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3 years ago

Question 10 of the picture

Mathematics

1 answer:

cricket20 [7]3 years ago

6 0

This question is pretty hard, but not impossible.
The key to solving this is to spot triangles.

Since we want to prove that ∠XBP and ∠YBQ are equal, we need to know their relationship towards one another.
If we look at Δs PQB and XYB, we can note down their relationship.

Thus, the way to begin is to prove either similar or congruent triangles.
In Δs PQB and XYB,
∠QPB = ∠YXB (angles in the alternate segment standing on the same arc, PX, are equal)
Similarly, ∠XYB = ∠PQB (" ^ ") note: this means see reasoning above

Since we proved two angles are equal, by definition, the third angle must be equal.
Thus, ∠PBQ = ∠PBY (by definition, they are equal)
Since the two angles share a common angle between them, namely the angle marked on the diagram, then this means ∠XBP must be equal to ∠YBQ, as required.

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Answer:

$9\frac{1}{3}hours$

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All three cooks take time to prepare the same number of pies=2 hours

In 1 hour,all three cooks prepare pies= $\frac{y}{2}$

According to question

$\frac{y}{4}+\frac{y}{7}+\frac{y}{x}=\frac{y}{2}$

$y(\frac{1}{4}+\frac{1}{7}+\frac{1}{x})=\frac{y}{2}$

$\frac{1}{4}+\frac{1}{7}+\frac{1}{x}=\frac{1}{2}$

$\frac{1}{x}=\frac{1}{2}-\frac{1}{4}-\frac{1}{7}$

$\frac{1}{x}=\frac{14-7-4}{28}=\frac{3}{28}$

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Look at the figure shown below:

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These are the steps, with their explanations and conclusions:

1) Draw two triangles: ΔRSP and ΔQSP.

2) Since PS is perpendicular to the segment RQ, ∠ RSP and ∠ QSP are equal to 90° (congruent).

3) Since S is the midpoint of the segment RQ, the two segments RS and SQ are congruent.

4) The segment SP is common to both ΔRSP and Δ QSP.

5) You have shown that the two triangles have two pair of equal sides and their angles included also equal, which is the postulate SAS: triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.

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Step-by-step explanation:

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