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natita [175]
3 years ago
7

Using geometry, calculate the volume of the solid under z=64−x2−y2and over the circular disk x2+y2≤64

Mathematics
1 answer:
Anarel [89]3 years ago
3 0
Perhaps you mean to find the volume under z=\sqrt{64-x^2-y^2}? It seems like you have to rely on calculus otherwise (in the case that you indeed mean z=64-x^2-y^2).

Assuming this, note that z=\sqrt{64-x^2-y^2} describes the top half of a sphere with radius 8, which means the volume below this surface over the disk x^2+y^2\le64 is simply half the volume of the sphere. Thus the volume is

\dfrac43\pi8^3=\dfrac{2048}3\pi
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Question 30 The Royal Fruit Company produces two types of fruit drinks. The first type is pure fruit juice, and the second type
Flura [38]

Answer:

The answer is below

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?

Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).

Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:

x + y = 80                              .                  .                 .    1)

Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:

0.65x + 0.9y = 68               .                 .                  .        2)

We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:

0.65x + 0.65y = 52            .                  .               .        3)

Subtract equation 3 from 2 and solve for y:

0.25y = 16

y = 16/0.25 = 64

y = 64 pints

Put y = 64 in equation 1:

x + 64 = 80

x = 80 - 64 = 16

x = 16 pints

Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.

4 0
3 years ago
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