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3 years ago

Find an equation for the plane that passes through the point [1, 1, 8] and that has [-1, -6, 3] as normal vector.

1 answer:

3 0

The normal to the plane is (Fx, Fy, Fz) = (1, 1, 8)
We have (x0, y0, z0) = (-1, - 6, 3)

Equation of the plane:
Fx(x - x0) + Fy(y - y0) + Fz(z - z0) = 0
=> (1)(x + 1) + (1)(y + 6) + (8)(z - 3) = 0
=> x + 1 + y + 6 + 8z - 24 = 0
=> x + y + 8z = 17

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What must be the magnitude of a uniform electric field if it is to have the same energy density as that possessed by a 0.50 T ma

Sindrei [870]

Answer:

E = 1.50 × $10^{8}$ V/m

Explanation:

given data

B = 0.50 T

solution

we know that energy density by the magnetic field is express as

$\mu _b = \frac{B}{2\mu _o}$ ...............1

and

energy density due to electric filed is

$\mu _e = \frac{\epsilon _o E^2}{2}$ ...............2

and here $\mu _b = \mu _ e$

so that

E = $\frac{B}{\sqrt{\mu _o \times \epsilon _o}}$ ...................3

put here value and we get

$E = \frac{0.50}{\sqrt{4\pi \times 10^{-7} \times 8.852 \times 10^{-12}}}$

E = 3 × $10^{8}$ × 0.50

E = 1.50 × $10^{8}$ V/m

6 0

3 years ago

Drawing a shows a displacement vector (450.0 m along the y axis). In this x, y coordinate system the scalar components are Ax 0

Alisiya [41]

Answer:

x ’= 368.61 m, y ’= 258.11 m

Explanation:

To solve this problem we must find the projections of the point on the new vectors of the rotated system θ = 35º

x’= R cos 35

y’= R sin 35

The modulus vector can be found using the Pythagorean theorem

R² = x² + y²

R = 450 m

we calculate

x ’= 450 cos 35

x ’= 368.61 m

y ’= 450 sin 35

y ’= 258.11 m

4 0

3 years ago

Name and describe the two layers inside Earth that are undergoing convection and indicate one major consequence of each.

Lilit [14]

Answer:

Mantle and core

Explanation:

The Mantle and Core are the two components within Earth experiencing convection. In several ways the mantle is significant. The one outcome of convective current is the creation of the fresh oceanic lithosphere around OCEANIC RIDGES, formed by mantle upwelling. Core is indeed the planet's innermost layer.

5 0

3 years ago

A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block

MariettaO [177]

Answer:

v₀ = 0.5058 m/s

Explanation:

From the question, for the block to hit the bottle, the elastic potential energy of the spring at the bottle (x = 0.08 m) should be equal to the sum of the elastic potential energy of the spring at x = 0.05 m and the kinetic energy of block at x = 0.05 m

Now, the potential energy of the block at x = 0.08 m is ½kx²

where;

k is the spring constant given by; k = ω²m

ω is the angular velocity of the oscillation

m is the mass of the block.

Thus, potential energy of the spring at the bottle(x = 0.08 m) is;

U = ½ω²m(0.08m)²

Also, potential energy of the spring at the bottle(x = 0.05 m) is;

U = ½ω²m(0.05m)²

and the kinetic energy of the block at x = 0.05 m is;

K = ½mv₀²

Thus;

½ω²m(0.08)² = ½ω²m(0.05)² + ½mv₀²

Inspecting this, ½m will cancel out to give;

ω²(0.08)² = ω²(0.05)² + v₀²

Making v₀ the subject, we have;

v₀ = ω√((0.08)² - (0.05)²)

So,

v₀ = 8.1√((0.08)² - (0.05)²)

v₀ = 0.5058 m/s

7 0

3 years ago

How is the frequency of an electromagnetic wave related to energy

aivan3 [116]

Answer: The energy carried by an electromagnetic wave is proportional to the frequency of the wave.

Explanation:

Electromagnetic waves that are of higher energy than visible light (higher frequency, shorter wavelength) include ultraviolet light, X-rays, and gamma rays.

7 0

3 years ago