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Freda is starting an exercise program - Junior Cycle Mathematics - Question 13 - 2019

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Question 13

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Freda is starting an exercise program. She wants to increase her power output (P). One formula for P is: $$P = 36w + 62h + 1800$$ where w is Freda's weight (in kil... show full transcript

Worked Solution & Example Answer:Freda is starting an exercise program - Junior Cycle Mathematics - Question 13 - 2019

Step 1

(a) Work out the value of P when w = 70 kg and h = 0.65 m.

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Answer

To find the value of P when w = 70 kg and h = 0.65 m, we can substitute these values into the formula:

P=36(70)+62(0.65)+1800P = 36(70) + 62(0.65) + 1800

Calculating each term:

  • For the first term: 36×70=252036 \times 70 = 2520
  • For the second term: 62×0.65=40.362 \times 0.65 = 40.3
  • Constant term: 18001800

Now adding them together:

P=2520+40.3+1800=4360.3P = 2520 + 40.3 + 1800 = 4360.3

Thus, the value of P is approximately 4360.30.

Step 2

(b) Work out the new value of P after this week, correct to two decimal places.

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Answer

After one week, Freda's power output has increased by 8, so we add this to the previous value of P:

Pnew=4360.3+8=4368.3P_{new} = 4360.3 + 8 = 4368.3

The new value of P after this week is 4368.30.

Step 3

(c) Draw a graph to show the values of P for different heights (h) when w = 80 kg.

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Answer

When w = 80 kg, we use the same formula:

P=36(80)+62h+1800P = 36(80) + 62h + 1800

Calculating the constant term:

  • First term: 36×80=288036 \times 80 = 2880,
  • The relationship simplifies to:

P=2880+62h+1800=4680+62hP = 2880 + 62h + 1800 = 4680 + 62h

To draw the graph, set values for h (for example: 0, 1, 2, ... up to 5, etc.) and calculate corresponding P values. Mark the line based on the calculated points and ensure the y-axis cuts at 4680.

Step 4

(d) Use this to write h in terms of w and f.

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Answer

Starting from the given identities:

60w+80h−15f−130=36w+62h+180060w + 80h - 15f - 130 = 36w + 62h + 1800

Reorganizing gives:
60w−36w+80h−62h=15f+130−180060w - 36w + 80h - 62h = 15f + 130 - 1800

This simplifies to: 24w+18h=15f+167024w + 18h = 15f + 1670

Now isolating h: 18h=15f+1670−24w18h = 15f + 1670 - 24w

Divide through by 18 gives: h=15f+1670−24w18h = \frac{15f + 1670 - 24w}{18}

This expresses h in terms of w and f.

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