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vova2212 [387]
3 years ago
14

How much time has passed 4:33-8:12

Mathematics
1 answer:
kirill115 [55]3 years ago
3 0

Answer:

3 hours 39 minutes

Step-by-step explanation:

4:33 + 0:39 = 5:12

5:12 + 3:00 = 8:12

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Step-by-step explanation:

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The y-intercept of the line whose equation is 2x + y = 4 is
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y\ intercept\ for\ x=0\\\\
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Find a parabola with equation y=ax2+bx+c that has slope 8 at x = 1, slope -16 at x = -1 and passes through the point (2, 2).
morpeh [17]

Answer:

y=6x^2-4x-14

Step-by-step explanation:

y=ax^2+bx+c

We are given the slopes (the derivatives) at x=1 and x=-1.

So let's find the derivative of our equation:

y'=2ax+b

At x=1 we have y'=8:

8=2a(1)+b

8=2a+b

At x=-1 we have y'=-16:

-16=2a(-1)+b

-16=-2a+b

So we have the system:

8=2a+b

-16=-2a+b

We can solve this by elimination. I'm going to add the equations allowing me to solve for b.

-8=2b

Divide both sides by 2:

-4=b

Let's find a.

8=2a+b with b=-4:

8=2a+(-4)

8=2a-4

Add 4 on both sides:

12=2a

Divide both sides by 2:

6=a

So we have the equation so far is:

y=6x^2-4x+c.

We can find c by using the point (2,2):

2=6(2)^2-4(2)+c

2=6(4)-4(2)+c

2=24-8+c

2=16+c

Subtract 16 on both sides:

-14=c

So the equation is y=6x^2-4x-14.

Let's do a final check.

y'=12x-4

Check to see if we have (1,8) and (-1,-16) satisfies this. (Note: (x,y'))

Check for (x,y')=(1,8):

8=12(1)-4

8=8 which is true.

Check for (x,y')=(-1,-16):

y'=12x-4

-16=12(-1)-4

-16=-16 which is true.

Let's check to see (2,2) is on y=6x^2-4x-14:

2=6(2)^2-4(2)-14

2=6(4)-8-14

2=24-8-14

2=24-22

2=2 which is true.

The equation y=6x^2-4x-14 has been verified with the given conditions.

8 0
3 years ago
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