All categories

3 years ago

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

You might be interested in

(-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