For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form A x + B y = C with fractional coefficients. (See Example 3-4) Passes through 3.6 , 1 .2 and is perpendicular to the line defined by 4 x = 9 − y .
For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form A x + B y = C with fractional coefficients. (See Example 3-4) Passes through 3.6 , 1 .2 and is perpendicular to the line defined by 4 x = 9 − y .
Solution Summary: The author explains how to calculate the slope of a line passing through (3.6,1.2) and perpendicular to 4x=9-y.
For exercises 37-44, write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form (if possible) and in standard form
A
x
+
B
y
=
C
with fractional coefficients. (See Example 3-4)
Passes through
3.6
,
1
.2
and is perpendicular to the line defined by 4
x
=
9
−
y
.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.