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Alex Ar [27]
3 years ago
10

Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water. This rate is const

ant
Mathematics
1 answer:
exis [7]3 years ago
6 0
The ratio should be 2 /17 
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Select the TWO units that would be reasonable to use to measure the length of a pencil.
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Answer:

1 and 2

Step-by-step explanation:

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Find two numbers whose sum is 1 and whose difference is -3.<br> Your answer is:
podryga [215]

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-2 -4

Step-by-step explanation:

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Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)

We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>

The vector product pq x pr gives a vector perpendicular to both pq and pr.  This vector is the normal vector of a plane passing through all three points
pq x pr
=
  i   j   k
-4 -2 -4
-3  5  1
=<-2+20,12+4,-20-6>
=<18,16,-26>

Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>

The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).

The equation of the required plane is therefore
Π :  9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π  :  9x+8y-13z=24

Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.

3 0
3 years ago
What is the distance covered by a train while slowing down from
alukav5142 [94]

Answer:

The distance covered is 113.75 m

Step-by-step explanation:

As per the question:

The initial velocity of the train, v = 20 m/s

The final velocity of the train, v' = 6 m/s

Uniform deceleration, a = 1.6m/s^{2}

Or uniform acceleration, a = - 1.6m/s^{2}

<em>Here, the body decelerates, i.e., slows down at a uniform rate thus we take acceleration with negative sign.</em>

Now, to find the distance covered, s:

Using the eqn of Kinemetics:

v'^{2} = v^{2} + 2as

6^{2} = 20^{2} + 2(- 1.6)s

36 - 400 = - 3.6s

s = \frac{- 364}{- 3.6} = 113.75\ m

5 0
3 years ago
Look at the image for the question and answers​
Karo-lina-s [1.5K]

Answer:

C

Step-by-step explanation:

3 0
2 years ago
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