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kirill [66]
2 years ago
15

If f is a linear function, f(k)=16 and f(-k)= -4 then what is the value of f(0)?​

Mathematics
1 answer:
ira [324]2 years ago
3 0

f(0) =  ( f(k) +f(-k) ) / 2

f(0) = (16 - 4) / 2

f(0) = 12 / 2

f(0) = 6  → ANSWER

*Remember that f(0) = m(0) + n = n

If we have f(x) = mx + n, then:

f(k)= mk + n     and       f(-k)= -mk + n

If we add them:

  f(k) + f(-k)

= mk + n -mk + n

= 2n

= 2f(0)

So we conclude that:

f(0) = [f(k) + f(-k)] / 2

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(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2
SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

8 0
3 years ago
According to the rational root theorem, which of the following are possible
White raven [17]

Given:

The polynomial function is

F(x)=4x^3-6x^2+9x+10

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of \dfrac{p}{q}, where, p is a factor of constant and q is the factor of leading coefficient.

We have,

F(x)=4x^3-6x^2+9x+10

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}

Therefore, the correct options are A, C, D, F.

7 0
2 years ago
Can someone help me plzzzz!
oksian1 [2.3K]

8.2is the answer

Step-by-step explanation:

|CB|+8

7 0
2 years ago
I need to Decrease 6400 by 9%
Advocard [28]

Answer:

5824

Step-by-step explanation:

10% of 6400 =640

1% 0f 6400 = 64

640-64=576

6400-576= 5824

5 0
2 years ago
Insert grouping symbols in the expression below so that the value of the expression is 25. Justify your answer.
slava [35]

Have you used PEMDAS if not the abbreviation stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. So you start with 3² = 3x3 = 9 now 5x6=30 so now you have a equation of (4 + 7 x 9 - 30) = 4 + 63 - 30 = 67 - 30 = 37 I hope I helped!!!!

6 0
3 years ago
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