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4 years ago

Consider f(x) = -4x2 + 24x + 3. Determine whether the function has a maximum or minimum value. Then find the

Physics

1 answer:

murzikaleks [220]4 years ago

4 0

Answer:

The function has a maximum in $x=3$

The maximum is:

$f(3) = 39$

Explanation:

Find the first derivative of the function for the inflection point, then equal to zero and solve for x

$f(x)' = -4*2x + 24=0$

$-4*2x + 24=0$

$8x=24$

$x=3$

Now find the second derivative of the function and evaluate at x = 3.

If $f (3) ''< 0$ the function has a maximum

If $f (3) '' >0$ the function has a minimum

$f(x)''= 8$

Note that:

$f(3)''= -8$

the function has a maximum in $x=3$

The maximum is:

$f(3)=-4(3)^2+24(3) + 3\\\\f(3) = 39$

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A 5.0-μC charge is placed at the 0 cm mark of a meter stick and a -4.0 μC charge is placed at the 50 cm mark. At what point on a

Maksim231197 [3]

Answer:

The distance from charge 5 μ C = 26.45 cm and the distance from - 4 μ C is 23.55 cm.

Explanation:

Given that

q₁ = 5 μ C

q₂ = - 4 μ C

The distance between charges = 50 cm

d= 50 cm

Lets take at distance x from the charge μ C ,the electrical field is zero.

That is why the distance from the charge - 4 μ C = 50 - x cm

We know that ,electric field is given as

$E=K\dfrac{q}{r^2}$

$K\dfrac{5\ \mu}{x^2}=K\dfrac{4\mu }{(50-x)^2}\\\\\dfrac{5}{x^2}=\dfrac{4 }{(50-x)^2}\\\\\\5(50-x)^2=4x^2\\(50-x)^2=0.8x^2\\\\50-x =0.89x\\\ x=\dfrac{50}{1.89}\ cm\\\\\\x=26.45\ cm\\$

Therefore the distance from charge 5 μ C = 26.45 cm and the distance from - 4 μ C is 23.55 cm.

3 0

3 years ago

Which is a future NASA research project? Check all that apply.

Nat2105 [25]

All of the given options represent NASA future projects:

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Conduct research from a space station- Humans are already living and working on board of the International Space Station which is one-of-a-kind research laboratory in microgravity. A portion of the astronauts time aboard the space station has been designated for national laboratory investigations.

Collect samples on an asteroid- First asteroid sample return mission, OSIRIS-REx, arrives at the near-Earth asteroid Bennu in December 2018 and should return a sample for study in 2023.

Conduct an unmanned space mission- InSight Mars lander is set to study the planet’s interior. The Mars 2020 rover will search for signs of past microbial life, gather samples for future return to Earth and investigate resources. The James Webb Space Telescope will be the premier observatory of the next decade, studying every phase in the history of our Universe in infrared

6 0

3 years ago

Which expression describes the third vector in the diagram, which leads from the tip of B to the tip of Ā?

podryga [215]

Answer:

axb

Explanation:

because the singular order

6 0

3 years ago

A point charge A of charge +4micro coloumb and another B of -1 micro coloumb are placed at a distance in air 1m apart then the d

andrew11 [14]

Answer:

Explanation:

Given that,

A point charge is placed between two charges

Q1 = 4 μC

Q2 = -1 μC

Distance between the two charges is 1m

We want to find the point when the electric field will be zero.

Electric field can be calculated using

E = kQ/r²

Let the point charge be at a distance x from the first charge Q1, then, it will be at 1 -x from the second charge.

Then, the magnitude of the electric at point x is zero.

E = kQ1 / r² + kQ2 / r²

0 = kQ1 / x² - kQ2 / (1-x)²

kQ1 / x² = kQ2 / (1-x)²

Divide through by k

Q1 / x² = Q2 / (1-x)²

4μ / x² = 1μ / (1 - x)²

Divide through by μ

4 / x² = 1 / (1-x)²

Cross multiply

4(1-x)² = x²

4(1-2x+x²) = x²

4 - 8x + 4x² = x²

4x² - 8x + 4 - x² = 0

3x² - 8x + 4 = 0

Check attachment for solution of quadratic equation

We found that,

x = 2m or x = ⅔m

So, the electric field will be zero if placed ⅔m from point charge A, OR ⅓m from point charge B.

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3 years ago

A microwave oven operates with sinusoidal microwaves at a frequency of 2400 mhz. the height of the oven cavity is 25 cm and the

Natali [406]

It takes Δt time to travel the Em wave which is on top of the microwave to bottom of the microwave.
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P = E / Δt = cE/h
P = 3× 10⁸ ₓ 0.5 10⁻⁶ / 0.25
600w.

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3 years ago