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jarptica [38.1K]
3 years ago
13

In still water Kevin and Virginia can paddle a canoe at 12mph.It takes them a total of 6hours to paddle 32 miles up a river and

then return the same distance to their starting point. What is the rate of the current?
Mathematics
1 answer:
denpristay [2]3 years ago
4 0
Let c represent the speed of the current.

time = distance/speed

Upriver, the current is subtracted from the canoe speed; downriver, it adds.
  6 = 32/(12 -c) +32/(12 +c)
  6(12² -c²) = 32(12 +c) +32(12 -c) . . . . . multiply by (12 +c)(12 -c)
  0 = 6c² -96 . . . . . . . . . . . . . . . . . . . . . . subtract the left side
  96/6 = c² . . . . . . . . . . . . . . . . . . . . . . . . add 96, divide by 6
  4 = c . . . . . . . . . . . . . . . . . . . . . . . . . . . . take the square root

The rate of the current is 4 mph.
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<h2>Equations of Circles</h2>

Generally, you'd see the equation of a circle organized in the following format:

(x-h)^2+(y-k)^2=r^2

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  • r is the radius

To determine the equation given the center and the radius:

  1. Plug both pieces of information into the general equation
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<h2>Solving the Question</h2>

We're given:

  • Radius: 99
  • Center: (-1,-8)

Plug the radius and center into the equation as r and (h,k):

(x-(-1))^2+(y-(-8))^2=99^2\\(x+1)^2+(y+8)^2=9801

<h2>Answer</h2>

(x+1)^2+(y+8)^2=9801

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What is the surface area of the figure? Use 3.14 for π.
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Answer:

Option 3

Step-by-step explanation:

We want to work out the surface-area

This is a cylinder and the formula for the surface area of a cylinder is :

2πrh+2πr^2

^ means to the power of

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The length is 18

2(3.14)(15)(18) + 2(3.14){15}^2

Part 1:

(6.28)(15)(18)

(6.28)(270)

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Part 2:

First, we do the exponents,

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(6.28)(225)

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Part 3:

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Answer: 3108.6

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Answer:

Step-by-step explanation:

16^3 - 8^3

Take out 8^3 as a common factor.

16^3 = 2^3 * 8^3

8^3(2^3 - 1)  

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72

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Conclusion

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7*9 = 63

So any number containing 63 will divide into the reduced form of

(16^3–8^3)(4^3 +2^3)

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