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2 years ago

10 determine c as a function of r1,r2, and r3 for the feedback control system shown in fig. p2.10

1 answer:

6 0

did u get this question from https://www.chegg.com/homework-help/questions-and-answers/210-determine-cas-function-ri-rz-r-feedback-control-system-shown-fig-p210-fig-p210-q14464211 ?

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Line l contains the points (1,5) and (4, -4). point P has the coordinates (-1, 1)

Colt1911 [192]

Answer:

The distance from p to l is $\sqrt{10}\ units$

Step-by-step explanation:

we know that

The distance between point p from line l is equal to the perpendicular segment from line l to point p

step 1

Find the slope of line l

we have the points

(1,5) and (4, -4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-4-5}{4-1}$

$m=\frac{-9}{3}$

$m=-3$

step 2

Find the equation of the line l

The equation in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=-3$

$point\ (1,5)$

substitute

$y-5=-3(x-1)$ -----> equation A

step 3

Find the slope of the line perpendicular to the line l

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (The product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-3$ ---> slope of line l

therefore

$m_2=\frac{1}{3}$ ----> slope of the line perpendicular to line l

step 4

Find the equation of the line perpendicular to line l that passes through the point p

The equation in point slope form is equal to

$y-y1=m(x-x1)$

we have

$m=\frac{1}{3}$

$point\ p(-1,1)$

substitute

$y-1=\frac{1}{3}(x+1)$ -----> equation B

step 5

Solve the system of equations

$y-5=-3(x-1)$ -----> equation A

$y-1=\frac{1}{3}(x+1)$ -----> equation B

Solve the system by graphing

The solution of the system is the intersection point both graphs

The solution is the point q(2,2)

see the attached figure

step 6

we know that

The distance between the point p and the line l is equal to the distance between the point p and the point q

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the points

p(-1,1) and q(2,2)

substitute the values

$d_p_q=\sqrt{(2-1)^{2}+(2+1)^{2}}$

$d_p_q=\sqrt{(1)^{2}+(3)^{2}}$

$d_p_q=\sqrt{10}\ units$

3 0

3 years ago

Factor the trinomial 3x^2+12x+9

blondinia [14]

Answer:

x^2 + 4x + 3

Step-by-step explanation:

divide everything by 3

8 0

3 years ago

How many times can 5/8 go in to 1 2/3

Jlenok [28]

Answer:

2 2/3 is what I have

Step-by-step explanation:

5/3÷5/8

=2 2/3

5 0

3 years ago

How many combinations of four books can be made from eight different books? 24 70 1,680?

djverab [1.8K]

Answer:

Step-by-step explanation:

four books can be made from eight different books

4 books to be chosen from 8 books

The order does not matters so we use Combination.

four books can be made from eight different books, so we find 8C4

$nCr= \frac{n!}{r!(n-r)!}$

$8C4= \frac{8!}{4!(8-4)!}$

$8C4= \frac{8!}{4!(4)!}$

$8C4= \frac{8*7*6*5*4!}{4!(4)!}=70$

3 0

3 years ago

A system of equations has definitely many solutions. If 2y-4x=6 is one of the equations, which could be the other equation?

NISA [10]

The given equation is ⇒⇒⇒ 2y - 4x = 6

∴ 2y = 4x + 6 ⇒ divide all the equation over 2

∴ y = 2x + 3 and it can be written as ⇒⇒⇒ y - 2x = 3

The last equation represents a straight line with a slope = 2 and y-intercept = 3

To construct a system of equations with definitely many solutions and the equation ( 2y-4x=6 ) is one of the equations, the other equation must have the same slope and the same y-intercept.

so, the general solution of the other equation is ⇒ a ( y - 2x ) = 3a

Where a is constant and belongs to R ( All real numbers )

The system of equations which has definitely many solutions is consisting of Coincident lines.

8 0

2 years ago