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2 years ago

What is the area of the figure

Mathematics

1 answer:

Free_Kalibri [48]2 years ago

8 0

Answer:

112.5ft^2

Step-by-step explanation:

10 x 9 = 90

9 × 5 × .5 = 22.5

90 + 22.5 = 112.5

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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,

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

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

5 0

3 years ago

At the fair, 220 balloons are given to 40 children, 3/8 of whom are girls. Each boy receives the same number of balloons. Each g

mixer [17]

Po
Methane(CH4)
Ethane(C2H6)
Propane(C3H8)
Butane(C4H10)
Pentane(C5H12)
Hexane(C6H14)
Jul 3, 2018
http://www.gcesystems.com › what-...

5 0

2 years ago

Customers at an ice cream shop took a survey. The results showed that 144 customers rated the shop as being "very satisfactory."

stepladder [879]

Answer:

320 customers is the answer

Step-by-step explanation:

1. You have to divide 144 by 45% to find one percent of the customers (you get 3.2).

2. Once you get one percent of all of the customers (3.2) you multiply it by 100 to get 100 percent of the customers (or total number of customers).

So, 320 total customers

Have a great day, I hope you like the explination.

7 0

3 years ago

A baker’s dozen (13) of cookies is on sale for $2.08.

poizon [28]

So taking this as if there are 13 dozens of cookies. First we do 13 times 12 which would be 156 cookies in total. Then 156 cookies times 2.08 is 324.48

4 0

3 years ago

Read 2 more answers

Which expression is a factor of 10x^2+11x+3

Ulleksa [173]

Answer:

The factors are (5x + 3) and (2x + 1)

Step-by-step explanation:

When you need to factor a quadratic, and the coefficient of the x² is not 1, use the slide and divide method.

The general form of a quadratic is ax² + bx + c

Factor: 10x² + 11x + 3

Here a = 10, b = 11, and c = 3

Step 1: Multiply ac, we SLIDE a over to c. Notice the 10 is gone for now..

x² + 11x + 30

Step 2: Factor this (this step will always factor)

x² + 11x + 30 = (x + 5)(x + 6)

So the factors are (x + 5)(x + 6), but we now need to DIVIDE by a, since we multiplied it into c before. We divide the constants in the factors...

(x + 5/10 )(x + 6/10 )

Now reduce the fractions as much as possible...

(x + 1/2 )(x + 3/5)

*If they don't reduce to a whole number, SLIDE the denominator over as a coefficient of x....

(2x + 1)(5x + 3) *2 slide over in front of x, 5 slide over in front of x, the fractions are gone!

These are our factors!

5 0

3 years ago