The radius of the base is 10 cm.
Solution:
Height of a cone = 15 cm
Volume of the cone = 1570 cm³
To find the radius of the base of the cone:
Volume of the cone =
Divide by 15.7 on both side of the equation, we get
Taking square root on both sides of the equation, we get
⇒ r = 10
Hence the radius of the base is 10 cm.
The value of the given surface integral is 4.
The given plane intercepts the coordinate axes at (2, 0, 0), (0, 2, 0), and (4, 0, 0). These point are the coordinates of a triangular region that we can parameterize using.
A surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate a scalar field over the surface or a vector field.
with 0≤u≤1 and 0≤v≤1. Then the surface element ds is equivalent to
The surface integral is then
Therefore the value of the given surface integral is 4.
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Answer:
Step-by-step explanation:
The equation of the line slope-intercept form is:
Where m is the slope and b is the y-interecept.
The standard form is:
You know that must be parallel to , therefore both have the same slope. So you must solve for y:
Substitute the slope m=-1. Since the line passes through the origin b=0:
Then in standar form is: