Find the derivative of the inverse of the function y=(2/(x+3))

GalinKa [24]

Part A. What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7?

Rewrite the equation −2y=3x+7 in the form $y=-\dfrac{3}{2}x-\dfrac{7}{2}.$ Here the slope of the given line is $m_1=-\dfrac{3}{2}.$ If $m_2$ is the slope of perpendicular line, then

$m_1\cdot m_2=-1,\\ \\m_2=-\dfrac{1}{m_1}=\dfrac{2}{3}.$

Answer 1: $\dfrac{2}{3}$

Part B. The slope of the line y=−2x+3 is -2. Since $-\dfrac{3}{2}\neq -2\quad \text{and}\quad \dfrac{2}{3}\neq -2,$ then lines from part A are not parallel to line a.

Since $-2\cdot \left(-\dfrac{3}{2}\right)=3\neq -1\quad \text{and}\quad -2\cdot \dfrac{2}{3}=-\dfrac{4}{3}\neq -1,$ both lines are not perpendicular to line a.

Answer 2: Neither parallel nor perpendicular to line a

Part C. The line parallel to the line 2x+5y=10 has the equation 2x+5y=b. This line passes through the point (5,-4), then

2·5+5·(-4)=b,

10-20=b,

b=-10.

Answer 3: 2x+5y=-10.

Part D. The slope of the line $y=\dfrac{x}{4}+5$ is $\dfrac{1}{4}.$ Then the slope of perpendicular line is -4 and the equation of the perpendicular line is y=-4x+b. This line passes through the point (2,7), then

7=-4·2+b,

b=7+8,

b=15.

Answer 4: y=-4x+15.

Part E. Consider vectors $\vec{p}_1=(-c-0,0-(-d))=(-c,d)\quad \text{and}\quad \vec{p}_2=(0-b,a-0)=(-b,a).$ These vectors are collinear, then

$\dfrac{-c}{-b}=\dfrac{d}{a},\quad \text{or}\quad -\dfrac{a}{b}=-\dfrac{d}{c}.$

Answer 5: $-\dfrac{a}{b}=-\dfrac{d}{c}.$

5 0

3 years ago

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The sum of two numbers is 76 and their difference is 52. Find the two numbers.<br> Please explain

Yanka [14]

Step-by-step explanation:

hope it helps first find one number and then multiply one number by 2

6 0

2 years ago

A rectangular field 50 meters in width and 120 meters in length is divided into two fields by a diagonal line. What is the lengt

DochEvi [55]

Answer:

E. 300

Step-by-step explanation:

A rectangle split in half diagonally yields 2 right triangles.

((For this problem, you are probably supposed to use the pythagorean theorem to find the diagonal length, and then calculate perimeter (length of fence around triangular field). In other words:

(sqrt( (50m)^2 + (120m)^2 )) + 50m + 120m)

))

By definition, the hypotenuse (diagonal) is the longest side.

This means that it must be longer than 120m.

If you add the 2 sides (50m + 120m), you get 170m.

Since the third side has to be longer than 120m, the answer _must_ be over 290m (170m + 120m).

300m is the only answer that fits.

7 0

3 years ago

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8. Find m Using the parallelogram

Semmy [17]

Answer:

w = 80

Step-by-step explanation:

Common geometry math

7 0

3 years ago

What is 772/7 s mixed number?

maxonik [38]

It would be equal to 110 2/7

4 0

3 years ago