A proton is a subatomic particle that carries a __________

Wilma can mow a lawn in 80 minutes. Rocky can mow the same lawn in 120 minutes. Construct an equation that would allow you to de

xeze [42]

Answer:

$t = 96 minutes$

Explanation:

Time to mow 1 lawn by Wilma is 80 minutes

so work done in 1 minute by Wilma is given as

$W_1 = \frac{1}{80}$

Similarly Rocky mow same lawn in 120 minute

so work done in 1 minute by Rocky is given as

$W_2 = \frac{1}{120}$

now we know that they both worked by "t" time

so total work performed by them

$W = \frac{t}{80} + \frac{t}{120}$

they both mow 2 lawns then it is given as

$2 = (\frac{1}{80} + \frac{1}{120})t$

$t = 96 minutes$

5 0

3 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:

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:

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

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

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

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

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

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

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

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

3 years ago

Explain why secondary succession usually occurs more rapidly than primary succession.

kiruha [24]

Answer:

Explanation:

As it mostly occurs on a surface where an ecosystem has previously existed. Primary succession only occurs on a surface where no ecosystem existed ever before!

6 0

3 years ago

Suppose that you hear a clap of thunder 16 s after seeing the associated lightning strike. How far are you from the lightning st

riadik2000 [5.3K]

Answer:

$d=5.376km$

Explanation:

Since <em>light is so fast</em> we can assume no time passes between the lightning strikes and we observe it. We want to know then how far away did the strike occur for the sound to take 16s to reach our ears. Since the definition of velocity tells us that $v=d/t$ , we can write $d=vt=(336m/s)(16s)=5376m=5.376km$

4 0

3 years ago

Good morning friends

Hatshy [7]

Answer:

Good morning. Whats about you

4 0

3 years ago

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A proton is a subatomic particle that carries a ___________ charge