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What is the value of x in the equation below 1+2e^x+1=9

GuDViN [60]

<h2>Answer: 1.252</h2>

Explanation:

We are given this equation and we need to find the value of $x$ :

$1+2e^x+1=9$ (1)

Firstly, we have to clear $x$ :

$2e^x=9-1-1$

$2e^x=7$

$e^x=\frac{7}{2}$ (2)

Applying<u> Natural Logarithm</u> on both sides of the equation (2):

$ln(e^x)=ln(\frac{7}{2})$ (3)

$xln(e)=ln(\frac{7}{2})$ (4)

According to the Natural Logarithm rules $xln(e)=x$ , so (4) can be written as:

$x=ln(\frac{7}{2})$ (5)

Finally:

$x=1.252$

3 0

3 years ago

If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height above the ground (in meters) after t seconds

s2008m [1.1K]

(a) The velocity (in m/s) of the rock after 1 second is 11.28 m/s.

(b) The velocity of the rock after 2 seconds is 7.56 m/s.

(c) The time for the block to hit the surface is 4.03.

(d) The velocity of the block at the maximum height is 0.

<h3>Velocity of the rock</h3>

The velocity of the rock is determined as shown below;

Height of the rock after 1 second; H(t) = 15(1) - 1.86(1)² = 13.14 m

v² = u² - 2gh

where;

g is acceleration due to gravity in mars = 3.72 m/s²

v² = (15)² - 2(3.72)(13.14)

v² = 127.23

v = √127.23

v = 11.28 m/s

<h3>Velocity of the rock when t = 2 second</h3>

v = dh/dt

v = 15 - 3.72t

v(2) = 15 - 3.72(2)

v(2) = 7.56 m/s

<h3>Time for the rock to reach maximum height</h3>

dh/dt = 0

15 - 3.72t = 0

t = 4.03 s

<h3>Velocity of the rock when it hits the surface</h3>

v = u - gt

v = 15 - 3.72(4.03)

v = 0

Learn more about velocity at maximum height here: brainly.com/question/14638187

8 0

2 years ago

Suppose a plane accelerates from rest for 30 s, achieving a takeoff speed of 80 m/s after traveling a distance of 1200 m down th

Margaret [11]

Answer:

300 m

Explanation:

The train accelerate from the rest so u = 0 m/sec

Final speed that is v = 80 m/sec

Time t = 30 sec

The distance traveled by first plane = 1200 m

We know the equation of motion $S=ut+\frac{1}{2}at^2$ where s is distance a is acceleration and u is initial velocity

Using this equation for first plane $1200=0\times 30+\frac{1}{2}a30^2$

$a=2.67\frac{m}{sec^2}$

As the acceleration is same for both the plane so a for second plane will be 2.67 $\frac{m}{sec^2}$

The another equation of motion is $v^2=u^2+2as$ using this equation for second plane $40^2=0+2\times 2.67\times s$

s = 300 m

5 0

2 years ago

an electromagnetic wave propagates in a vacuum in the x-direction. In what direction does the electric field oscilate

sweet [91]

Answer:

<em>The electric field can either oscillates in the z-direction, or the y-direction, but must oscillate in a direction perpendicular to the direction of propagation, and the direction of oscillation of the magnetic field.</em>

Explanation:

Electromagnetic waves are waves that have an oscillating magnetic and electric field, that oscillates perpendicularly to one another. Electromagnetic waves are propagated in a direction perpendicular to both the electric and the magnetic field. If the wave is propagated in the x-direction, then the electric field can either oscillate in the y-direction, or the z-direction but must oscillate perpendicularly to both the the direction of oscillation of the magnetic field, and the direction of propagation of the wave.

5 0

3 years ago

________ can occasionally cause the North Atlantic to appear green and murky.

castortr0y [4]

Answer:

algae

Explanation:

The Atlantic off the East Coast of the United States usually appears green. This is due to the presence of algae and plant life.

4 0

2 years ago