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3 years ago

Consider the points below. P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)

Mathematics

1 answer:

Zina [86]3 years ago

3 0

Answer: the vector orthogonal is ( 0, 26, -13 )

Step-by-step explanation:

Given that;

P(2, 0, 2), Q(−2, 1, 4), R(7, 2, 6)

PQ = Q - P = (−2, 1, 4) - (2, 0, 2) = (-4, 1, 2)

PR = R - P = (7, 2, 6) - (2, 0, 2) = ( 5, 2, 4)

orthogonal vector = PQ × PR

= ║ i j k

-4 1 2 = i(1×4 - 2×2) + j(5×2 - (-4×4)) + k(-4×2 - 5×1) = 0i + 26j - 13k

5 2 4 ║

= ( 0, 26, -13 )

Therefore the vector orthogonal is ( 0, 26, -13 )

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Pat drank 1 1/3 cups of punch in the beginning of the party as she drank 2 and4/6 cups of punch at the end of the party.How much

SOVA2 [1]

Answer:

Pat drank 26/6 (4 1/3 or 13/3) cups of punch.

Step-by-step explanation:

Here is how I would solve this-

What is the question? How much punch did she drink in all?

What do we need to know? 11/3 + 4/6 cups of punch.

How can we make them have a common denominator? 22/6 + 4/6

Add them together! (22 + 4 = 26) so you get 26/6

Final Answer = Pat drank 26/6 (4 1/3 or 13/3) cups of punch.

Hope this helps! Good luck and let me know if this is right!

7 0

3 years ago

luvenia can row 4mph in still water. She takes as long to row 7 mi upstream as 21 mi downstream. how

xeze [42]

Answer:

The speed of the river is 2mph.

Step-by-step explanation:

I guess that we want to find the speed of the river.

First, remember the relation: speed*time = distance

If the speed of the river is Sr, when Luvenia moves downstream (in the same direction that the flow of the water) the total speed will be equal to the speed of Luvenia in still water plus the speed of the water:

Sd = 4mph + Sr

and at this speed, in a time T, she can move 21 miles, so we have:

Sd*T = (4mph + Sr)*T = 21 mi

When moving upstream, the speed will be:

Su = (4mph - Sr)

and in the same time T as before, she moves 7 miles, so we have the equation:

Su*T = (4mph - Sr)*T = 7 mi

Then we have two equations:

(4mph + Sr)*T = 21 mi

(4mph - Sr)*T = 7 mi

Now we can take the quotient of those two equations and get:

((4mph + Sr)*T)/((4mph - Sr)*T) = 21/7

The time T vanishes, and we can solve it for Sr.

(4mph + Sr)/(4mph - Sr) = 3

4mph + Sr = 3*(4mph - Sr) = 12mph - 3*Sr

4*Sr = 12mph - 4mph = 8mph

Sr = 8mph/4 = 2mph.

7 0

4 years ago

One of Mr. Newman’s architecture students states that prisms and pyramids are different shapes, but the volume of a pyramid is h

Shalnov [3]

Answer:

The second student is correct. The volume of a prism is bh, but the volume of a pyramid is (1/3)bh. The volume of a pyramid will be one-third the volume of a prism if they have the same base area and height.

Step-by-step explanation:

I took the quiz :)

7 0

4 years ago

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Graph the line through(-5,-10), m=3

koban [17]

Answer:

below

Step-by-step explanation:

first put it in point-slope then slope intercept:

y+10=3(x+5)

y+10=3x+15

y=3x+5

now graph it

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3 years ago

a laptop cost $550 you gave coupon in the mail for 30% off if you use the coupon what is the sale price of laptop

zavuch27 [327]

Hello!

First we need to find 30% of our laptop. To do so we multiply by 0.3

550(0.3)=165

Now we subtract this cost from our original.

550-165=385

Therefore, the sale price would be $385.

I hope this helps!

4 0

3 years ago

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