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vodomira [7]
2 years ago
5

GeometryNeed help finding A and B

Mathematics
1 answer:
MariettaO [177]2 years ago
4 0

Answer:

  a = 8

  b = 4√5

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

  short side/long side = a/16 = 4/a

  a² = 64 . . . . . . multiply by 16a

  a = 8 . . . . . . take the square root

__

  hypotenuse/short side = b/4 = 20/b

  b² = 80 . . . . . . . multiply by 4b

  b = 4√5 . . . . . take the square root

_____

<em>Additional comment</em>

These relations for the right triangle can be summarized by the rule "the length of a segment that touches the hypotenuse is the geometric mean of the two hypotenuse segments it touches." In the case of b, that means ...

  b = √((4)(4+16)) = 4√5

The same sort of relation applies to the unmarked vertical segment on the left:

  c = √((16)(16+4)) = 8√5

And, we saw ...

  a = √((4)(16)) = 8

Of course, if this rule is to make sense, you need to know that the geometric mean of two numbers is the square root of their product. (In general, the geometric mean of n numbers is the n-th root of their product.)

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Tanya took a cab from her home to the airport. Her total fare including a tip of $5.00, was $28.50. EZ Cab Company has a pick-up
ValentinkaMS [17]
16.2 miles.

Since she paid a $5 tip, the cost for her fare was $23.50.  Let x be the number of 0.2-mile increments in the trip:
23.50 = 2.50 + 1 + 0.25(x-1)

This equation comes from the 2.50 home pick-up fee; $1 for the first 0.2-mile increment; and 0.25 for each other 0.2-mile increment.

Using the distributive property, we have:
23.50 = 2.50 + 1 + 0.25*x - 0.25*1
23.50 = 2.50 + 1 + 0.25x - 0.25

Combining like terms,
23.50 = 0.25x + 2.75

Subtracting 2.75 from both sides, we have:
23.50 - 2.75 = 0.25x + 2.75 - 2.75
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Dividing both sides by 0.25, we have:
20.25/0.25 = 0.25x/0.25
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6 0
4 years ago
F(1)=-12, f(n)=2f(n-1) <br> find first 4 terms
amid [387]
<h3>First four terms are:   -12, -24, -48, -96</h3>

============================================

Explanation:

The notation f(1) = -12 tells us that the first term is -12.

The equation f(n) = 2*f(n-1) indicates that we're multiplying the (n-1)th term by 2 to get the nth term. Basically we multiply each term by 2 to get the next term.

-12*2 = -24

-24*2 = -48

-48*2 = -96

So the first four terms are -12, -24, -48, -96.

-----------------------------------

Alternative Approach

f(1) = -12 .... first term

f(n) = 2*f(n-1) ... nth term recursive formula

f(2) = 2*f(2-1) ... plug in n = 2

f(2) = 2*f(1)

f(2) = 2*(-12) ... plug in f(1) = -12

f(2) = -24 ... second term

f(n) = 2*f(n-1) .... resetting for the next computation

f(3) = 2*f(3-1) ... plug in n = 3

f(3) = 2*f(2)

f(3) = 2*(-24)  ... plug in f(2) = -24

f(3) = -48 .... third term

f(n) = 2*f(n-1) ... one more reset

f(4) = 2*f(4-1) .... plug in n = 4

f(4) = 2*f(3)

f(4) = 2*(-48) ... plug in f(3) = -48

f(4) = -96 ... fourth term

We get the first four terms to be -12, -24, -48, -96, which was the same as earlier.

4 0
3 years ago
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