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3 years ago

Find the equation of a line that passes through (0,0) that is perpendicular to 2x+3y=-6

Mathematics

1 answer:

Dovator [93]3 years ago

8 0

The slope-intercept form of a line:

$y=mx+b$

m - slope

b - y-intercept

Convert 2x + 3y = -6 to the slope-intercet form:

$2x+3y=-6$ subtract 2x from both sides

$3y=-2x-6$ divide both sides by 3

$y=-\dfrac{2}{3}x-2$

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have $m_1=-\dfrac{2}{3}$

Therefore

$m_2=-\dfrac{1}{-\frac{2}{3}}=\dfrac{3}{2}$

We have the equation of a line:

$y=\dfrac{3}{2}x+b$

Put the coordinates of the point (0, 0) to the equation:

$0=\dfrac{3}{2}(0)+b$

$0=b\to b=0$

Answer: $\boxed{y=\dfrac{3}{2}x}$

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Express as a fraction in the simplest form: 43.5%

frez [133]

Answer:

Step-by-step explanation:

43.5 x 10 = 435

435/1000 = 87/200 (simplified)

7 0

2 years ago

Z^2 + 2z + 5 , when z = 2 , z^2 is "z squared

OverLord2011 [107]

Answer:

=13

Step-by-step explanation:

=2^2+2×2+5

=4+4+5

=8+5

=13

3 0

2 years ago

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 1 unit

padilas [110]

Answer:

An electronics company can be produce 350 transistors and 340 computer chips, they can´t produce resistors.

Step-by-step explanation:

1. We will name the variables for transistors, resistors and the computer chips.

a = Transistors

b= Resistors

c = Computer chips

2. We propose three linear equations, one for the copper, one for the zinc and one for the glass.

$\left \{ {{3a+3b+2c=1730} \atop {a+2b+c=690}}\atop {2a+b+2c=1380}} \right.$

3. We write the matrix form as Ax=d

$A=\left(\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right)$

$x=\left(\begin{array}{ccc}a\\b\\c\end{array}\right)$

$A=\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)$

With this formula the solution of x is $x=\frac{d}{A}$ or $x=A^{-1}d$

4. We will find the inverse matrix $A^{-1}$ using the formula:

$A^{-1} = \frac{1}{detA} (C_{A})^{T}$

a. det A

$det A=\left[\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right] =3*(4-1)-3*(2-2)+2*(1-4)=9-0-6=3$

b. $(C_{A})^{T}$

$C_{A}=\left(\begin{array}{ccc}4-1&.(2-2)&1-4\\-(6-2)&6-4&-(3-6)\\3-4&-(3-2)&6-3\end{array}\right)$

$C_{A}=\left(\begin{array}{ccc}3&.0&-3\\-4&2&3\\-1&-1&3\end{array}\right)$

$(C_{A}) ^T=\left(\begin{array}{ccc}3&0&-3\\-4&2&3\\-1&-1&3\end{array}\right)^T$

$(C_{A}) ^T=\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)$

c. $A^{-1}$

$A^{-1}=\frac{1}{3} \left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)$

5. As $x=\frac{d}{A}$ or $x=A^{-1}d$ , the solution of x is:

$x=\frac{1}{3}\left(\begin{array}{ccc}3&-4&-1\\0&2&-1\\-3&3&3\end{array}\right)\left(\begin{array}{ccc}1730\\690\\1380\end{array}\right)$

$x=\frac{1}{3}\left(\begin{array}{ccc}(3*1730)+(-4*690)+(-1*1380)\\(0*1730)+(2*690)+(-1*1380)\\(-3*1730)+(3*690)+(3*1380)\end{array}\right)$

$x=\frac{1}{3}\left(\begin{array}{ccc}1050\\0\\1020)\end{array}\right)$

$X=\left[\begin{array}{ccc}350\\0\\340\end{array}\right]$

Therefore:

a= 350 Transistors

b=0 Resistors

c=340 Computer chips

4 0

2 years ago

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas

pantera1 [17]

Answer:

974

Step-by-step explanation:

Initial × Increase percentage ^ Time

500 × (1 + 10%)^(70/10)

500 × 1.1^7

= 974.36

The population of the town in 70 years will be 974.

5 0

3 years ago

I need help and please show me work?!

jek_recluse [69]

Answer:

44,51

Step-by-step explanation:

It is cut off, but according to the Order of Operations [GEMS(A)\BOMDAS\PEMDAS etc.], parentheses are dealt with first:

(13,1 × 3) + 5,21 = 44,51

39,3

Just like whole numbers, you multiply the exact same way.

I am joyous to assist you anytime.

3 0

3 years ago