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ra1l [238]
3 years ago
7

The solution set of a linear system whose augmented matrix is [a b c d] is the same as the solution set of Ax = d, where A = [a

b c]. Note: a, b, c, d are all column vectors.True/false
Mathematics
1 answer:
Charra [1.4K]3 years ago
6 0

Answer:

True

Step-by-step explanation:

First statement

[a b c | d][x]

[a b c]x=d

ax+bx+cx=d

Second statement

Ax=d

Given that A = [a b c]

[a b c]x=d

ax+bx+cx=d

ax+bx+cx=d

Then, they are going to have the same solutions

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Really need help! Brainliest to correct!
zlopas [31]

Answer:

<u>Given</u>:

  • R(x) = 59x - 0.3x²
  • C(x) = 3x + 14

<u>Find the following</u>:

  • P(x) = R(x) - C(x) = 59x - 0.3x² - 3x - 14 = -0.3x² + 56x - 14
  • R(80) = 59(80) - 0.3(80²) = 2800
  • C(80) = 3(80) + 14 = 254
  • P(80) = 2800 - 254 = 2546
7 0
2 years ago
) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra
artcher [175]

Answer:

y(t)=2e^{3t}(2-5t)

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2  

Using the theorem of the Laplace transform for derivatives, we know that:

\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)

Replacing the initial values y(0)=4, y′(0)=2 we obtain

\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4

and our differential equation (*) gets transformed in the algebraic equation

\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0

Solving for Y(s) we get

\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}

Now, we brake down the rational expression of Y(s) into partial fractions

\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here  

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}

and

\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}

we know that

\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}

and for the first translation property of the inverse Laplace transform

\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}

and the solution of our differential equation is

\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}

5 0
3 years ago
A circle with the diameter of 20 mm is showing what is the exact Sir conference obvious and then question to what is the approxi
yaroslaw [1]

Answer:

The approximate circumference is 62.8 mm

Step-by-step explanation:

Circumference is basically the perimeter of the circle

Circumference is given by

2 *\pi *r

Here the diameter is 20 mm, so the radius will be half of diameter = 10 mm

Substituting the given values, in above equation, we get -

Circumference =

2 *3.14 * 10 \\62.8mm

The approximate circumference is 62.8 mm

3 0
2 years ago
HELP ME OUT PLS!!!!!​
pantera1 [17]

The Answer Is C. 64, hope I helped

4 0
2 years ago
Read 2 more answers
If a2= 18 and a4= 8, find two possible common ratios. Then, write two sequences lhaving five terms each.
Marizza181 [45]

common ratio = a4/a3 = a3/a2

8/a3 = a3/18

(a3)^2 = 8 * 18

(a3)^2 = 144

a3 = 12 or a3 = -12

common ratio = 8/12 or common ratio = 8/(-12)

common ratio = 2/3 or common ratio = -2/3

Answer: 12 or -12

3 0
3 years ago
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