Denote the cylindrical surface by , and its interior by . By the divergence theorem, the integral of across (the outward flow of the fluid) is equal to the integral of the divergence of over the space it contains, :
The given velocity vector has divergence
Then the total outward flow is
Converting to cylindrical coordinates gives the integral
Answer:
4.49 more yards
Step-by-step explanation:
Given data
If 8 yards of fabric cost $35.60
then let x yards cost $20
cross multiply
35.60*x= 20*8
35.60*x= 160
x= 160/35.60
x= $4.49
Hence the $20 will purchase 4.49 more yards
Answer: 25 cars
Step-by-step explanation:
This is a box plot and it is a useful graph for showing the minimum, maximum, median and quartile values of a data distribution.
The box you see in the middle is the Interquartile range. In other words, the first line on the box is Q1 and the line at the end of the box is Q3.
The line in the middle of the box is the median or Q2.
The distance between Q1 and the median is 25%.
The number of cars between 40 and 48 miles per hour is therefore 25% of the total.
= 100 * 25%
= 25 cars
What you have here is a situation with two <em>similar triangles.
</em>The triangle in the lower left is similar to the triangle in the upper right - I've included an image with "cutouts" of those triangles so you can see the similarities. Similar triangles have a very important property: <em>the ratios of their corresponding sides are equivalent</em>. Here, we can set up a ratio between the sides of length 64 and x on the larger triangle, and the corresponding sides of length x and 36 on the smaller triangle. Setting the two equal to each other, we have
Multiplying both sides of the equation by 36 and x, we get
finally, we take the square root of both sides of the equation to find x:
Answer:
- area = 14 square units
- perimeter = 19.1 units
Step-by-step explanation:
The base of the triangle extends from x=2 to x=6, a distance of 4 units.
The height of the triangle is 9 - 2 = 7 units.
Then the area is ...
A = (1/2)(4 units)(7 units) = 14 units^2
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The length of the hypotenuse is given by the Pythagorean theorem.
h^2 = 4^2 +7^2 = 16 +49 = 65
h = √65 ≈ 8.1
The perimeter is the sum of the side lengths:
P = 4 + 7 + 8.1 = 19.1 . . . units