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PtichkaEL [24]
1 year ago
5

MATH: Composition of two functions...help needed with this problem

Mathematics
1 answer:
Evgesh-ka [11]1 year ago
3 0

The equation of Q(n) is Q(n) = \frac89 * (88n + 23)

<h3>How to determine the formula of Q(n)?</h3>

The functions are given as:

R(d) = \frac89 d

P(n) = 88n + 23

From the question, we understand that:

d = P(n)

This means that:

d = 88n + 23

Substitute d = 88n + 23 in R(d)

R(n) = \frac89 * (88n + 23)

Also, from the question

Q(n) = R(n)

So, we have:

Q(n) = \frac89 * (88n + 23)

Hence, the equation of Q(n) is Q(n) = \frac89 * (88n + 23)

Read more about composite functions at:

brainly.com/question/10687170

#SPJ1

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A scuba diver dove from the surface of the ocean to an elevation of −49 9/10 feet at a rate of −9.5 feet per minute. After spend
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Answer:

Rate of change  =  4,06 f/min

Step-by-step explanation:

The ascendent length  28 9/10   =  289/ 10

The time for that ascendent maneuver is total time 17 1/8 minutes  - spended time in the elevation 10 minutes, then

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137/8  - 10   =  ( 137 - 80 ) /8   =  57/8 minutes

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HW#1 Square Root and Cube Root
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3 years ago
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ohaa [14]

9514 1404 393

Answer:

  • scale factor: 3
  • rule: (x, y) ⇒ (3x +15, 3y -24)
  • center: (-7.5, 12)

Step-by-step explanation:

The scale factor can be found by comparing the length of CB to the length of RQ.

  B-C = (-2, 8) -(-4, 9) = (2, -1)

  Q-R = (9, 0) -(3, 3) = (6, -3)

The length of RQ is clearly 3 times the length of CB, so the scale factor (k) is ...

  ratio of corresponding differences = 6/2 = -3/-1 = 3 . . . . . scale factor

__

We know that for dilation about a point O, the distance from O is multiplied by the scale factor. For dilation of point B to point Q, this means ...

  k(B -O) = (Q -O)

Solving for Q, we get ...

  Q = kB -kO +O . . . . this is what our dilation rule will look like.

The quantity O-kO can be found by subtracting kB:

  Q -kB = O -kO = O(1 -k)

This is what we need for our dilation rule.

  Q -kB = (9, 0) -3(-2, 8) = (9+6, 0-24) = (15, -24)

So, our dilation rule is ...

  (x, y) ⇒ k(x, y) +(15, -24)

  (x, y) ⇒ (3x +15, 3y -24) . . . . . dilation rule

__

The center of dilation can be found from ...

  (Q -kB)/(1 -k) = O

  O = (15, -24)/(1 -3) = (-7.5, 12)

The center of dilation is (-7.5, 12).

_____

<em>Additional comments</em>

On the graph, the center of dilation can be found by drawing a line through a point and its image. (Points are always dilated along a line through the center of dilation.) The intersection of two such lines is the center of dilation.

On this graph, the center is just above the top edge of the chart, at point (-7.5, 12). You can see this if you carefully draw lines BQ and AP.

You usually have coordinates for two original points and two image points, so finding the scale factor the way we did is not difficult. If you just have one point on the original and the image, the scale factor is found by finding their distances from the center of dilation. Each image point is k times as far as each original point from that center.

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vlabodo [156]

Answer:

10 hrs

Step-by-step explanation:

just divide 24 km by 8 hrs to get 3km per hour then

divide 30 by 3 to get 10 hrs

3 0
3 years ago
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