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ryzh [129]
4 years ago
6

I NEED HELP ASAP! THANKS :)

Mathematics
1 answer:
Whitepunk [10]4 years ago
3 0

Answer:  A) stretched vertically by 2 and shifted up 6 units

<u>Step-by-step explanation:</u>

y = A log(Bx - C) + D    where

  • A = vertical stretch by a factor of A
  • B = horizontal shrink by a factor of 1/B
  • C = horizontal shift C units (positive = right, negative = left)
  • D = vertical shift D units (positive = up, negative = down)

Given: f(x) = log x

          g(x) = 2 log x + 6

→ A = 2   vertical stretch by a factor of 2

→ D = +6  vertical shift UP 6 units

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Two poles are connected by a wire that is also connected to the ground. The first pole is 18 ft tall and the second pole is 24 f
9966 [12]

Answer:

  72 feet from the shorter pole

Step-by-step explanation:

The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.

The shorter pole height as a fraction of the total pole height is ...

  18/(18+24) = 3/7

so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:

  d/168 = 3/7

  d = 168·(3/7) = 72

The wire should be anchored 72 feet from the 18 ft pole.

_____

<em>Comment on the problem</em>

This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.

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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:

  L = √(18²+x²) + √(24² +(168-x)²)

and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.

7 0
3 years ago
The earned run average (ERA) a of a baseball pitcher varies directly as the number of earned runs r and inversely as the number
7nadin3 [17]

Answer:

The number of earned runs is 28.

Step-by-step explanation:

Earned runs average:

The earned runs average of a pitcher is the number of runs the he/she gives each 9 innings on average.

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Solved by proportions, using a rule of three.

For each 9 innits, the pitcher gives 2.25 runs. How many runs for 112 innings?

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Applying cross multiplication:

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x = \frac{2.25*112}{9}

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The number of earned runs is 28.

6 0
3 years ago
What is empathy?
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Answer:

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Step-by-step explanation:

When we talk about empathy we mean the human capacity to connect emotionally with others, being able to not only understand but also perceive, recognize, and share the suffering, happiness,feelings and emotions of another person. Empathy is a highly valued characteristic in human behavior.

7 0
4 years ago
Whitney needs to rent a car while on vacation. The rental company charges $18.95, plus 16 cents for each mile driven. If Whitney
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50 - 18.95 = 31.05
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90% of 20 is x

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