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3 years ago

-4x –12 = 48 a.x = 9 b.x = -9 c.x = 15 d.x = -15

Mathematics

1 answer:

Mumz [18]3 years ago

3 0

Answer:

d) x= -15

Step-by-step explanation:

-4x-12=48

1. Add 12 to both sides

-4x-12+12=48+12

2. -4x=60

3. Divide -4 from both sides

Final Answer: x= -15

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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

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follow

guajiro [1.7K]

Answer:

a) x = 1.52

b) s = 1.16

Step-by-step explanation:

We have that:

5 students watched 0 movies.

9 students watched 1 movie.

5 students watched 2 movies.

5 students watched 3 movies.

1 student watched 4 movies.

(a) Find the sample mean x.

Sum divided by the number of students. So

$x = \frac{5*0 + 9*1 + 5*2 + 5*3 + 1*4}{5 + 9 + 5 + 5 + 1} = \frac{38}{25} = 1.52$

(b) Find the approximate sample standard deviation, s.

Standard deviation of the sample.

Square root of the sum of the squares of the values subtracted from the mean, divided by the sample size subtracted by 1. So

$s = \sqrt{\frac{5*(0-1.52)^2 + 9*(1-1.52)^2 + 5*(2-1.52)^2 + 5*(3-1.52)^2 + 1*(4-1.52)^2}{24}} = \sqrt{\frac{32.24}{24}} = 1.16$

3 0

3 years ago

(a) 5.33 cm

PolarNik [594]

Answer:

es la b 6.33 amigo ;) adios

3 0

3 years ago

(1,4) and (2,6) in slope-intercept form

bogdanovich [222]

Answer:

Slope is 2

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

in a study evaluating the relationship between stress and muscle cramps, half the subjects are randomly assigned to be exposed t

stiks02 [169]

The study creates stress in a(0ne) way that might affect muscle cramps.

What is muscle cramps ?

Overuse of a muscle, dehumidification, muscle strain or simply holding a position for a prolonged period can beget a muscle cramp. In numerous cases, still, the cause is not known.
Although utmost muscle cramps are inoffensive, some may be related to an beginning medical condition, similar as shy blood force.
Cramps can have causes that are not due to underpinning complaint. exemplifications include dehumidification, emphatic exercise or lack of muscle use. Muscle cramps are unforeseen muscle condensation.
Also called muscle spasms or charley nags, a muscle cramp can be a common symptom of numerous effects, like exercise strain or a medical condition. Muscle cramps generally go down without treatment and can be watched for at home.

The study creates stress in a(0ne) way that might affect muscle cramps. If an elevator falls, fleetly and stops suddenly, that could affect muscle cramps more because of the physical action than by the stress it convinced. I don’t suppose this trial would help answer whether there's a unproductive relationship between increases stress and muscle cramps.

Learn more about muscle cramp here:

brainly.com/question/19064082

#SPJ4

7 0

1 year ago