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2 years ago

14

[4] A tortoise and a hare cover the same distance in a race. The hare goes very fast but stops frequently while the tortoise has

a steady pace and finish first

1 answer:

nadya68 [22]2 years ago

7 0

Answer:

I know that story where the hare sleeps

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The phrase change in which a substance changes from a gas directly to a solid is

mr_godi [17]

Answer is Deposition…

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1 year ago

An airplane flies 12 m/s due north with a velocity of 35.11 m/s. how far east does it fly?

goblinko [34]

The plane's velocity of 35.11 m/s is actually due in a north-eastward direction. The 12 m/s velocity is the vertical component of the plane's velocity, hence it is pointing northwards. We will use the formula:

Vy = Vsin∅

To determine the angle ∅ at which the plane is flying. This is:

12 = 35.11 * sin∅
∅ = 20.0 degrees

The eastward velocity is:

Vx = Vcos∅
Vx = 35.11 * cos(20)
Vx = 33.0 m/s

The plane's eastward velocity is 33.0 m/s

3 0

2 years ago

Read 2 more answers

Suppose you have a 75-watt light bulb that you leave turned on for two minutes. How much energy

victus00 [196]

Answer:

9000 J

Explanation:

Convert minutes to seconds.

2 min = 120 s

Power = energy / time

75 W = E / 120 s

E = 9000 J

5 0

1 year ago

The mechanical advantage of a wheel and axle is the radius of the wheel divided by the radius of the axle. TRUE or FALSE.

viva [34]

True! The mechanical advantage of the wheel and axle is equal to the ratio of the radius of the wheel over the radius of the axle.

4 0

2 years ago

Consider the points below. P(1, 0, 1), Q(−2, 1, 4), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the poi

kozerog [31]

Answer:

a) (0, -33, 12)

b) area of the triangle : 17.55 units of area

Explanation:

<h2>a) </h2>

We know that the cross product of linearly independent vectors $\vec{A}$ and $\vec{B}$ gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.

Luckily for us, we know that vectors $\vec{A} = \vec{P}-\vec{Q}$ and $\vec{B} = \vec{R} - \vec{Q}$ are living in the plane through the points P, Q, and R, and are linearly independent.

We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).

If they weren't linearly independent, we will obtain vector zero as the result of the cross product.

So, for our problem:

$\vec{A} = \vec{P} - \vec{Q} \\\\\vec{A} = (1,0,1) - (-2,1,4)\\\\\vec{A} = (1 +2,0-1,1-4)\\\\\vec{A} = (3,-1,-3)$

$\vec{B} = \vec{R} - \vec{Q} \\\\\vec{B} = (6,2,7) - (-2,1,4)\\\\\vec{B} = (6 +2,2-1,7-4)\\\\\vec{B} = (8,1,3)$

$\vec{A} \times \vec{B} = (A_y B_z - B_y A_z) \ \hat{i} - ( A_x B_z-B_xA_z) \ \hat{j} + (A_x B_y - B_x A_y ) \ \hat{k}$

$\vec{A} \times \vec{B} = ( (-1) * 3 - 1 * (-3) ) \ \hat{i} - ( 3 * 3 - 8 * (-3)) \ \hat{j} + (3 * 1 - 8 * (-1) ) \ \hat{k}$

$\vec{A} \times \vec{B} = ( - 3 + 3 ) \ \hat{i} - ( 9 + 24 ) \ \hat{j} + (3 + 8 ) \ \hat{k}$

$\vec{A} \times \vec{B} = 0 \ \hat{i} - 33 \ \hat{j} + 12 \ \hat{k}$

$\vec{A} \times \vec{B} =(0, -33, 12)$

<h2>B)</h2>

We know that $\vec{A}$ and $\vec{B}$ are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:

$|\vec{A} \times \vec{B} | = 2 * area_{triangle}$

so:

$\sqrt{(-33)^2 + (12)^2} = 2 * area_{triangle}$

$\sqrt{1233} = 2 * area_{triangle}$

$35.114= 2 * area_{triangle}$

$17.55 \ units \ of \ area = area_{triangle}$

5 0

2 years ago