Write an equation of the line that is:

1 answer:

3 0

Lines that are parallel will have the same slope. Lines that are perpendicular will have slopes that are the negative reciprocal of each other.

(a) parallel to the line y=2x-4, and has a y-intercept of 7
slope of first line: 2
slope of second line: 2
y=mx + b
y=2x+7

(b) parallel to the line y-3x=6, and has a y-intercept of -2
y=3x+6
slope of first line: 3
slope of second line: 3
y=mx + b
y=3x-2

(c) parallel to the line 2x+3y=12, and that passes through the origin
3y=-2x+12
y=-2/3x+4
slope of first line: -2/3
slope of second line: -2/3
origin: (0,0)
y=mx + b
y=-2/3x + 0
y=-2/3x

(d) perpendicular to the line y=3x+2, and has a y-intercept of 2
slope of first line: 3
slope of second line: -1/3
y=mx + b
y=-1/3x + 2

(e) perpendicular to the line 3y+4x=18, and that passes through the origin
3y=4x+18
y=4/3x+6
slope of first line: 4/3
slope of second line: -3/4
origin: (0,0)
y=mx + b
y=-3/4x + 0
y=-3/4x

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Step-by-step explanation:

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A wooden log 10 meters long is leaning against a vertical wall with its other end on the ground. The top end of the log is slidi

Andre45 [30]

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is $\frac{dx}{dt}$ when y = 6 and $\frac{dy}{dt}=-2$ .

The equation for Pythagorean's Theorem is

$x^2+y^2=c^2$ where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ and divide everything by 2 to simplify:

$x\frac{dx}{dt}+y\frac{dy}{dt}=0$ . Looking at that equation, it looks like we need a value for x, y, $\frac{dx}{dt}$ and $\frac{dy}{dt}$ .

Since we are looking for $\frac{dx}{dt}$ , that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

$x^2+6^2=10^2$ and