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Nuetrik [128]
2 years ago
13

find the component equation of the plane which is normal to the vector -2i+5j+k and which contains the point (-10;7;5).​

Mathematics
1 answer:
maksim [4K]2 years ago
4 0

Given:

A plane is normal to the vector = -2i+5j+k

It contains the point (-10,7,5).​

To find:

The component equation of the plane.

Solution:

The equation of plane is

a(x-x_0)+b(y-y_0)+c(z-z_0)=0

Where, (x_0,y_0,z_0) is the point on the plane and \left< a,b,c\right> is normal vector.

Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is

-2(x-(-10))+5(y-7)+1(z-5)=0

-2(x+10)+5y-35+z-5=0

-2x-20+5y-35+z-5=0

-2x+5y+z-60=0

-2x+5y+z=60

Therefore, the equation of the plane is -2x+5y+z=60.

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Answer:

6500

Step-by-step explanation:

1 US ton is 2000 pounds so multiply that by 3.25 and you get 6500

5 0
3 years ago
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Jada walks up to a tank of water that can hold up to 10 gallons.When it is active, a drain empties water from the tank at a cons
worty [1.4K]

Answer:

<em>Part A)</em><em>The amount of water in the tank is changing at </em><em>-2/3 gallons per minute. </em>

<em>Part B) </em><em>it will take </em><em>7.5 minutes</em><em> for the tank to drain completely.</em>

<em>Part C) </em><em>The water tank was completely full </em><em>4.5 minutes</em><em> before Jada arrived.</em>

Step-by-step explanation:

<em>Information fetching:</em>

  • Tank of water can hold up-to 10 gallons.
  • When it is active, a drain empties water from the tank at a constant rate.
  • 7 gallons of water present in the tank when Jade first saw
  • 5 gallons of water left after 3 minutes

<em>Part A) At what rate is the amount of water in the tank changing?</em>

As the gallons were decreased from 7 to 5 in three minutes. It means in three minutes, 2 gallons were decreased.

So, gallons per minute change would be <em>-2/3 gallons per minute. </em>Hence, <em>the amount of water in the tank is changing at </em><em>-2/3 gallons per minute. </em>

<u><em>Note</em></u><u><em>: </em></u><u>negative sign indicates the number of gallons of water are decreasing.</u>

<em>Part B) How many more minutes will it take for the tank to drain completely.</em>

Let 'm' be the number of minutes will it take for the tank to drain completely.

As,

(2/3 gallons per minute) (m minutes) = 5 gallons

So,

    m = 5 (3/2)

      = 15/2

      = 7.5 minutes

<em>So, it will take </em><em>7.5 minutes</em><em> for the tank to drain completely.</em>

<em>Part C) How many minutes before Jada arrived was the water tank completely full</em>

As tank of water can hold up to 10 gallons. So, the tank of water is full when there is 10 gallons of water. So, this is 3 gallons of water more than the total 7 number of gallons at the time when Jada arrived.

As Jada arrived when the tank had left 7 gallons.

Let 'm' be the number of minutes before Jada arrived when the water tank was completely full.

So,

    (2/3) (m) = 3

    m = 3(3/2) = 9/2

        = 4.5 minutes

<em>So, the water tank was completely full </em><em>4.5 minutes</em><em> before Jada arrived.</em>

<em />

<em>Keywords: time rate of change, time</em>

<em> Learn more about time rate of change from brainly.com/question/6279456</em>

<em> #LearnwithBrainly </em>

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3 years ago
(GIVING BRAINLYIST) 5 cakes are shared equally between 6 people. What fraction of a cake does each person receive? use fraction
Keith_Richards [23]

Answer:

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maksim [4K]
Find the inside angle B of the smaller triangle using the base (4) and height (6)
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 full B = 90 degrees - smaller B gives you the other part of B for the left hand side

so 90 - 33.69 = 56.31

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The answer would be 14x+5 I’m pretty sure
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