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MissTica
3 years ago
5

A particle is moving along the parabola x^2=4(y+6). As the particle passes through the point (8,10), the rate of change of its y

-coordinate is 5 units per second. How fast, in units per second, is the x-coordinate changing at this instant?
Mathematics
1 answer:
Fofino [41]3 years ago
8 0
You'll need to use differentiation (specifically, implicit differentiation) here.

If x^2 = 4(y+6), differentiating both sides with respect to time t produces the following:

2x (dx/dt) = 4([dy/dt])   (note that (d/dt) 6 = 0)

We need to solve for (dx/dt).  Substitute 8 for x (y does not appear in this latest equation, so we do nothing with y=10).  Substitute the given 5 units/sec for dy/dt:

2(8)(dx/dt) = 4(5)(units/sec)

Solving for dx/dt, dx/dt = [20 units/sec]/16, or 5/4 units/sec, or 1.25 units/sec.
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In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t 2 , 2 + t − 5t 2 , 1 + 2t} to the standard basis of P2.
Serjik [45]

Complete Question:

In P2, find the change-of-coordinates matrix from the basis B = {1 − 3t² , 2+t− 5t² , 1 + 2t} to the standard basis C = {1, t, t²}. Then, write t² as a linear combination of the polynomials in B.

Answer:

The change of coordinate matrix is :

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

Step-by-step explanation:

Let U =  {D, E, F} be any vector with respect to Basis B

U = D [1 − 3t²] + E [2+t− 5t²] + F[1 + 2t]..............(*)

U = [D+2E+F]+ t[E+2F] + t²[-3D-5E]...................(**)

In Matrix form;

\left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right] \left[\begin{array}{ccc}D\\E\\F\end{array}\right] = \left[\begin{array}{ccc}D+2E+F\\E+2F\\-3D-5E\end{array}\right]

The change of coordinate matrix is therefore,

M = \left[\begin{array}{ccc}1&2&1\\0&1&2\\-3&-5&0\end{array}\right]

To find D, E, F in (**) such that U = t²

D + 2E + F = 0.................(1)

E + 2F = 0.........................(2)

-3D -5E = 1........................(3)

Substituting eqn (2) into eqn (1 )

D=3F...................................(4)

Substituting equations (2) and (4) into eqn (3)

-9F+10F=1

F = 1

Put the value of F into equations (2) and (4)

E = -2(1) = -2

D = 3(1) = 3

Substituting the values of D, E, and F into (*)

U = t² = 3 [1 − 3t²] - 2 [2+t− 5t²] + [1 + 2t]

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2 years ago
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Answer:

Step-by-step explanation:

16x^2 + 9 = 25

16x^2 = 16

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3 years ago
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Answer:

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Step-by-step explanation:

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Nina [5.8K]

Answer:

33.60 is your answer

Step-by-step explanation:

Remember to add based on place value.

Note that 10.70 is the same as 10.7

11.15 + 11.75 = 22.90

22.90 + 10.7 = 33.60


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