Evaluate 8^5/3 Helplpppp
2 answers:
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Answer:
S₃ = 37
Step-by-step explanation:
given a₁ = 16 and r = , then
a₂ = a₁ × = 16 ×
= 12
a₃ = a₂ × = 12 ×
= 9
then
S₃ = a₁ + a₂ + a₃ = 16 + 12 + 9 = 37
Answer:
Refer below explanation.
Step-by-step explanation:
Given : two triangles ∆QPK and ∆LMK.
We have to show ∆QPK ≅ ∆LMK.
Two triangles are similar if ratio of the corresponding sides are equal and measure of corresponding angles are equal.
Statement 1)
QK=16, PK=26, MK=65, KL=40 ( Reason: Given)
Statement 2 )
(reason : ratio of corresponding sides)
Statement 3)
Thus,
(reason: simplify ratios)
Statement 4)
∠MKL = ∠PQK (reason : Vertically opposite angles)
Statement 5)
∆QPK ≅ ∆LMK (reason : Side-angle-side)
Side angle side similarity criterion states that two angles are similar if the ratio of their corresponding sides and angle between these sides are equal then triangles are similar.
Answer:
12 hours
Step-by-step explanation:
Time taken by pipe A = 24 hours
Time taken by pipe B = 36 hours
Time taken by pipe C = 32 hours
To find:
How long would it take the three pipes to fill the pool if pipe B is turned on 3 hours after pipe A and pipe C is turned on 1 hour after pipe B?
Solution:
First of all, let us assume the total capacity of the pool.
Let us take LCM of 24, 36 and 32.
LCM of 24, 36 and 32 = 288
Let the total capacity of the pool = 288 units
Total units filled by pipe A in one hour =
Total units filled by pipe B in one hour =
Total units filled by pipe C in one hour =
Now, for the first 3 hours, only pipe A operates, so units filled in first three hours =
For the next one hour, A and B both operate together, so units filled in the next 1 hour = 12 + 8 = 20 units
Total number of units filled in 4 hours = 36 + 20 = 56 units
Units to be filled to completely fill the pool = 288 - 56 = 232 units
Now, after the 4th hours, all the pipes operate together.
So, number of units filled in each hour = 12 + 8 + 9 = 29 units
Time taken to fill 232 units =
Total time taken = 4 + 8 = <em>12 hours</em>