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pychu [463]
2 years ago
7

Let er be the unit radial vector and r=x2+y2+z2−−−−−−−−−−√. Calculate the integral of F=e−rer over: (a) The upper-hemisphere of

x2+y2+z2=25 , outward-pointing normal (b) The region on the sphere of radius r=5 centered at the origin that lies inside the first octant x,y,z≥0 (a) ∬SF⋅dS=

Mathematics
1 answer:
user100 [1]2 years ago
3 0

Answer:

72πe⁻⁶, 81/2πe⁻⁹

Step-by-step explanation: the complete question and answer is found in the attachment

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The equation r(t)= (2t)i + (2t-16t^2)j is the position of a particle in space at time t. Find the angle between the velocity and
ankoles [38]

Answer:

The answer is 135 degrees.

Step-by-step explanation:

As we are given the position. If we take the <u>derivative</u>, we get the velocity vector. If we take the <u>derivative</u> again, we find the acceleration vector of the particle.

r(t)=(2t)i+(2t-16t^{2})j

V(t)=2i+(2-32t)j

a(t)=-32j

At time t=0;

v(t)=2i+2j

a(t)=-32j

As i attach in the picture the angle between the velocity and acceleration vector is (45+90)=135 degrees

4 0
2 years ago
Point F is on circle C. What is the length of line segment GF? 12.5 units 15.0 units 17.5 units 20.0 units
geniusboy [140]
The answer:
According to the image, <span>the length of line segment GF can be found with
</span>GF= GC +CF
CF is one the radius, so CF=7.5
to find GC, we can apply Pythagorean theorem on the right triangle GEC
it is 
GC² =GE² + EC² = 10² +7.5² =156.25, and then GC= sqrt(156.25)=12.5

therefore, GF= GC +CF=12.5+7.5=20

so the answer is <span>20.0 units</span>
7 0
2 years ago
A particular convex pentagon has two congruent, acute angles. The measure of each of the other interior angles is equal to the s
NNADVOKAT [17]

1. First, you must apply the formula for calculate the sum of the interior angles of a regular polygon, which is shown below:


 (n-2) × 180°


 "n" is the number of sides of the polygon (n=5).


 2. Then, the sum of the interior angles of the pentagon, is:


 (5-2)x180°=540°


 3. The problem says that the measure of each of the other interior angles is equal to the sum of the measures of the two acute angles and now you know that the sum of all the angles is 540°, then, you have:


 α+α+2α+2α+2α=540°

 8α=540°

 α=540°/8

 α=67.5°


 4. Finally, the larger angle is:


 2α=2(67.5°)=135°


 5. Therefore, the answer is: 135°

6 0
2 years ago
One box of crackers costs $1.75. The crackers are advertised as “3 boxes for $5.25.” Which proportion can be used to represent t
Daniel [21]
A.  1/1.75 = 3/5.25 


Ignore this part I'm just trying to get at least 20 characters.
5 0
2 years ago
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Suppose a scheduled flight must average at least 60% occupancy to be profitable. A sample of 120 flights on a particular route w
garik1379 [7]

Answer: see the graphic

Step-by-step explanation:

A. Type I error helps us to conclude that the flight is not profitable, when in fact it is profitable.

B. a = 0.05

C. Type II error does not show that the flight is profitable

8 0
2 years ago
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