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.
Then, now you conclude that, since the two triangles are congruent, every pair of corresponding sides are congruent, and so the segments RP and PQ are congruent, which means that the distance from P to R is the same distance from P to Q, i.e. P is equidistant from points R and Q
To solve this, we work out the volume of the two shapes (the cuboid and the pyramid) and then add them together.
We get the volume of the cuboid by multiplying the base by the width by the length:
Volume of cuboid = 6 x 6 x 4
= 144m³
Now to get the volume of the pyramid, we multiply the base by the length by the height, and then we divide by three.
Volume of pyramid = 6 x 6 x 8 ÷ 3
= 96m³
-------------------------------------------------------------------------------------------------------------
Answer:
Now that we know the two volumes, we simply add them together:
144 + 96 = 240m³
So the volume of the composite sold is 240m³
Answer:
13.2 minutes or 13 minutes 12 seconds.
Step-by-step explanation:
1. Count how much water drains the first pump every minute. Let the volume of pool be D. Every minute first pump drains D/11 water.
2. Working together(6 minutes) First pump drains 6D/11 water, hence the second pump drains 5D/11 water.
3.Count how much water drains second pump per minute -> (5D/11)/6= 5D/66
4. It takes the second pump 66 minutes to drain pool 5 times, thus it takes 13.2(66/5) minutes to drain the pool, which is 13 minutes 12 seconds.
Photomath is useful for these kinds of problems
