The phrase all men are created equal is from what document

Suppose that each component of a certain vector is doubled. (a) by what multiplicative factor does the magnitude of the vector c

gladu [14]

<span>a. The magnitude of the vector is doubled as well. Let's say we have a 2-dimensional vector with components x and y. It's magnitude lâ‚ is given by: lâ‚ = âš(xÂ˛ + yÂ˛) If we double the components x and y, the new magnitude lâ‚‚ is: lâ‚‚ = âš((2x)Â˛ + (2yÂ˛)) With a bit of algebra... lâ‚‚ = âš(4xÂ˛ + 4yÂ˛) lâ‚‚ = âš4(xÂ˛ + yÂ˛) lâ‚‚ = 2âš(xÂ˛ + yÂ˛) We can write the new magnitude lâ‚‚ in terms of the old magnitude lâ‚. lâ‚‚ = 2lâ‚ Therefore, the new magnitude is double the old one. It should be clear that this relationship applies to 3D (and 1D) vectors as well. b. The direction angle is unchanged. The direction angle Î¸â‚ for a 2-dimensional vector is given by: Î¸â‚ = arctan(y / x) If we double both components, we get: Î¸â‚‚ = arctan(2y / 2x) Î¸â‚‚ = arctan(y / x) Î¸â‚‚ = Î¸â‚ The new direction angle is the same as the old one.</span>

7 0

4 years ago

g You are blowing air into a spherical balloon at a rate of 33 cubic inches per second. Given that the radius of the balloon is

Marina CMI [18]

Answer:

$\frac{3}{16\pi}in/sec$

Explanation:

We are given that

$\frac{dv}{dt}=3in^3/s$

r=2 in when t=4 s

We have to find the rate of change of radius.

We know that

Volume of sphere= $V=\frac{4}{3}\pi r^3$

Differentiate w.r.t t

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Substitute the values

$3=4\pi(2)^2\times \frac{dr}{dt}$

$\frac{dr}{dt}=\frac{3}{4\pi(2)^2}$

$\frac{dr}{dt}=\frac{3}{16\pi}in/sec$

8 0

3 years ago

What is the water pressure at a depth of 30m in pascals?

vaieri [72.5K]

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The water pressure at depth h from the water surface is obtained from the following equation.

$Pressure = (density) \times (gravity \: \: acceleration) \times (depth \: \: from \: \: the \: \: water \: \: surface) \\$

$density = 1000 \: \: \frac{kg}{ {m}^{3} }$

$gravity \: \: acceleration = 10 \: \: \frac{m}{ {s}^{2} }$

$depth \: \: from \: \: the \: \: the \: \: water \: \: surface = 30 \: \: m \\$

______________________________________

$P = 1000 \times 10 \times 30$

$P = 300,000 \: \: pascals$

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6 0

3 years ago

The volume of a cube shaped fish tank in guy Harvey's restaurant is 64 cubic feet the cube shaped fish tank in the gift shop is

trapecia [35]

Answer:

The difference between the length of the sides of the fish tank is guy Harvey's restaurant and a fish tank in gift shop is 2 feet.

Explanation:

The cube shaped fish tank in guy Harvey's restaurant has volume 64 cubic feet.

Volume of the cubic tank is given by,

V = $l^{3}$

64 = $l^{3}$

l = $\sqrt[3]{64}$

l = 4 feet

The cube shaped fish tank in the gift shop is 8 cubic feet

Volume of the cubic tank is given by,

v = $a^{3}$

8 = $a^{3}$

8 = $\sqrt[3]{8}$

a = 2 feet

The difference between the length of the sides is given by,

d = l - a

d = 4 - 2

d = 2 feet

The difference between the length of the sides of the fish tank is guy Harvey's restaurant and a fish tank in gift shop is 2 feet.

5 0

3 years ago

The round opening in the dome of the pantheon is called what?

mariarad [96]

<h2>Answer: Oculus </h2>

In the architectural context, the oculus is a small hole or circular window, built with the intention of entering light, air in circulation or simply for decorative purposes.

One of the oldest oculus is the one located at the Roman Pantheon (temple), a construction that began in the 27th century BC on the orders of Marcus Agrippa for Augustus and was completed by order of the Emperor Hadrian.

4 0

3 years ago