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Masteriza [31]
3 years ago
15

The equations for two distinct lines are given below.

Mathematics
1 answer:
Natali5045456 [20]3 years ago
4 0

answer for this question is (d) 3

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(-2 √(-49)(5 √(-100)
Tamiku [17]

Answer:

The answer is... 700

4 0
3 years ago
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
What is the lateral area of the prism? Assume the figure is resting on its base.
dolphi86 [110]
Check the picture below.

the lateral area, namely the area of the sides, as you see in the picture, is really just the area of 6 rectangles.

front and back, two rectangles of 5x25,

left and right, two rectangles of 2x25.

simply get the area of each and sum them up, that's the lateral area of the prism.

\bf \stackrel{\textit{front and back}}{2(5\cdot 25)}~~~~+~~~~\stackrel{\textit{left and right}}{2(2\cdot 25)}

8 0
3 years ago
Read 2 more answers
Which of the following represents a rotation of ΔEFG, which has vertices E (4, −3), F (−7, 5), and G (2, 8), about the origin by
9966 [12]
REMEMBER: A rotation of 180 degrees means you flip both x and y numbers

E(-4,3)
F(7,-5)
G(-2,-8)
3 0
3 years ago
-5x(4x+6)=21 whats the answer
AysviL [449]
1.) Multiply the parentheses by -5x
2.) Move the constant to the left
3.) Change the signs
4.) Solve the quadratic equation
5.) Evaluate the powers and multiply
6.) Calculate

Answer: No solution
4 0
4 years ago
Read 2 more answers
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