'll notice that two of the sides form a right angle together, which means this triangle will be a right triangle. If you're looking for something more specific, it would be a right scalene triangle, where all sides are different in a right triangle.

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3 years ago

Find the solution set for this inequality 12x-18=18 must be pairs (,) !!

oksian1 [2.3K]

Answer: 0 x 3
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3 years ago

A rectangular field is four times as long as it is wide. If the perimeter of the field is 520 yards, what are the field's dimens

juin [17]

Answer:

Width = 52 yards

Length = 208 yards

Step-by-step explanation:

(2 * 4x) + 2x = 10x

10x = 520

x = 52

52 * 4 = 208

(208 * 2) + (52 * 2) = 416 + 104 = 520 yards

Your welcome!

Kayden Kohl

8th Grade Student

4 0

3 years ago