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3 years ago

Need help with a and b parts

Mathematics

1 answer:

Masja [62]3 years ago

6 0

Answer:

a) 10/27 or 0.37037

b) -8/7

Step-by-step explanation:

a) Enter x=-5 into both equations and divide h(-5)/g(-5). That yields 10/27 or 0.37037037037 . . .

b) g(x) cannot be 0 (can't divide by 0. That would occur if x = -8/7, so it (-8/7) is not in the domain.

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What is 2x + 4x + 4 = 4(x + 4) and step by step and Highlight / circle the error

mario62 [17]

Answer:

x = 6 and the +4x is wrong

Step-by-step explanation:

2x + 4x + 4 = 4(x + 4)

6x + 4 = 4x + 16

+4x +4x <--( <u>This part is wrong</u> )

10x + 4 = 16

-4 -4

10x = 12

10 10

x = 1.2

Correct steps

2x + 4x + 4 = 4(x + 4)

6x + 4 = 4x + 16

-4x -4x

2x + 4 = 16

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2x = 12

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3 years ago

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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

A scuba diver is at an elevation of −38feet. The diver starts moving at a rate of −12 feet per minute. Identify an inequality th

solniwko [45]

Answer:

x = 13 1/2 or 13.5

Step-by-step explanation:

Flip Equation

-38 - 12x = -200

-12x -38 = -200

Add 38 to both sides

-12x -38 + 38 = -200 + 38

-12x = -162

Divide

-12x/-12 = -162/-12

x = 27/2

Simplify

27/2 = 13 1/2

x = 13 1/2

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3 years ago