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rodikova [14]
3 years ago
5

a ballon is released from the of a platform that is 50 meters tall. The ballon rises at the rate of 4 meters per second. Write a

n equation in slope- intercept form that tells the height of the ballon above the ground after given number of seconds.
Mathematics
1 answer:
Elanso [62]3 years ago
7 0
Y = 4x + 50

y is height, 4 meters per second (x), 50m initial height
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21 3/4

Step-by-step explanation:

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Which point is an intercept of the quadratic function
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Answer:

x=15

Step-by-step explanation:

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It rotates 360 degrees and 180 half way in a circular motion
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Amanda placed her finger on the origin of a regular coordinate plane. She marked a point after moving her finger 1 unit to the l
Lubov Fominskaja [6]

Answer:

( x , y ) = ( -1 , - 5 )

Step-by-step explanation:

Solution:-

- The rectangular coordinate system ( Cartesian ) is defined by two independent variables namely, "x and y".

- The values of both varibales lie on the horizontal and vertical line respectively, ( x & y ).

- The values on the horizontal axis also known as the x-axis is marked with a referece of x = 0 ( origin ). All the values to the right of the point of origin are denoted as positive units and all values to the left of the point of origin are denoted as negative units.

- Similarly, The values on the vertical axis also known as the y-axis is marked with a referece of y = 0 ( origin ). All the values to the above the point of origin are denoted as positive units and all values below of the point of origin are denoted as negative units.

- The axis are conventionally oriented such that 90 degrees angle is formed in between them and always denoted in the counter-clockwise direction.

In other words, if +x is pointing to the right then the +y will be pointed in the direction when +x is rotated counter clockwise to 90 degrees; hence, points upward.

- When Amanda starts off at the origin she is at the order pair  ( 0 , 0 ).

- She then moves her finger 1 unit to left ( -x ) and 5 units down ( -y ). Hence, she moves 1 unit along the -x direction and then moves 5 units down along -y direction.

Hence, she is at an ordered pair ( x , y ) = ( -1 , - 5 ) .

3 0
3 years ago
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nordsb [41]

The ODE has an equilibrium point at

\dfrac{\mathrm dy}{\mathrm dt}=ay+b=0\implies y=-\dfrac ba

We want y=2 to be an unstable equilibrium solution - in other words, we want all solutions with initial condition y(t_0)=c for c near 2 to diverge from y=2 - so -dfrac ba=2.

Divergence from y=2 would require that for y>2, any solution is increasing, and for y, and solution is decreasing. In order for that to happen, we need

\dfrac{\mathrm dy}{\mathrm dt}=ay+b>0\implies y>-\dfrac ba

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\dfrac{\mathrm dy}{\mathrm dt}=ay+b

if y.

Now we just pick a,b to satisfy these conditions. An easy choice is a=1, which forces b=-2, so that one possible ODE would be

\dfrac{\mathrm dy}{\mathrm dt}=y-2

I've attached a plot of the slope field to demonstrate the behavior of the solutions.

6 0
3 years ago
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