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bonufazy [111]
3 years ago
5

You are working with a quadratic equation and construct the following table.

Mathematics
1 answer:
Alecsey [184]3 years ago
6 0

Answer:

a) Vertex is at (-3, -1)

b) y-intercept is at (0,8)

c) x intercept is at (-4,0) and (-2,0)

d) x=-3

Step-by-step explanation:

We know the vertex is the lowest or highest part of a parabola meaning all the points are reflected across.  It is the only y value without a matching pair

E.x. -1 and 1, -3 and 3

The only point without a corresponding y value is (-3,-1) therefore the vertex is at (-3,-1)

The y-intercept is where the parabola meets the y axis or the x value is equal to 0, we just have to find when x = 0 to find the y intercept

y intercept: (0,8)

For the x intercept's it is just the reverse, you need to find where the parabola crosses the x axis or when y = 0

x intercept 1:(-4,0)

x intercept 2: (-2,0)

The axis of symmetry is also the x coordinate of the vertex which is 3 so

x = 3

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y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a sol
TEA [102]

Answer:

y = 2cos5x-9/5sin5x

Step-by-step explanation:

Given the solution to the differential equation y'' + 25y = 0 to be

y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.

According to the boundary condition y(0) = 2, it means when x = 0, y = 2

On substituting;

2 = c1cos(5(0)) + c2sin(5(0))

2 = c1cos0+c2sin0

2 = c1 + 0

c1 = 2

Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given

y(x) = c1cos5x + c2sin5x

y'(x) = -5c1sin5x + 5c2cos5x

If y'(π) = 9, this means when x = π, y'(x) = 9

On substituting;

9 = -5c1sin5π + 5c2cos5π

9 = -5c1(0) + 5c2(-1)

9 = 0-5c2

-5c2 = 9

c2 = -9/5

Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation

y = c1 cos(5x) + c2 sin(5x) will give

y = 2cos5x-9/5sin5x

The final expression gives the required solution to the differential equation.

3 0
3 years ago
Evaluate c-2 when c =7
LenaWriter [7]
If C = 7, You would do 7-2 = 5
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3 years ago
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I just need help with this table
Mashutka [201]

Answer:

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g(x) is being squared and then multiplied, so it should be (from top to bottom): 720, 2420, 2880, 3380

Step-by-step explanation:

6 0
4 years ago
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