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Yuki888 [10]
3 years ago
13

Use the piecewise function below to evaluate the points f(–3), f(0), and f(–1).

Mathematics
1 answer:
ehidna [41]3 years ago
6 0

Given:

The piecewise function is:

f(x)=\begin{cases}9x & \text{ if } x

To find:

The values of f(-3),f(0), f(-1).

Solution:

In the given piecewise function,

f(x)=9x for x and f(x)=x-4 for x\geq -1.

Putting x=-3 in f(x)=9x, we get

f(-3)=9(-3)

f(-3)=27

Putting x=0 in f(x)=x-4, we get

f(0)=0-4

f(0)=-4

Putting x=-1 in f(x)=x-4, we get

f(-1)=-1-4

f(-1)=-5

The required values are f(-3)=27,f(0)=-4,f(-1)=-5.

Therefore, the correct option is D.

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Step-by-step explanation:

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3 years ago
. The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to nd
Blababa [14]

The question is:

The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution y2(x) of the homogeneous equation

x²y'' - 7xy' + 16y = 0; y1 = x^4

Answer:

The second solution y2 is

A(x^4)lnx

Step-by-step explanation:

Given the homogeneous differential equation

x²y'' - 7xy' + 16y = 0

And a solution: y1 = x^4

We need to find a second solution y2 using the method of reduction of order.

Let y2 = uy1

=> y2 = ux^4

Since y2 is also a solution to the differential equation, it also satisfies it.

Differentiate y2 twice in succession with respect to x, to obtain y2' and y2'' and substitute the resulting values into the original differential equation.

y2' = u'. x^4 + u. 4x³

y2'' = u''. x^4 + u'. 4x³ + u'. 4x³ + u. 12x²

= u''. x^4 + u'. 8x³ + u. 12x²

Now, using these values in the original equation,

x²(u''. x^4 + u'. 8x³ + u. 12x²) - 7x(u'. x^4 + u. 4x³)+ 16(ux^4) = 0

x^6u'' + 8x^5u' + 12x^4u - 7x^5u' - 28x^4u + 16x^4u = 0

x^6u'' + x^5u' = 0

xu'' = -u'

Let w = u'

Then w' = u''

So

xw' = -w

w'/w = -1/x

Integrating both sides

lnw = -lnx + C

w = Ae^(-lnx) (where A = e^C)

w = A/x

But w = u'

So,

u' = A/x

Integrating this

u = Alnx

Since

y2 = uy1

We have

y2 = (Alnx)x^4 = (Ax^4)lnx

Therefore, the second solution y2 is

A(x^4)lnx

6 0
3 years ago
A tour director collected $258 for 13 tour packages. tour package a costs $18 and tour package b cost $22. how many of each tour
valkas [14]
A + b = 13
22 a + 18 b = 258
------------------------
a = 13 - b
22 * ( 13 - b ) + 18 b = 258
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b = ( - 28 ) : ( - 8 ) = 7
a = 13 - 7 = 6
Answer:
6 tour packages a and 7 tour packages b were sold.
7 0
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